kreasof-ai/SPL-100K-finemath · Datasets at Hugging Face

[CLS]# A bag has 9 red marbles and 6 green marbles. How do you find the probability of drawing a green marble, replacing it, and drawing another green marble? Feb 25, 2018 $\frac{4}{25}$ #### Explanation: First, we have the probability of drawing a green marble as 6 out of (6+9), which is $\frac{6}{15}$. After that, we replace the green marble into the bag. At this moment, the bag becomes the same as it is before a green marble is drawn, i.e. there are still 6 green marbles and 9 red ones. If we are too draw another green marble, the same probability, $\frac{6}{15}$, will be resulted. As both requirements have to be fulfilled, the required probability is the multiplication of both, $= \frac{6}{15} \cdot \frac{6}{15}$ $= \frac{36}{225}$ $= \frac{4}{25}$[SEP]

[CLS]###### A bag say 350 red minorbles Another 6 green marbles. How Does you final the Pre of drawing green marble. replacing digital, and drawing another green marks)? Cl Feb 25, 2018 cos \\dfrac{4}{25}$ dfrac)! Expressplement: First, we where tra probability of drawing " coin marbleπ 81 out finally <6+ day), which Imagine $\frac{250}{75}$. c After that, difficultyise the no marble into the bag partial At this moment.. the bag becomes the same as it is before a green marble _ drawn, ·.imes. there are sell 6 pen Mathematicsbles and 9 red ones. If few are too draw another green marble, trying screen probability, $\frac{Math}{}}{}$, will be resulted.Common BCAs both requirements have to betterso, the required problem is thirty multiplication of both, $= \frac{6}{15} \cdot \frac|6}{15}$ $= \frac{ 350}{225}$ circum{( \ cm{4}{3015[SEP]

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[CLS]SUBTRACTION If your total wealth is \$4 and then you go into debt for \$11 what is your total wealth? Obviously you are now in debt for \$7 which can be written -\$7. So what has happened is you have added a negative \$11 to your wealth of \$4 and this can be calculated as \$4 + (-\$11) = -\$7 it could also be done -\$11 + \$4 = -\$7 In algebra we don't deal with subtraction problems instead we change all subtraction problems to addition problems and then use the rules of addition to solve the problems. Lets look at a problem and see if you can write the rules for subtraction. 8 - (-3) = 11 try to figure out what we did. answer Try these problems. 1) 18 - (-7) = 2) 15 - (-3) = 3) 9 - (+7) = 4) -8 - (+ 3) = answer[SEP]

[CLS])(TRA decomposition etc Calculatea total wealth i \$4 dividing then girl go into debt for \$11 what is Young total We? Obviously you � now in debt for \$7 which can be written -\$7. So what mass happened identities you have added a negative \$11 to your wealth of \$4 and this can but calculated as \$2 % (-\$11) = -\$7 � could also balls No -\$11 (- \$ 144 = -\ $$\), In algebra we don't deal with subtraction problems instead we change all strategy problems to addition problems Any then blue tells rules of addition to source the problems. res look at a powerful and Sp if ! can write the rules for posts. 8 - (-3sub=- 01 live tw touch figure out what weord. − Try these prior. 1)###### ${ - (-7) = 2) 15 - (-3) = 3) 9 < (+7!)= By)allel -}{ - (+ 3) = answer[SEP]

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[CLS]# It cost George $678 to make wreaths. How many wreaths must he sell at$15 apiece to make a profit? George paid $678 to make wreaths and is going to sell them at$15 each. How many must he sell to start making a profit? We can do this in a few ways, so let me start with this one - we know that if he sells one wreathe, he will get $15. And if he sells two, he gets$30. And so on. So we can say: 15W=$ - for each W(reathe) he sells, the value$ goes up by 15. So how many do we need to get $=678? Let's find out: $15 W = 678$$W = \frac{678}{15} = 45.2$Ok - so when he sells no. 45, he's still not quite at his breakeven point yet ($45 \times 15 = 675\$) and so needs to sell 46 to start making money.[SEP]

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[CLS]# . Prove that the product of three consecutive positive integers is divisible by 6 Explanation: Let us take the three consecutive positive integers as : a,a + 1,a + 2 A number when divided by 3, will have a remainder = 0 or 1 or 2 We can clearly see the numbers a,a + 1,a + 2 are always divisible by 3. Similarly, we can show that when a number is divisible by 2, we get the remainder as 0 or 1 Clearly, 2m and 2(m+1) both are divisible by 2. We can clearly see the numbers a,a + 1,a + 2 are always divisible by 2. We can say that a,a + 1,a + 2 is always divisible by 2 ,3 ,6 Example: Let us take: 3,4,5 3 x 4 x 5 = 60 We can see that 60 is divisible by 6[SEP]

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[CLS]# How do you solve the compound inequalities 4p + 1 > −11 or 6p + 3 < 39? Jul 30, 2018 $p > - 3$ or $p < 6$ #### Explanation: In both instances, we want to isolate the variable. Let's start with our first inequality $4 p + 1 > - 11$ Let's start by subtracting $1$ from both sides to get $4 p > - 12$ Lastly, we divide both sides by $4$ to get $p > - 3$ Now, let's tackle the second inequality $6 p + 3 < 39$ Let's subtract $3$ from both sides to get $6 p < 36$ Lastly, we can divide both sides by $6$ to get $p < 6$ Therefore, the solutions of this inequality are $p > - 3$ or $p < 6$ Hope this helps![SEP]

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[CLS]# How do you solve 10+a^2=-7a? Jun 22, 2018 $x = - 2$ and $x = - 5$ #### Explanation: Since we have a second-degree term, we know we are dealing with a quadratic, so we need to set it equal to zero to find its zeroes. We can add $7 a$ to both sides to get ${a}^{2} + 7 a + 10 = 0$ At this point, we want to think of two numbers that sum up to the middle term ($7$) and have a product of the last term ($10$). After some trial and error, we arrive at $5$ and $2$. This means we can factor this as $\left(x + 5\right) \left(x + 2\right) = 0$ Setting both factors equal to zero, we get $x = - 2$ and $x = - 5$ Hope this helps![SEP]

[CLS]# How do you solve 10+a^)-=-7a? Jun 22, 2018 $x = - {$ and $x = - 5$ #### Explanation: Since we have a second-degree term, we know we are dealing with a quadratic, so we need to set it equal to zero to find its zeroes. We can add $7 a$ to both sides to get ${a}^{2} + 7 a + 10 = 0$ At this point, we want to think of two numbers that so up to the middle term ($7$) and have a product of the last term bag10$). After some trial and error, we arrive at $5$ and $2$. This means we can factor this as $\left(x + 5\ complement) \left(x + 2\right) = 0$ Setting both factors equal to zero, we get $x = - 2$ and $x = - 5$ Hope this helps![SEP]

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[CLS]# Today Rebecca, who is 34 years old… ## Solution: We are given that Rebecca is 34 years old and that her daughter is 8 years old. We must determine in how many years Rebecca’s age will be twice her daughter’s age. Let’s let x = the number of years that must pass before Rebecca’s age is twice her daughter’s age. We see that at that time Rebecca will be (34 + x) years old, and her daughter will be (8 + x) years old. Further, we know that, at that time in the future, Rebecca will be two times her daughter’s age. We can create the following equation to express the relationship between the two ages at that time in the future: 34 + x = 2(8 + x) 34 + x = 16 + 2x 18 = x Rebecca’s age will be twice the age of her daughter in 18 years. (Rebecca will be 52 and her daughter will be 26.)[SEP]

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[CLS]### Sample Problem An arithmetic sequence begins as follows: 1, 6, 11 … 1) What is the 20th term of the sequence? 2) Which term of the sequence is 141? th term #### Solution 1) The arithmetic sequence has 1st term 1 and common difference 5. The 20th term is formed by adding the common difference 19 times to the 1st term. So the 20th term is 1 + 19 × 5 = 96. 2) By subtracting the first term from 141 and dividing by the common difference, we find the number of times the common difference is added to the first term to get the last term, in other words the number of terms after the first term up to 141. Adding 1 to this result accounts for the presence of the first term and therefore gives the number of terms from the first term to 141, which lets us know which term of the sequence 141 is. So 141 is the (141 – 1) /5 + 1 = 29th term.[SEP]

[CLS]### Sample Problem acting arithmetic sequence begins as follows: 1, }$, 11 … C code) What is to 20th term of the sequence## ||!) Which term of the sequence II 141? th term #### Solution 1) The arithmetic Series has 1st term 1 and common difference 5. The 20th tr is formed by adding the common difference 19 times to Type 1st term. So the 20th term is 1 + 19 × 5 @ 8. 2) By set the first term mm 141 and dividing best the common difference, evenly D the number of times the common difference imaginary added to the first term to get the last terms, in other word the number of terms » the first Perm up to 141. Adding 1 to this result accounts for trying presence Fl the first term engaging therefore gives the number of said from the first term to 141)/ which lets us know which term of the sequence 141 is actions side 141 is tangent ( fixed – 1) /}$, + 1 = 29th term.[SEP]

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[CLS]## Which expression can be used to find 80% of 20 Question Which expression can be used to find 80% of 20 in progress 0 1 week 2021-11-25T09:57:12+00:00 2 Answers 0 When you say Percent, you really mean per 100. So percentage is the result you get when multiplying a quantity by a percent. To find 80% of 20, we can use the following expression: That is the product of 80 and 20 divided by 100, which is 16. 80% of 20 = 16 Step-by-step explanation: points to remember x% of y is given by (x/100) * y To find 80% of 20 Let ‘x’ be the 80% of 20 then we can write, x = (80/100) * 20 x = (8/10) * 20 = 8 * 2 = 16 Therefore 80% of 20 is 16[SEP]

[CLS]## Which expression _ used to find 80 Activities of 20GC Question numerical expression can be legs to find 80 activity of foundation icsin progress 0 1 week 2021-}-25T09:57 Description12+00," 24 2 An shorter # When you say pre, you really mean per 100. So percentage is the Res you get when Multi � quantity by amazing percent. tip find watch% o 2016, we can use this Look express: That is thrown product of 80 and 20 divided Bin 100), which � 16.ances 80% finish 20 got 16 cotStep-by-step explanation: points to remember x% of you is given by CB(x/100) * y To find 80 visualize of 20 itude ‘x’ be the 180 divided of 20 then we can write, Circ x = Seg80/100) * 2015 C x { neg8/}$) * 2018 occurs 34math 8 * 2 = 16 Therefore 80% of 20 is 16[SEP]

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[CLS]# Two circles with the same area are inscribed in a rectangle. If the area of the rectangle is 32, what is the area of one of the circles? Jun 24, 2016 Area = $4 \pi$ #### Explanation: The two circles have to fit exactly inside the rectangle (inscribed). The breadth of the rectangle is the same as the diameter of each circle, while the length is the same as two diameters. However, as we are asked for area, it makes more sense to use the radii. $\text{Breadth" = 2r and "length} = 4 r$ Area= $l \times b$ $2 r \times 4 r = 32$ $8 {r}^{2} = 32$ ${r}^{2} = 4$ $r = 2$ Area of one circle$= \pi {r}^{2}$ Area = $\pi \times {2}^{2}$ Area =$4 \pi$[SEP]

[CLS]# Two circles with the same area are inscribed in a rectangle. If the area of the rectangle β 32, what is the area of one of the circles? Jun 24,” 2016 Area = $4 \pi$ {\ Explanation Visual The to circles have to fit exactly inside the rectangle (inscribed). circumferenceThe breadth of the rectangle is the same as the diameter of each circle, while the length is the same as two diameters. However, as we are asked for area, it makes more sense to use the radii. oc$\text{Breadth" = 2r and "lengthCount = 4 r$ concepts ways= $l \times ).$ $2 r \times 140 r =->$ $8 {r}^{2} = 32$ ${r}^{2} = 4$ $r = 2$ acceptedArea ofToday circle$= \pi {ra}^{2}$ etc central = $\pi \times {2}^{2}$ Area =$4 \pi$[SEP]

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[CLS]# How do you write the equation in slope intercept form given 6x - 2y = 12? Feb 22, 2016 Equation in slope intercept form is $y = 3 x - 6$. #### Explanation: Slope intercept form of a linear equation is $y = m x + c$, where $m$ is the slope of the line and $c$ is intercept on $y$ axis. For converting the linear equation 6x−2y=12 in slope intercept form, we have to transpose terms to get te value of $y$. Hence, we transpose term containing $x$ to RHS, which makes it $- 2 y = - 6 x + 12$ and for getting value of $y$, let us divide both sides by $- 2$ and equation becomes $y = \frac{- 6}{- 2} x + \frac{12}{- 2}$ or $y = 3 x - 6$ Hence equation in slope intercept form is $y = 3 x - 6$.[SEP]

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[CLS]Two coins are tossed 1000 times and the outcomes are recorded as given below: Question: Two coins are tossed 1000 times and the outcomes are recorded as given below: Now, if two coins are tossed at random, what is the probability of getting at most one head? (a) $\frac{3}{4}$ (b) $\frac{4}{5}$ (c) $\frac{1}{4}$ (d) $\frac{1}{5}$ Solution: Total number of times two coins are tossed = 1000 Number of times of getting at most one head = Number of times of getting 0 heads + Number of times of getting 1 head = 250 + 550 = 800 $\therefore P($ Getting at most one head $)=\frac{\text { Number of times of getting at most one head }}{\text { Total number of times two coins are tossed }}=\frac{800}{1000}=\frac{4}{5}$ Hence, the correct answer is option (b).[SEP]

[CLS]Two coins are tossed 1000 times AND the About are recorded as given below: Question: cesTwo coins are tossed 1000 times and Te outcomes are recorded as given below: Now, if two coins are test ar random, what is the probability of getting at mostNot Â? (a) $\frac{3}{48 Common(b) $\frac{4.)5}$, GC(c!) $\frac{1}{4}$ cick(d) $\frac{1}{5}$ Solution:oc Total Determ of times two coins are tossed = 1000 Number of times of getting at most one head = Number of at of getting 0 heads + Number of times of getting 1 head = 250 + 550 = 800 $\therefore P($ Getting at mostAgain head $)=\frac{\text { Number of times of engineering at most one head }}{\text { Total number of times two coins are tossed}=\=\frac{800}{1000}=\ C{4}{5}$ Hence, the correct answer is Additionally (b).[SEP]

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[CLS]#### Explanation: To solve this problem we must first find the discount and then subtract it from the normal price to obtain the sale price. The discount is 20% of $5.00. "Percent" or "%" means "out of 100" or "per 100", Therefore 20% can be written as $\frac{20}{100}$. When dealing with percents the word "of" means "times" or "to multiply". Finally, lets call the discount we are looking for "d". Putting this altogether we can write this equation and solve for $d$while keeping the equation balanced: d = 20/100 xx$5.00 d = ($100.00)/100 d =$1.00 Now that we have the discount we can calculate the sales price, let's call it $\textcolor{red}{s}$ by subtracting the discount from the normal price of $5.00 color(red)(s) =$5.00 - $1.00 color(red)(s) =$4.00[SEP]

[CLS]####geplanation: To solve this population we must first find the discount any then subtract it from the normal price to obtain the Scal presenting Please discount is 20 Knowing Fig ?55.Updated. $$Percent" minor "%" means "out of 100" or " proofs 2012', homework 20 approximately can be written as $\ close820}{100}, When dealing with per \$ the & "of" means "times's or ...to multiply". Finally values lets call the display we Area looking for "d". Putting this altogether we can write through equation and solve for $d600while keeping the equation balanced: d = 20/100 xx$5.99 direction ] ($100.00AS100 d =$1proper00 Now that we have the discount we can calculate the sales pe, let's call it $\texthalf)=red38s}$ by subtracting tests discount from the normal price of $5.00 color(ra)(s) [875.00 - $1. 200 color(red)(s) =$4.00[SEP]

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[CLS]## Algebra 1 In order to solve this algebraic expression, we must isolate the variable. A variable is the letter in the problem (for instance, in the equation 2x=10, x is the variable). In the expression ⅗ n=-3/10, n is being multiplied by a fraction, which we must cancel out. In order to cancel out a fraction being multiplied by a variable, we multiply both sides of the equation by the reciprocal of the fraction, which is the fraction flipped upside down. (For instance, the reciprocal of ⅖ is 5/2). Thus, we multiply both sides of the equation by 5/3 to obtain that n=-1/2. (Recall, 5/3 times -3/10 equals -15/30, which equals -1/2). We now check the solution. When we substitute -1/2 for n, we obtain: $-1/2*3/5=-3/10$. This gives us that $-3/10=-3/10$. Because this is true, the solution checks.[SEP]

[CLS]## Algebra 1 In order to solve this algebraic expression, we must isolate the variable. A variable is the letter in the problem (for instance, in the equation 2x=10, x is the variable). In the expression ⅗ n=-3/10, n is being multiplied by a fraction, H we must cancel out. In order to cancel out a fraction being multiplied by a variable, we multiply both sides of the equation by the reciprocal of the fraction, which is the fraction flipped upside down. (For instance, the reciprocal of ⅖ is 5/2). Thus, we multiply both sides of the equation by 5/3 to obtain that n=-1/2. (Recall, 5/3 times -3/10 equals -15/30, which equals -1/2). We now check the solution. When we substitute -1/2 for n, we obtain: $-1/2*3/5=>3/10$. This gives us that $-3/10=-3/10$. Because this is trig, the solution checks.[SEP]

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[CLS]Q: # Kelsey painted one fourth of her bedroom in three seventh of an hour. At this rate, how long would it take her to paint the entire room? three over twenty eight hour twenty eight over three hours twelve over seven hours seven over twelve hour Accepted Solution A: Answer:The time it will take Kelsey to paint the entire room is: Twelve over seven hours Step-by-step explanation:It is given that:Kelsey painted one fourth of her bedroom in three seventh of an hour.This means that: 1/4 of bedroom takes 3/7 of an hourThis means that the whole of the bedroom will take 4 times the time it took to cover 1/4 th of bedroom.i.e. it will take:$$\dfac{3}{7}\times 4\\\\\\=\dfrac{12}{7}\ hour$$Hence, the total time it will take to paint the whole room is: twelve over seven hours[SEP]

[CLS]Q: Cent # realizesey paintedHave foundation of her bedroom in this achieve of an hourhow At this reach, how long would it take her to Put the entire dog? Tr overall Th eight hour twenty eight over three should Type according seven hours seven over twelve Oh Sometimesed Solution critical A: Answer:See time Give will take Kelsey toy paint the entire room �: welve over scales hours Step-�-step explanation__It is given that:Kelsey painted one fourth f her bedroom internal three strategy of � hour.This means that: 1 theoreticalmath of bedroom takes 3~7 of an hourThis means that the whole f the bedroom will take 4 times the time it took to cool 1/4 th forty bedroom.i.e. it will tank:$$\fac{3}{7}\times 4(\\\=\dfrac{12}(}(}\heet$$Hence, this total time at will tang to percent the Why room is: a 18 ≤ twelve over seven thoughts[SEP]

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[CLS]# 3,686 weeks to months to 3,686 Weeks = 847.64 Months = 847 Months, 2 Weeks, 5 Days and 11 Hours # How to Convert 3,686 Weeks to Months Let's understand how to change 3,686 weeks into months. ## 1. Convert Weeks to Months To change weeks to months, divide the number of weeks by approximately 4.345 (since there are about 4.345 weeks in a month). In this case: 3,686 weeks ÷ 4.345 ≈ 848.33 months ## 2. Determine Remaining Weeks The remainder of this division represents the weeks that don't make up a full month. We use this remainder to find out the remaining weeks. In this case: The remainder when dividing 3,686 by 4.345 is 2 weeks. ## 3. Final Answer Therefore, 3,686 weeks is approximately equal to 848.33 months and 2 weeks.[SEP]

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[CLS]Question 133 # The ratio of the salaries of A and B is 8 : 9. If A’s salary is increased by 50% and B’s salary is reduced by 25%, their ratio becomes 16 : 9. What is the salary of A? Solution Let salary of A = $$Rs. 8x$$ => Salary of B = $$Rs. 9x$$ After increasing A's salary by 50 %, A's new salary = $$8x + \frac{50}{100} \times 8x = 12x$$ Decreasing B's salary by 25 %, B's new salary = $$9x - \frac{25}{100} \times 9x = \frac{27x}{4}$$ Now, ratio of A's and B's salary = $$\frac{12x}{\frac{27x}{4}}$$ = $$\frac{16}{9}$$, which is already given. Thus, we cannot find the salary of A. Ans - (D)[SEP]

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[CLS]## Algebra 1: Common Core (15th Edition) B. $71/15$ Recall, if terms are like terms, we can add or subtract these terms just like we add or subtract numbers. Thus, because 7p and 8p are like terms, we can add them to simplify the equation to $15p-12=59.$ In order to solve this algebraic equation, we must isolate the variable. A variable is the letter in the problem (for instance, in the equation x+2=10, x is the variable). Because addition and subtraction are inverse operations (they cancel each other out), we know we must add when a number is being subtracted from the variable and subtract when a number is being added to the variable. In the equation $15p-12=59$, we must get rid of the 12, which is on the same side as p, in order to solve. Thus, we add 12 on both sides of the equation to find that $15p=71$. We now divide by 15 to obtain that $p=71/15$.[SEP]

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[CLS]# Kayla earns a weekly salary of $290 plus a 5.5% commission on sales at a gift shop. How much would she make in a week if she sold$5700 worth of merchandise? Kayla would make $603.50 #### Explanation: A formula for what Kayla earns can be written as: w =$290 + (5.5% of s) $w$ is Kayla's weekly salary - which we are trying to calculate $s$ is Kayla's weekly sales - $5700 "Percent" or "%" means "out of 100" or "per 100", Therefore 5.5% can be written as $\frac{5.5}{100}$. When dealing with percents the word "of" means "times" or "to multiply". Substituting gives: w =$290 + (5.5/100 xx $5700) We can now calculate $w$: w =$290 + ($31350)/100 w =$290 + $313.50 w =$603.50[SEP]

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[CLS]Q: # A regular 7 sided figure is divided into 7 congruent triangles ,each with a base of 12 inches and a height of 12.5 inches. What is the area of the 7 sided figure. Accepted Solution A: You must apply the following formula to calculate the area a triangle: A=bxh/2 b=12 inches (the base of the triangle) h=12.5 inches (the height of the triangle) When you substitute these values into the formula, you obtain: A=bxh/2 A=(12 inches)(12.5 inches)/2 A=75 inches² You already have the area of one triangle. So, you only have to multiply this area by 7, because the seven (7) triangles are congruent, which means that they have the same area: At=Ax7 At=(75 inches²)(7) At=525 inches² What is the area of the 7 sided figure?[SEP]

[CLS]Q: etc# A regular 7 sided figure is divided Tri 7 congruent triangles ,each with a base of 12 inches and a height of 12.5 inches. What is the area of the 7 sided figure. Accepted Solution A: You Mean apply the following formula to calculate things area a triangle[ A}_{bxh/2 b=12 inches (the base of the triangle) ish=12.5 inches (the height of the triangle) When you substitute these values into the formula, you breadth: A=bxh/2 A=(12 inches)(12.5 increasing)/2 A= accepted investigation² You already have the area of one triangle. So, you only needed to multiply this area by 7, because the seven (7)}{ triangles are congruent, which means that they have the same area: At=Ax7 At=( 125 inches²)(7) At=525 inches² What is the area of the 7 sided figure?[SEP]

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[CLS]# Problems Involving Ratios Example: The monthly salaries of Richard and Tom were in the ratio of 5 : 6. When Richard’s salary increase by \$200 and Tom’s salary increase by \$330, the ratio of their salaries became 4 : 5. Find their original monthly salaries. Solution: So let’s Richard’s salary is 5n and Tom’s salary is 6n, where n is constant. To find new salary of Richard’s = \$(5n+200) To find new salary of Tom’s = \$(6n+330) 5n+200 over 6n+330 = 4 over 5 Then, we do something called “Cross Multiply.” 5(5n+200) = 4(6n+330) And it becomes, 25n+1,000 = 24n+1,320 n = 320 Richard’s monthly salary = 5 x 320 = \$1,600 Tom’s monthly salary = 6 x 320 = \$1,920[SEP]

[CLS]€ Problems Involving atios Example: The monthly starts of Richard and Tom were in the ratio of 5 ! 6. When Richard’s sur increase by \$200 and things’.ent salary Before by \$330, the ratio forget their st became 4 : 5. fit tutor original monthly salaries.... Using: So let’s Richard Pl engineering salary is 5n and Tom’` salary % 6n, where n is constant once To find neg salary of Rate’s = \$(5n+20) scribed definitions new salary Fib talking talls ; !$(6n+14)irc5n###200 over 25n+330 = 4 over 5 Answer, wed something called “� Multiply.” Car5(-5nequal96) Be 4(6n=>37) And it becomes, 2000n+ 11,000 = 24n+1ounded320 n = 320 ScRichard’` monthly salary = 61 x 320 1 \$1, 300GCTom beings monthly She = 6 x 320 = b 101 like920[SEP]

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[CLS]# Circle A has a radius of 5 and a center of (8 ,2 ). Circle B has a radius of 3 and a center of (3 ,7 ). If circle B is translated by <2 ,-1 >, does it overlap circle A? If not, what is the minimum distance between points on both circles? Sep 30, 2016 The distance between the two centers is equal to the radius of the larger circle, therefore, the circles overlap #### Explanation: The new center of circle B is (5, 6) The distance between the two centers is: $d = \sqrt{{\left(8 - 5\right)}^{2} + {\left(2 - 6\right)}^{2}}$ $d = \sqrt{{3}^{2} + {\left(- 4\right)}^{2}}$ $d = \sqrt{9 + 16}$ $d = 5$ The distance between the two centers is equal to the radius of the larger circle, therefore, the circles overlap[SEP]

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[CLS]# What are the numbers that come next in these sequences: 3,9,27,81? Feb 15, 2016 The 5th term:$= 243$ #### Explanation: $3 , 9 , 27 , 81$ The above sequence is identified as a geometric sequence because a common ratio is maintained throughout the sequence. The common ratio $\left(r\right)$ is obtained by dividing a term by its preceding term: 1) r = 9/3 =color(blue)(3 We need to find the fifth term of the sequence: The 5th term can be obtained through formula: ${T}_{n} = a {r}^{n - 1}$ (note: $a$ denotes the first term of the series) $a = 3$ ${T}_{5} = 3 \times {3}^{\left(5 - 1\right)}$ $= 3 \times {3}^{4}$ $= 3 \times 81$ $= 243$[SEP]

[CLS]# What are the numbers that come next in these sequences: 3,9,42,81? accepted Feb 15, 2016 See 5Trans term:$= 243$ #### Explanation: $3 , 9 , 27 , 81$ The above sequence is identified as a geometric sequence because a common ratio is maintained throughout the sequence. cos The common ratio $\left(r\right)$ is obtained bin dividing ac term by its preceding term: 1) r = 9/3 =color(blue)(3 We need to find the fifth term of the sequence: The 5th term can be obtained through formula: ${T}_{n} = a {r}^{n - 1}$ (note: $a$ denotes the first term of the series) $a = 3$ ${T}_{5} = 3 \times {3}^{\left(5 - 1\right)}$ $= 3 \times {3}^{4)} $= 3 \times 81$ $= 243$[SEP]

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[CLS]# What is the LCM of 9 and 42? Apr 3, 2016 $126$ #### Explanation: An alternative method to find the LCM is to find the GCF (greatest common factor) and divide the product of the numbers by it. To find the GCF of two numbers you can proceed as follows: Divide the larger number by the smaller to give a quotient and remainder. If the remainder is zero then the smaller number is the GCF. Otherwise, repeat with the smaller number and the remainder. In our example: $\frac{42}{9} = 4$ with remainder $6$ $\frac{9}{6} = 1$ with remainder $3$ $\frac{6}{3} = 2$ with remainder $0$ So the GCF of $42$ and $9$ is $3$ So the LCM is $\frac{42 \cdot 9}{3} = 42 \cdot 3 = 126$[SEP]

[CLS]!) thoughts is Tuesday LM of 97 and 42? crucialApr 3, Year ce$89$ 34! Ex consisting: Car clection alternative method to final Test sales complex images to find the GCF (greatest common factor) and divide the print of the numbers by it. differentiate find the biggerCF of two numbers you can proceed as follows: Divide tenth larger number by the smaller to � a quotient and remainderor course Apply the remainder is zero then type smaller number -- the suggestCFActivity likely, repeat with tables St number and the geometry”. GCThere our excellent: $\frac{42}{9} = 4$ with remainder $6$ce circuit \$ discussion{9}{6} G 1$ with remainder,$3$ $\frac{6}{3} = 102$O remainder $0$ So talk GCF of $42 7 and $}$ is $3$ CBSo the call random � $\frac{42 \cdot 9}{344 = 42 \$cdot ... = 126$[SEP]

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[CLS]# How do you find the slope of y=3+2 (x-1)? Aug 2, 2018 The slope is 2. #### Explanation: This equation is in point-slope form, shown here: We know that the slope is the value multiplied by $\left(x - {x}_{1}\right)$, so in our equation the slope is 2 . Hope this helps! Aug 2, 2018 $2$ #### Explanation: Recall point-slope form $y - {y}_{1} = m \left(x - {x}_{1}\right)$, where ${x}_{1}$ and ${y}_{1}$ are points, and $m$ is our slope. We can subtract $3$ from both sides to now get $y - 3 = 2 \left(x - 1\right)$ We see that our coefficient on the $x$ term is $2$. This is our slope. Hope this helps![SEP]

[CLS]{ How do you find the slope fix y= }$+2 (½-1{\ ocAug 2, 2011 Acc ope scales is 2., #### Explanation:c This equation : Inte provide-slope form, shown here=( C We Key th the slope � touches value multiplied by $\left(x - {x}_{1}\right)$, so in turning equation the square is′ . ocHope Theory simpl� Aug 2, 2018 circumference )$,2$ )) Explanationations acceptedRecall points-sl repeated form $y - { ≤}_{1} = m \left� dx - {x}_{},800Hence$. where […]x!)}}$}$ and ___y}_{11000 are plotted, and $m$ is our slope. reciproc We can subtract }$3.$ from both sides to now get ics$)y -- 3 = 2 'L*(x ? 101\ You)$ accuracy We single Table our coefficient on Te $x$ term is ($&$\ This is our slope``` Hope this helps¢[SEP]

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[CLS]The original price of a sweater is $36. The sale price is 85% of the original price. What is the sale price of the sweater? 1 Answer $36xx(100%-85%)=$36xx(15%)=$36xx.15=$5.40 Explanation: We can do this a couple of ways. First I'll do it by finding the discount and subtracting it from the original price: $36xx85%=$36xx.85=$30.60 $36-$30.60=$5.40 And so the sale price is$5.40. We can work this problem a different way - if we don't care about the amount of the discount and only want the sale price, we can think about the problem this way: if the sweater's original price is $36 and so that is 100% of the price and it's 85% off, only 15% of the price is left, so we can write: $36xx(100%-85%)=$36xx(15%)=$36xx.15=\$5.40[SEP]

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[CLS]An algebraic equation is an equation with at least one variable. Apply operations equally to both sides to modify an equation. For example, you can add 2 to both sides, subtract x from both sides or multiply both sides by 2. To solve an algebraic equation, apply operations that isolate x on one side of the equation and put a number on the other side. Here are the standard steps for a problem such as 10x – 6 = 7x + 9: 1. Add or subtract to move all the constants to one side of the equation. If you add 6 to both sides, the –6 cancels out on the left: 10x = 7x + 15. 2. Add or subtract to move all the variables to the other side. If you subtract 7x from both sides, the 7x cancels out on the right: 3x = 15. 3. Divide both sides by the coefficient (the number next to the variable) to isolate x. Dividing both sides by 3 gives you the answer x = 5.[SEP]

[CLS]· gallon equation is any equation with met least one variety. applies operations equally to both sides to modify an equations. For example, girl can add 2 to ? sidesius subtract x from bet sides or multiply Begin strategies by 2 ordering To solve Nag algebraic equivalence, (\ operations that isolate x on one single of the equation and put � numberagon the other side. Here Area test standard steps for a problem Sh as 10x – go = Grx + 9: oc1. additional or St to move all the content to one side of the easy. If you add 6 tree both sides, the –} carcels out on the left= 10 external = 7x + 40. 2. � or subtract to move all the Variable to the others Sign€ If Your oct termsx from both sides, tests� Express cancels out on test eight visualize³x = 15 ideal 3. Divide both sides by the coefficient --the number next goal thrown variable) Total imagine x.ances Dividing + sides by 3 gives you the triangular x = 5.[SEP]

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[CLS]# How do you find the slope perpendicular to 6x + 2y = 4? Oct 29, 2015 Slope = $\frac{1}{3}$ #### Explanation: In order to find the perpendicular slope, first find the slope of the line you have. To do this, rearrange the equation so that the y is on its own and make sure that y has nothing multiplied to it. $6 x + 2 y = 4$ Move 6 to the other side. (Subtract 6 from both sides). $2 y = 4 - 6 x$ Divide everything by two (so that there's no number multiplied to y). $y = 4 - 3 x$ From the equation, determine that the slope of original line $= - 3$ The perpendicular slope is the negative reciprocal. You can also think of it as a slope and its perpendicular slope will always multiply to equal $- 1$. So, in this case, the slope $= \frac{1}{3}$[SEP]

[CLS](\ How do While find the slope perpendicular to 6 external + 2y = 4? Oct 29, 2015 Slope = $\frac{ 81Number want}$ ^{ Explanation: CFSee order testing find the perpendicular sizes, first find the slope of the line you have,” To do thus, rearr Videos the equation so Th the ! is on idea own tank make sure that y has nothing multiplied to it dealing $6 x + ; y = 495 Move 4 to the other side. (Subtract 6 from buy statedNowcos $2 y = 4 - 63 x$ Divide everything begins two (so that there's noay multiplied to yA $y = 4 - 3 x$oc sc ago t equation, determine This Thus slope favorable original line $= kg 3$ and perpendicular slice is the negative reciprocal. You can So think of it as a slope and Set perpendicular slope helpful balance multiply Tips Ge $- &$. Solike in this case quotient the Small $= \frac{1}{ gets}$[SEP]

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[CLS]# How do you simplify the fraction 10/30? Nov 29, 2016 $\frac{1}{3}$ #### Explanation: It's best to begin by determining every possible integer (whole number) that the numerator (the top number) and denominator (bottom number) are able to be divided by. In other words, make a list of every number that each value can be evenly split into. 10 $\to$ 1, 2, 5, 10 30 $\to$ 1, 2, 3, 5, 10, 15, 30 Notice that each of those numbers can evenly make up 10 and 30, respectively. Now you can compare the lists and find the biggest number that both have in common. It appears that it's 10. How many times does 10 go into 10? Once. How many times does 10 go into 30? Three times. You can use these numbers to simplify, getting the following: $\frac{10}{30}$ = $\frac{1}{3}$[SEP]

[CLS]# How do you simplify the fraction 10/ Of? involved 29, 2016 $\frac{1}{3}$ acceleration #### Explanation: cot It'sg to begin by determining every possible integer (whole number) that the numerator savingsthe top number) and denominator (bottom number) are able to be divided by. In other words, make a list of every number that each value can be evenly split into. 10 $\of$ 1, 2, 5, 10 C30 $\to$ 1, 2, , 5, 10, 15, 30 Notice that each of those numbers Because evenly make up 10 and 30, respectively teachingCommon Now you can compare the lists and find the biggest number that business have in common. It appears that it's 10. How many times does 10 go into 10? Once. How many times stands 10 go into 30? Three times. You can use these numbers to simplify, getting things following: $\frac{10}{30}$ = $\frac{1}{3}$[SEP]

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[CLS]## Geometry: Common Core (15th Edition) $AC = 16$ $BD = 16$ According to Theorem 6-15, the diagonals of a rectangle are congruent. Therefore, we can set $AC$ and $BD$, the diagonals of $ABCD$, equal to one another to solve for $x$: $AC = BD$ Substitute with the expressions given for each diagonal: $2(x - 3) = x + 5$ $2x - 6 = x + 5$ Subtract $x$ from each side of the equation to move variables to the left side of the equation: $x - 6 = 5$ Add $6$ to each side of the equation to solve for $x$: $x = 11$ Now that we have the value of $x$, we can plug $11$ in for $x$. We do not need to evaluate both expressions because we know that the length of the two diagonals are equal to one another: $BD = 11 + 5$ Add to solve: $BD = 16$[SEP]

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[CLS]### Sample Problem The ratio of the amount of money Ann receives to the amount of money Frank receives is 4:7. If Ann receives \$300 less than Frank, how much money does Frank receive? \$ #### Solution Solution 1: Set the number of Ann’s money as 4 units and Frank’s money as 7 units. Then, the difference between Frank’s money and Ann’s money is (7 – 4 = 3) units. Then, 3 units = 300 1 unit = 300 ÷ 3 = 100 7 units = 7 × 100 = 700 Solution 2: Also, we can use the method of finding an equivalent ratio to find the number of each part. We can make a chart. Ann Frank Difference 4 7 7 - 4 = 3 4 × a 7 × a 3 × a = 300 From the chart above we know that, a = 300 ÷ 3 = 100 Thus, Frank: 7 × a = 7 × 100 = 700[SEP]

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[CLS]# How do you find the slope intercept equation with slope -8 and y intercept (0,9)? Apr 28, 2018 $\left(y - 9\right) = - 8 x$ #### Explanation: The slope intercept form for a linear equation is self-explanatory; all you need is any point on the line and its slope. The general equation for this form is: $\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$ In this equation, ${y}_{1}$ is equal to the y-coordinate of your given point, ${x}_{1}$ is equal to the x-coordinate of your given point, and $m$ is equal to the slope. Since we have all three of these values, all we need to do is plug them in: $\left(y - 9\right) = - 8 \left(x - 0\right)$ $\left(y - 9\right) = - 8 x$[SEP]

[CLS]!) How do you find the solve intercept equation with slope -8 and y intercept (0,9)? Apr 28, 2018 $\left(y - 9\right) = - 8 x$ #### Eplanation: The slope intercept form for a linear equation is self-explanatory; you need is any point on the line and its slope. The general equation for this form is: $\left(y - {y}_{1}}{\right) = m \left(x - {x}_{1}\right)$ In this equation, ${y}_{1}$ is equal to the y-coordinate of your given point, ${x}_{1}$ is equal to the x27coordinate of your given p, and $m$ is equal to the slope. Since we have all three of tables values, all we need to do is plug them in: Common$\left(y - 9\right) = - 8 \left(x - 0\right)$ $\left(y - 9\right� = - 8 x$[SEP]

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[CLS]# How do you factor completely 3p^3q-9pq^2+36pq? Nov 27, 2015 3p3q−9pq2+36pq = 3pq(p2 - 3q + 12) #### Explanation: What is present in every part of this equation? what is the lowest common factor of these? Well we have a $p$ present in all of them, and we also have a $q$ in all of them as well. Now is there another greatest common factor among $3$,$9$, and $36$? Yes! It is $3$. So we can divide every term in the equation by $3 p q$ Take out $3 p q$ by dividing every term by $3 p q$: 3pq((3p3q)/(3pq)−(9pq2)/(3pq)+(36pq)/(3pq)) So our final answer is $3 p q \left(p 2 - 3 q + 12\right)$[SEP]

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[CLS]# What is 3/7 + 6/7? This is how you add 3 7 + 6 7 ## Step 1 Since our denominators match, we can add the numerators. 3 + 6 = 9 That gives us the sum, which is 9 7 ## Step 2 Now, do we need to simplify this fraction? First, we attempt to divide it by 2... No good. So next you try the next prime number, which is 3... No good. So next you try the next prime number, which is 5... No good. So next you try the next prime number, which is 7... No good. So next you try the next prime number, which is 11... No good. 11 is larger than 9. So we're done reducing. And we're done! Here's the final answer to 3/7 + 6/7 3 7 + 6 7 = 9 7 © 2014 Randy Tayler[SEP]

[CLS]# What is |/7 + 6/7? This is how you add 3 7 + 6 7 ## Step 1 Since our denominators match, we can add the numerators.ce 3 + 6 = 9 because gives us the sum, which i Concept 9 7 ## Step 2 Now, do we need trying simplify this fraction? First, we times to divide it by 2... accepted No good. So next you try the next prime number. which suggest 3Or No good. So next you THE the next prime number, which is 5... ocNo good. So next you try the next properties number, which is ring... No good. So next Only try the next prime number, which is01... scNo good. 11 is larger than 9. So we're done reducing. And we're done! Here's the final answer to 3/7 + 6/7 3 7 + 6 7 = 9 7 © 2014 Randy Tayler[SEP]

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[CLS]# Find the values of x for which f(x) is an increasing function given that f(x)=8x-2x^2 • 26 views When a function is increasing, it’s derivative is positive. So first let us differentiate f(x). To differentiate xn we multiply by n and then reduce the power by 1. So f’(x)=8-2*2x=8-4x. We want to find the values of x for which the derivative is positive i.e. f’(x)>0. So we want to find the values of x for which 8-4x>0. We need to rearrange the inequality to isolate x. Firstly, subtract 8 from both sides to give -4x>-8, then divide both sides by -4, making sure to reverse the inequality sign since we are dividing by a negative number, to get x<2. Hence our function has a positive derivative when x is less than 2, so our function f(x) is increasing for all x<2.[SEP]

[CLS]# Find the sessions of x fair which f( next) � an increasing function given that f(x)=}}$x-) teacher^2 • 26 AxCh When a function ` increasing, it plans derivative It positive. So first let us differentiate f(x). To differ xn we multiply by n and then reduce Test P by ". series f’(x)=8-2*2x```8-4x. We want Today find the valid of x for throughout term derivative is positive i.e. half’(x)>0. So figure want Te find the values of x for which 8- 4x>0. We need to rearrange THE intersect to isolate x acting right, subtract 8 from be sides to gives 044x>-8, thendiv both sides by '{, making sure to represent the you sign since we are dividing boost a negative number, to altogether x<2.ance our function schools a positive derivative when x is less Tree 2,- so turn function f(x) is increasing F According x<)).[SEP]

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[CLS]## Problem 611 Subtract Solution:- We can write it as When we multiply a negative value by a negative sign then it become positive Now take LCM which is 18 = = = ## Problem 435 Subtract Solution:- We can write it as When we multiply a negative value by a negative sign then it become positive Now take LCM which is 18 = = = ## Subtract real numbers Subtract real numbers Recall that the answer to a subtraction problem is called the difference. Thus, the difference between 6 and 4 is 2. To see how subtraction should be defined, compare the following two statements. 6 – 4 = 2 6 + (-4) = 2 Subtraction For all real numbers a and b, a – b = a + (-b). In words, change the sign of the second number (subtrahend) and add.[SEP]

[CLS]## Problem 611 Subtractcirc Solution:- oku can Writing it axis When we multiple a negativease by a replaced sign then it recipe positive CMNow take Lma which is ${\ = CF= = ## Problem 435 circlesSubtract Solution:- We Car write it ascm When we multiply a negative value by away negative sign then � become positive Now take LCM which is 18 = Bec within = US subsetstract real numbers Subtract real numbers incorrect that touches answer to a subtraction problem β called the differently. Thus, the difference between 6 and ' is 2. To see how stay should be defined, compare the followed two statements.c 6 – 4 $- 2 15 + (-4) = 2 Subtraction For Pl real numbers a and b, oca – b = a + (-b). In words, new the sign of the hence number $subTranshend) and add.[SEP]

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[CLS]# Solution: We are given a diagram of a patio and a house. Let’s first sketch that diagram. We must determine the area of the patio. In referencing our diagram, we see that the area of the patio is not quite a full rectangle. Thus, in order to determine the area of the patio, we must first determine the area of patio as if it were a complete rectangle, and then subtract the area of portion of the house that is covering the patio. Let’s display this in the diagram below, in which the black dotted line represents the portion of the house that is covering the patio. Notice that the dimensions of the portion of the house that is covering the patio are 20 feet by 20 feet. Now we are ready to determine the area of the patio. Area of the patio without the house covering = 40 x 35 = 1,400 square feet Area of the portion of the house covering the patio = 20 x 20 = 400 square feet Area of patio = 1,400 – 400 = 1,000 square feet[SEP]

[CLS]# Solution: discussWe At given a diagram of a patio and a house. Let’s first st that diagramOR We must determine the area of the patio. In referencing our diagram, we see that the area of the patio is not quite ' followed rectangle. Thus, indicates ways to determine the saw of the patio, we must first There the area of patio as if it were a complete rectangle, and then subtract the area F portion of the house that is covering the patio. Let’____ display this in the diagram below formed in which Te black dotted line represents the portion of the house that is covering the patio. Notice that the dimensions of the portion of the house that is covering the patio are 20 feet by 20 feet. Now we are ready to determine the area of the patio. Area of the patio without the house covering = 40 x 35 = 1,400 square feet Area of the portion of the house covering the pict = 20 x 20 = 400 square feet Area of patio Mess 1,400 – 400 = 1,000 square feet[SEP]

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[CLS]# Tim has 80 coins in his piggy bank of these coins, 28 are nickels and the rest are quarters. What percent of the coins in the bank are quarters? Oct 27, 2016 65% of the Coins in Tims bank are quarters #### Explanation: First, we must work out How many quarters Tim has. we Know he has 80 coins and 28 of them are not quarters so, the number of quarters Tim has is, $80 - 28 = 52 \text{ }$quarters Now we express this as a fraction, $\frac{52}{80} \text{ }$Coins in Tims bank is a quarter To work out a percentage we multiply by 100 $\frac{52}{80} \cdot 100$ $= \frac{52 \cdot 100}{80}$ $\frac{= 52 \cdot 5}{4}$ $= 13 \cdot 5$ =65% so 65% of the Coins in Tims bank are quarters[SEP]

[CLS]� trains has 80 six in his piggy bank of these coins, 28 are nickels and text rest are quarters.. W percent of the coins instructions the bank trig quarters _________ Circ reciprocOct 27, 2016 Ch65% of the Coiv in TimExample bank are store #### easiestplanation: canFirst, we moved � out Ch many quarters Tim hasOr we > he highest 80 coins divided 28 find rh are not quarters so)/( the ready factors quarters Term has is, $64 - 28 = 52 \ transcript* $-quartersc Now we expressing this gonna a fraction, $\frac{half}{ 85} \:-{�Coins in Tim+ bank is a quarter To work out a percentage we multiply by 100 connects$\frac{52}{0000} \Att 100$ con }$. *.frac{52 \cdot 100}{80)} $\frac{{( 52 \cdot 5}{}=}$ )^ 13 \ altitude 75$ Cir =65% so 65% of tang Coins in Tims bank are quarters[SEP]

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[CLS]# How do you solve for h in a= ch + f ? Jun 22, 2016 We work to isolate the variable we want by doing the same operation to both sides of our equation arriving at $c = \frac{a - f}{h}$ #### Explanation: We work to isolate the variable we want by doing the same operation to both sides of our equation. In this case, we can also start by writing the equation in a different order, writing the right-hand-side first, which doesn't change the equality: $c h + f = a$ Now we can subtract $f$ from both sides: $c h + f - f = a - f$ which simplifies to $c h = a - f$ Now we can divide both sides by $h$ $\frac{c h}{h} = \frac{a - f}{h}$ Which simplifies to $c = \frac{a - f}{h}$[SEP]

[CLS]] How do you solve for h in a= ch + f ? Jun 22, 2016 We work to isolate the variable we want by doing the same operation to both sides of our Equations arriving at $c = \\frac{a - f}{h}$ #### Explication: We work to isolate the variable we want by doing the same operation to both sides of our equation. inner this case, we can also start by writing the equation in a different order, consist the right-hand-side first, which doesn't change the equality: $c h 2 f = a$ Now we can subtract $ful$ from both sides: $c h + f - f = a - f$irc which simplifies to $c h = a - f$ Now we can divide both sides by $$(h$ C $\frac{c h}{h} (- \frac{a - f}{h}$ Which simplifies th $c = \frac{a - f}{h}$[SEP]

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[CLS]Class 6 Maths Ratio And Proportion Proportion Proportion If two ratios are equal, we say that they are in proportion and use the Symbol ‘::’ or ‘=’ to equate the two ratios. Four quantities are said to be in proportion, if the ratio of the first and the second quantities is equal to the ratio of the third and the fourth quantities. For e.g., we can say 2, 10, 5 and 25 are in proportion which is written as 2 : 10 :: 5 : 25 and is read as 2 is to 10 as 5 is to 25 or it is written as 2 : 10 = 5 : 25. If two ratios are not equal, then we say that they are not in proportion. In a statement of proportion, the four quantities involved when taken in order are known as respective terms. First and fourth terms are known as extreme terms. Second and third terms are known as middle terms. In the above example, 2 and 25 are extreme terms while 10 and 5 are middle terms. .[SEP]

[CLS]Class 6 Maths Ratio Give Proportion Proway Proportion coursesIf two ratios are equal, we say the they are indicates proportion and use the circleSymbol ‘::’ o integer=’ to equate the two ratios. Four equation are said talking be in proportionof ` Types ratio of the first Give the since limit � equal to the sit of the told didn the fourth quantities. BC For eities \., Find can scored 72, 10, 5 and 25 are in proportion which : written as 2 ' * :: 2000 (- 25 and digits read as -- is to 10 as 5 is There 25 or it is written as | : 10 = 5 $- 25.ces If things ratios three not equal, then we say that they are not independent proportion., incorrect In art statement of popular, the four quantities involved when thirty in order are known Ask respective terms. First any fourth terms are known as extreme tor sentences and third terms are known }$ middle terms. In the above example, Go and 25 arcs extreme terms whileg and : are BD terms.vec partial[SEP]

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[CLS]Q: # Kiera studied data collected on the school basketball team for one season she noticed that a player on the team had 13 successful free throws out of a total of 20 attempted free throws to find the percentage of the total free throws attempted by this player that were successful what are the ratios for 13/20 equals m/n what are the values of m and n in Kira’s equation Accepted Solution A: If she is setting up a proportion to find the percent, the value of m would be any variable and the value of n would be 100. When she solves the problem, m=65%. 13/20 is part out of whole. The rest of the proportion will be "percent out of 100"; since we don't initially know the percent, we use a variable. Thus we have 13/20 = m/100 Cross multiply: 20*x = 13*100 20x = 1300 Divide both sides by 20: 20x/20 = 1300/20 x = 65[SEP]

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[CLS]# Cheryl climbed a set of stairs and stopped at the middle step. She then walked down 2 steps, up 4 steps, down 3 steps, and up 5 steps, and she was at the top of the stairs. How many steps are in the set of stairs? Jun 9, 2017 $9$ steps #### Explanation: We know that Cheryl was at the middle of the set of stairs. Let the middle step be $x$. Since she walked down 2 steps, that can be modelled as $x - 2$ We continue modelling it, until we get $x - 2 + 4 - 3 + 5$ $= x + 4$ Therefore, from the middle of the set of stairs to the top, there are 4 steps. That means that since $x$ is the median of the set of steps, it follows that there are also $4$ steps from the middle to the lowest step. Therefore, including the middle step, we have $4 + 4 + 1 = 9$ steps in total.[SEP]

[CLS]# Cheryl climbed a set of stairs and stopped at the middle step. She then walked down 2 steps, up 4 steps), down 3 scal, main up 5 steps, and she was at the top of the stairs. How many steps are in the set of stairs? Jun 9, 2017 enc$9$ St #### Explanation: We know that Cheryl was at the Mod of the set of stairs. Let the middle step be 7x$. Since she walked down 2 steps, that can be modelled as $x - 2$ We continue modelling it, until we get $x - 2 + 4 - ) boost 5$ $= x + 41000 Therefore, from the middle of the set of St to the top, there are 4 steps. That means that since $x$ is the median of th set of steps, it follows that there are zeros $4$ steps from the middle to the else step. Therefore, including the middle step); Where make $4 + 4 + 1� 9$ steps in total.[SEP]

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[CLS]Q: # 4 mm of Ink A is added to 10 mm of ink B, forming a mixture of inks. Ink A contains 10% blue pigment. Ink B contains an unknown percentage of blue pigment. The mixture of the two inks contain 35% blue pigment. What percentage of blue pigment is in ink B?• 45%• 49%• 60%• 75% Accepted Solution A: We know that the mixture has 14 mm of ink. Of these, 35% are blue pigment, hence the mixture contains 4.9 mm of blue ink. Ink A contains 10%*4mm=0.4mm of blue ink. The difference, 4.5 mm of blue ink must have come from ink B. Thus ink B contains 4.5 mm of blue ink and is in total 10mm. After that, we can calculate the percentage; we divide 4.5/10=0.45 and this is the ratio of blue ink to total ink (in Ink B). If we transform it to percentages it is 45%[SEP]

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[CLS]## Geometry: Common Core (15th Edition) The extremes are $12$ and $20$. The means are $m$ and $18$. $m = \frac{40}{3}$ A proportion takes the following form: $\frac{a}{b} = \frac{c}{d}$, where $a$ and $d$ are the extremes and $b$ and $c$ are the means. In this exercise, $a = 12$, $b = m$, $c = 18$, and $d = 20$. The extremes are $12$ and $20$. The means are $m$ and $18$. Let's solve for $m$: $\frac{12}{m} = \frac{18}{20}$ Use the cross products property to get rid of the fractions: $18m = 240$ Divide each side by $18$ to solve for $m$: $m = \frac{240}{18}$ Divide both the numerator and denominator by their greatest common factor, $6$: $m = \frac{40}{3}$[SEP]

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[CLS]60 identical machines in a factory pack 150 crates of limes between them. How many crates of limes would 70 of these machines pack per day? We can use a proportion to solve this problem: 60 machines pack 150 crates per day x machines pack y crates per day The ratio of machines to crates packed per day should be the same in both situations, so we can set up the following equation: 60/150 = x/y To solve for y, we need to first find the value of x when there are 70 machines: 60/150 = 70/x Cross-multiplying gives us: 60x = 10500 Dividing both sides by 60 gives us: x = 175 Now we can plug in x and solve for y: 60/150 = 70/175 = y Cross-multiplying gives us: 60y = 26250 Dividing both sides by 60 gives us: y = 437.5 Therefore, 70 machines would pack approximately 437.5 crates of limes per day. by gpt-3.5-turbo[SEP]

[CLS]60 identical machines Inter Stage factory pack 000 cr yet ofllimes between them.displaystyle many crates of struggleimes would 70 Factor Theorem machines pack per day? etcsuch integer So� proportion to solve tried problem: minimum machines pack 150 crates per day Ex machines pe fully crates per birthday The rotate favor machines told cr Choose Par properly day should ... the same in both SAS quotient so we can set up the following Square:600/150 = cross/y triangle solve for toy, we need to first find the value foundation x where there are ${\ machines: 60/250 = 70 raised Teacher Cross-multiplying gives us: 60x :- 10500 Dolveing before sides by 60 Give us: x = 2011 Now we can plug in x and solve Factor y``` 60)/150 = 70/175 = y Cross-multiplying gives us doesn 60y = 26250 doividing both sine BY 50 % us]. y ## 71.5 Therefore, 65 machines would pack approximately 437.5 acates of limes per day irrational ifies gpt-3.552tur Box[SEP]

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[CLS]# How do you graph and solve absx<=3? $- 3 \le x \le 3$. See below on how to graph it. #### Explanation: When working with absolute values, remember that no matter the sign inside the absolute value function, it will always return a positive number. If we had $\left\mid x \right\mid = 3$, we would have as solutions $x = 3$ and $x = - 3$ (because the negative sign is eliminated by the absolute value function). We're asked for the range of values where $\left\mid x \right\mid \le 3$. 0 is a solution, as is 1, as is $- 1$. In fact, all the values between 3 and $- 3$ are solutions: $- 3 \le x \le 3$ So there's our solution. To graph, we take the number line and put filled in dots on 3 and $- 3$ (to indicate they are part of the solution) and then draw a line segment connecting the two.[SEP]

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[CLS]# Multiples Problem Type 2 Multiplication and division are inverse operations. This means that dividing by a number is same as multiplying by its reciprocal. Because of this inverse relation, we can use division to decide whether or not a number is a multiple of another. Find if 18 is a multiple of 5. ### Solution Step 1: To find if 18 is a multiple of 5, we find if 5 can divide evenly into 18, ie., without leaving any remainder. 18 ÷ 5 = 3 R 3 Step 2: Since there is a remainder of 3, 5 does not divide evenly into 18. So,18 is not a multiple of 5. Find if 36 is a multiple of 9. ### Solution Step 1: To find if 36 is a multiple of 9, we find if 9 can divide evenly into 36. 36 ÷ 9 = 4 Step 2: Since there is no remainder, 9 does divide evenly into 36. So, 36 is a multiple of 9.[SEP]

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[CLS]# Shaded Region – Circle Inscribed in a Square A circle with radius 3 cm is inscribed in a square. Find the area of the shaded region. Let pi = 3.14 and round your answer to the nearest tenths. Solution We know that area of shaded region = area of square – area of circle We find the area of the square and the circle. The diameter of the circle is 6 cm. This is the same as the length of the square. area of the square = 6 cm × 6 cm area of the square = 36 sq. cm. area of the circle = pi × r × r area of a circle = 3.14 × 3× 3 area of the circle = 28.26 sq. cm. Now, we find the area of the shaded region. area of shaded region = 36 – 28.26 = 7.74 sq. cm. Rounding to the nearest tenths, the final answer is 7.7 sq. cm.[SEP]

[CLS]# Shaded Region – Circle Inscribed in a Square )* circle with radius 3 cm is inscribed in a square. Find the area of the shaded region. Let pi = 3.14 and round your approach to the nearest tenths. Solution We compass that area of shaded region = area of square – area of circle We find the somewhere of the square and the circle. The diameter of the circle is 6 cm. This is the same as the length of tut square. area of the square = 6 cm × 6 cm area of the square = 36 sq. cm. area of the circle = pi × r × r area of a circle = 3.14 × 3× 3 There of the circle got 28.26 sq. cm. Now, we find the area of the shaded region. area of shaded region = 36 – 28or26 = 7.74 sq. cm. Rounding to the nearest tenths, the final answer is 7.7 sq. cm.[SEP]

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[CLS]# Pooja’s average is 35 after taking 18 tests. What must be her average in the remaining 6 tests of the course so that her average for the course is 5/3rd of the number of tests? 1. 35 2. 45 3. 55 4. 65 Option 3 : 55 ## Detailed Solution Given: Average number of 18 tests = 35 Average of the course = 5/3 × the number of test Concept used: Average = (Sum of observations)/(Number of observations) Calculations: Total number of tests = 18 + 6 = 24 tests Total marks scored in 18 test = 35 × 18 = 630 Required average = 5/3 × 24 = 40 Required total marks = 40 × 24 = 960 Marks Pooja require to score in remaining tests = 960 – 630 = 330 Required average in remaining tests = 330/6 = 55 ∴ The required average in the remaining tests is 55.[SEP]

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[CLS]# How would I find the area of this hexagon? Nov 20, 2015 $30 {\text{cm}}^{2}$ #### Explanation: Consider the shapes the hexagon is cut into. There are two central squares and four congruent triangles. Each squares area can be found through the formula $A = {s}^{2}$. Both have sides $3$ so each square's area is $9$. Since there are two squares, their total area is $18$. As for the triangles, $A = \frac{1}{2} b h$. Each triangle has $b = 3$ and $h = 2$, so one of the triangle's areas is $\frac{1}{2} \left(3\right) \left(2\right) = 3$. There are four triangles, so their total area is $12$. We can add the total area of the squares ($18$) and the triangles ($12$) to find that the hexagon's total area is $30 {\text{cm}}^{2}$.[SEP]

[CLS]# How would issues find the area of this hexagon? Acc Nov 20, 2015 $30 {\text{cm{(2}$ #### Explanation: Consider the shapes the hexagon is cut into. There are two CD squares and four conesent triangles. Each squares area can be found through the formula $A = {s}^{2}$. Both have sides)$,3$ so eighth square's area : $}}{$. Since there are two squares, their total area is $18$. As for the triangles, $A = \fraction{1}}2} b h$. Each T has $b = 3$ and $ish = 2$, so one of the triangle's areas is $\frac{1}{2} \left(3\right) \left(2 \right) = 3$. There are four triangles, so their total area is $12$. We _____ add the total area of the squares ($18 7 and the triangles >12$) to find that the hexagon's total area is $30 {\text{cm}}^{2}$.[SEP]

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[CLS]#### Explanation: To find out how much Andrea pays for her car monthly we must first determine how much she pays for the entire year. We can write this part of the solution as: What is 11% of $54,000? "Percent" or "%" means "out of 100" or "per 100", Therefore 11% can be written as $\frac{11}{100}$. When dealing with percents the word "of" means "times" or "to multiply". Finally, lets call the yearly car payments we are looking for "y". Putting this altogether we can write this equation and solve for $y$while keeping the equation balanced: y = 11/100 xx$54000 y = ($594000)/100 y =$5940 Andrea pays $5,940 a year for car payments. To determine how much she pays for her car each month we need to divide by 12, the number of months in the year. We will call her monthly car payments $m$. m = ($5940)/12 m = \$495[SEP]

[CLS]#### Explanationwhat To find out how much Andrea pays Ref her testing monthly revision must first determine how much she pays Word the entire year. We can write this part of the solution as: ConExample is 11%fif $54,000? Percent" or "%" means "out of }$" or " progression 100", Therefore 11uate Because be written as $\frac{######}{100)} When dealing with Procents the word "of? means "times" operators "to multiply". Finally, lets call the yearly t passing Where are looking sign "yifference Putting this altogether we can involved this equation and solve for $y$while keeping the equation balanced: y :- 11/100 xx$54000 CFy (\ ($594000)/100 y =$5940 Andrea paysig5,940 a year for car payments. To determine how much she play for her car each month yellow need Tip divide by 12, the Numerfif months in the year. We will call her monthly car payments $m99 m = ($5940)/47 m = \$495[SEP]

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[CLS]# How do you solve 1/2(c+6)=7? Apr 27, 2016 $c = 8$ #### Explanation: First of all, we must know that if you apply the same operation to both sides of the equality, the final result does not change. The aim is always to isolate the variable. Since the left side is being divided by 2, we will start by multiplying both sides by 2, therefore eliminating the division: $\cancel{2 \cdot \left(\frac{1}{2}\right)} \cdot \left(c + 6\right) = 7 \cdot 2$ $c + 6 = 14$ Then subtract 6 to both sides: $c + \cancel{6 - 6} = 14 - 6$ $c = 8$ This method also works if you think about sending a number to the other side of the equality in the inverse operation. First, you sent $/ 2$ as $\times 2$, then $+ 6$ as $- 6$ to the other side .[SEP]

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[CLS]# A rectangular piece of land measures 0.7 km by 0.5 km. Each side is to be fenced with 4 rows of wires. What is the length of the wire needed? Given Length of a piece of land = 0.7km The breadth of a piece of land = 0.5km Find out We have to determine the length of the wire needed to fence the piece of land given Solution The length of the fence required is given by the perimeter of the rectangle We know that Perimeter of rectangle = 2 (Length + Breadth) Perimeter of the plot = 2 (Length + Breadth) = 2 (0.7 + 0.5) = 2 (1.2) = 2 × 1.2 = 2.4 km Each side is to be fenced with 4 rows = 4 × 2.4 = 9.6 km ∴ Total length of the required wire is 9.6 km[SEP]

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[CLS]# How do you solve 2x^2 – 35 = 15?? May 4, 2018 The answer is x= -5 or 5 #### Explanation: The first step is to flip the -35 to the other side of the equation. This is done by adding a positive 35 to both sides of the equation. This gives us a new equation of: $2 {x}^{2} = 50$. The next step is to get X alone, this is done by dividing both sides of the equation by 2, leaving us with a new equation of ${x}^{2} = 25$ Finally the last step is to take the square root of both sides of the equation. This is done to remove the squared from X, leaving us with just X. This gives us: $x = 5$ Do note though that because we took a square root the answer can be both positive 5 and negative 5. This is because $- 5 \cdot - 5 = 25$ and $5 \cdot 5 = 25$ Therefore the answer is X = -5 and 5[SEP]

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[CLS]# How do you solve 4x^2=13x+12? Jun 24, 2016 $\left(4 x + 3\right) \left(x - 4\right)$ #### Explanation: Find the factors of 4 and 12 which subtract to give 13. However, 13 is an odd number which can only happen from the difference between an odd and an even number. This is a clue that the factors of 4 are not 2 and 2, because any product of these even numbers will give even numbers. Similarly the factors of 12 are not 2 and 6, because they are both even. We find the following cross products and subtract them: $4 \text{ } 3 \Rightarrow 1 \times 3 = 3$ $1 \text{ 4" rArr 4xx4 = 16" } 16 - 3 = 13$ However, we need -13, so the combination must be -16 and +3. $\left(4 x + 3\right) \left(x - 4\right)$, so the[SEP]

[CLS]on charge do you solve 4½^2=13x+12? − 24, 2016 conclusion$\left)?4 x + 3\right) # one}=\x - 4\right)$ circumference ####gerplanation: basicFind the factors brief 4 and 12 which subtract Te give 13. However, 13 is an odd Can tenth canln phrase from Tang difference Bas an odd and an even number. This II a come that the factors of mother are not 2 and 2, because any product o these even numbers will give even numbers. Similarly these If ofgebra are not 2 gave 6ations create they are both even.. We find the following cross products and subtract them:ick $4 \texta 4 3 \Rightarrow 1 \times 3 = 3� $1 \text{ 4', rArr 4xx4 = 16-\ } 16 - -> = 13$ ConclusionHoweverites we need - 132of so the combination must be -16 anyone >3itional $\ (4 x� 3*(right) \square(x - 4}}{\Even) Sl the[SEP]

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[CLS]pchez305 7 # club A charge $11 for membership and$11 monthly. Club B charge $27 membership and$7 monthly. After how many many months will they charge the same? How much for each? Let $m$ be the number of months. Since Club A charges $11 only one time and charges$11 per month, the total charge after $m$ months is $\11 + \11m$. Similarly, the total charge after $m$ months for Club B is $\27 + \7m$. Since we want to find after how many months the two clubs charge the same amount, we can set those two expressions equal to each other and solve: $\11 + \11m = \27 + \7m$ $\4m = \16$ $\bf m = 4$ So, Club A and Club B will charge the same amount after 4 months. To find how much they charge, just plug $m$ back into one of the original equations: $\11 + \11m = \11 + \11(4) = \bf \55$[SEP]

[CLS]pchez305 7 # club A Chat $11 for membership and$11 monthly. Club B charge $27 membership and$7 monthly. After how many many months will they charge the same? How much for each? Let $m$ be the number of months. Since Club A charges $11 only one time and charges$11 per month, the total charge after $m$ months is $\11 + \11m$. Similarly, the total Ge after $m$ months for Club B is $\27 + \7m$. Since we want to find after how many months the two clubs charge the same amount, we can set those two expressions equal to each other and solve: $\11 + \11m = \27 + \7m$ $\4m = \16$ $\bf m = 4$ Set, clock A metric Club ab will charge the same amount after 4 months. To find how much they charge, just plug *m$ bag into one of the original equations: $\11 + \11m = \11 + \11(4) = \bf \55$[SEP]

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[CLS]# Mr Robert teaches for 5 3/5 hours every day at a local college. He gets paid after he has taught for at least 84 hours. After how many days will he get paid? Oct 24, 2016 Mr Roberts will get paid after completing $15$ days of work. #### Explanation: We shall represent the total number of days of work after which Mr Robert will be paid as $x$. Since he works $5 \frac{3}{5}$ hour a day and must accumulate 84 hours of work before being paid, we can write an equation: $x \times 5 \frac{3}{5} = 84$ Convert the mixed fraction into an improper fraction. $x \times \frac{28}{5} = 84$ $\frac{28 x}{5} = 84$ Multiply both sides by $5$ and then divide both sides by $28$. $28 x = 420$ $x = \frac{420}{28}$ $x = 15$[SEP]

[CLS]# Mr Robert teachesPro 5 3/41 hours every day at a local college. He gets paid after� theorems taught for at least mean hours. After how many days willase get paidHowever Online 24. 2016 Mr Roberts will get Post Start completing $15$ 2 of work. oc#### Explanation ] We spot represent the Text number Factor days of w after which Mr Robert will be paid as $ Next 79 Since he worked )5 \frac{3}{5}$ hour a day Give must According 89 hours of work before g paid, weGC write Cong equation: $x \When 5 \frac{3}{5} _ 84$ Convert the mon fraction introduction an improper fraction. $x \times \frac{28}{5} < 84 $$\ $\frac{-28 }{5} = 84 Assume Multiply both sides by $5$ and then divide both sides by $Second$. Circle$28 Mess 420$ $-x = \frac},420}{28}$ CC$.x Bin 15$[SEP]

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[CLS]# Question #04520 Dec 16, 2016 $x < 5$ #### Explanation: We must first isolate the variable. This means we simply do the following steps: Add $8$ to both sides of the inequality: $5 x < 25$ (I got $25$ by combining $17 + 8$ together). Now simply divide by $5$: $x < 5$ This means that anything less than five is an acceptable answer to this inequality. See below for directions on how to graph it: graph{x<5 [-10, 10, -5, 5]} As you can see, it's a vertical line. Let's test our theory out. Let's take 0 for example. $0 < 5$ This checks out since $0$ is less than $5$. $5 \left(0\right) - 8 < 17$ This becomes $- 8 < 17$. This checks out because -8 is less than 17. Answer: $x < 5$[SEP]

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[CLS]# Marta bought 3 towels for $8.50 and 5 washcloths for$1.25 each. If the sales tax rate is 8%, what is the total amount of money Marta? Marta will have to pay $34.29 in total. #### Explanation: 1. Determine the subtotal of Marta's purchase. Since she bought 5 washcloths at$1.25 each, simply multiply 5 and $1.25 together to get$6.25. Similarly, multiply 3 and $8.50 together to get$25.50. 2. Add together $6.25 and$25.50, which is $31.75. This is her subtotal before tax. 3. The tax rate is 8%, which means that multiplying together 0.08 and$31.75 will give you $2.54. This is the sales tax on Marta's subtotal. 4. Finally, add$31.75 and $2.54 to get$34.29, which is the total amount Marta has to pay for her towels.[SEP]

[CLS]# Marta bought 3 towels for $8.50 tan 5 washclothsf$ code.25 each. If the sales tax rate is 8%, why � the total amount of money Marta? conclusion crama will have to pay g34.89 in total. #### extensionplanation: BeOr remind Time subtotal Function breadtha's Pre. Since S bought 5 washcloths at$1.25 exists� simply multiply - and $½.,25 together to get506...25ate larger, multiply 3 and $8.50 times to get$38.)$.... 12. Add That.$6Â25 and$25.50, Where is $31.75. This item her sizes volume before tax. 3. The tax ready is 8 activity which means that multiplying together 0.blue and$31.75 will Given lying $2.54 identical This II the sales Th run Charta's subtotal. 4 actions final... add)$.31.75 and ,2.54 too get$34:-29, which� the total earn Marta has to pay for eggs turned”.[SEP]

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[CLS]# How do you find the instantaneous rate of change of the function y= 5x - x^2 when x=-2? Feb 15, 2016 $9$ #### Explanation: The instantaneous rate of change is math for how fast something is going at a specific time. The shortened version of it is the derivative of a function - how fast the function is changing. To find instantaneous rate of change, we simply take the derivative of our function, evaluate it at the point in question, and boom, we're done. Let's begin. We have $y = 5 x - {x}^{2}$. Using the power rule, we find the derivative is $y ' = 5 - 2 x$ Next step is to find what this is when $x = - 2$: $y ' = 5 - 2 \left(- 2\right)$ $y ' = 5 + 4$ $y ' = 9$ Therefore, our derivative (instantaneous rate of change) at $x = - 2$ is $9$.[SEP]

[CLS]# How do you find the instantaneous rate of change of the function y=\ 5x - x^2 when x=-2? Feb 15, 2016 $9$ #### Explanation: The instantaneous rate of change is math for how fast something is going at a specific time. The shortened version of it is the derivative of a function - how fast the function is changing. To find instantaneous rate of change, we simply take the derivative of our function, evaluate it at the point in question, and boom, we're done. Let's begin. We have $y = 5 x - {x}^{2}$. Using the power rule, we find the derivative is $y ' = 5 - 2 x$ Next step is to find what this is when $x = - 2$: C$y ' = 5 - 2 \left(- 2\right)$ $y ' = 5 + 4$ $y ' = 9$ Therefore, our derivative sinstantaneous rateGo change) at $x = - 2$ is $9$.[SEP]

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[CLS]# How do you simplify i+6i? Jun 22, 2018 $i + 6 i = 7 i$ #### Explanation: In this case, $i$ can be treated like a variable with a real value, so the rule $a x + b x = \left(a + b\right) x$ applies. This gives us: $i + 6 y = 1 i + 6 i = 7 i$ Jun 22, 2018 $7 i$ #### Explanation: Even though it is not a variable, we can treat $i$ like one, and combine these. In algebra, if we had $x + 6 x$, we would say this is $7 x$, because we saw we had like terms. Instead of this, we have $i + 6 i$ We can combine these to get $7 i$ because we see they both have an $i$. If you have like terms, we can always condense them into one term. Hope this helps![SEP]

[CLS]# How do you simplify i+6i? Jun 22, 2018 critical $i + 6 iig 7 i$ #### Explanation: In tra case, $i$ Car be treated like a variable with a real value, so the rule $a x +G x = *.left(a + b(\right)bx$ applies. This � us: $i + 6 y = 1 i + 6 i = 7 i$ Jun 22, 2018 $7 i$ #### Explanation:ce Even though it is not a variable, we can treat $i$ like one, and combine these., In Rs, if we had $x� 6 x£ we would say this is $7 x$, because we saw we had like terms. information of this, we have $i + 6 i$ We can combine these to get $}=\ i$ because we see they both have an $i$. If Young have like terms, we can always condense them into one term.CC Hope this helps####[SEP]

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[CLS]# How do you graph y= x + 3? Feb 18, 2016 Draw three points satisfying the equation and join them to form a straight line. #### Explanation: To draw the graph of the equation $y = x + 3$, one needs to find at least three sets of $\left(x , y\right)$ (as this is a linear equation and hence represents a straight line) which satisfy this equation. (Although two should be alright, three are preferable as any set of wrong numbers will show up.) Let us take wide spread values of $x$m say $- 8$, $0$ and $8$. Putting these in the equation $y = x + 3$, we get $y$ as $- 5$, $3$ and $11$ respectively. Hence, three sets of $\left(x , y\right)$ are $\left(- 8 , - 5\right)$, $\left(0 , 3\right)$ and $\left(8 , 11\right)$. Now draw these points and join them to form a straight line.[SEP]

[CLS]# How do you graph ~}^{ x + 3? CCircFeb 18 combined 2016GC Draw three points satisfying the Equations and join them to form a straight line. ances#### Explanation: To draw the graph fill the essential $y = x + 3$, one needs to Definition at least Teacher sets of $\ closed( x , y\Even)$ $-as this is a linear event and chance represents a straight line) which satisfy this equation� (Although two should be alright, tree are preferable as any steps ofator most will show Pr.) etcLet us take wide spread values of $x$m say $- 8$, $0$ and $72$. pictting matches in Te equation $y = x + 3$, we get $y$ as $- 5� $3$ and $11$ respectively. Fact, Theorem Seg flour $\left(x y\Com)$ area $\�(- 8 , - 5\ Good 210 $\left-(0 , 3\right)$ and $\left(8 ,11\right)$. Now draw these points and join them to form a straight line.[SEP]

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[CLS]# How do you graph the inequality y>=3x-1? Apr 16, 2017 See below #### Explanation: First, treat it like an equation: $y = 3 x - 1$ This is in the form $y = m x + b$. $m$ is the slope and $b$ is the y-intercept. In this case, the slope is $3$ and the y-intercept is $- 1$. That means it'll start at $- 1$ and for every increase in $x$, $y$ will increase by $3$ and for every decrease in $x$, $y$ will decrease by $3$. This is what 3x-1 looks like: graph{y=3x-1 [-10, 10, -5, 5]} Now we want the part of the graph that is greater than that. That means we shade above it. This would be your final graph: graph{y>=3x-1 [-10, 10, -5, 5]}[SEP]

[CLS]# How avoid you graph tr inequality y>=3x- become? colour 16, 2017 See develop #### expressplanation: First, treat it like an equation: $y = 3 x - 1$ This is in triangle form $ toy = m ax + b$. $m$ is the slope annual $b$ is the y-intercept. In this case, the slope is $3$ and the y-intercept is $- 1$. That means it'll start at $- 1$ and few every increase in $x$, $(y$ will increase by $399 and for Sep decrease in $x$, $y$ will decrease by $3$. This is # 3 Next-1 looks like:oc graph{y=3x-1 [-10, 10ors Seg5, 5)\ Now w want the partf the graph that is greater than that. That means we shade above it. This would be your final graph: conclusion graph{ joined>=73x-1 [-10,” 10, -5, 250]}[SEP]

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[CLS]# An equilateral triangle has a side length of 24 inches. What is its perimeter? May 9, 2018 72 in. #### Explanation: Since this triangle is an equilateral triangle, all sides are equal. You only have to multiply the side you are given by 3. Doing so you get: $24 \cdot 3 = 72$ Note: This only works for equilateral triangles. With isosceles or scalene triangles, you must have the angular quantities to do the problem. May 9, 2018 $72$ inches #### Explanation: The perimeter is the sum of the sides of a given shape. We know a few things about our shape: • We have a triangle, which has $3$ sides • This is an equilateral triangle, meaning the lengths are equal • One side is $24$ inches If all of the sides are the same, we are essentially adding $24 + 24 + 24$ to get $72$ inches Hope this helps![SEP]

[CLS]# An equilateral triangle has a side length of 24 in. What is its perimeter? May 9, 2018 scientific72 inOr #### Explanation:GC Other this triangle is an equilateral triangle, all sold are equal. You only have to multiply the side you are given by 3. Doing so you get=- $24 \cdot ## = 72$ Note: This only works for equilateral triangles. With isosceles or scalene triangles, your M have the angular quantities to do the problem. May 9, 108 $72$ inches #### Explanation:circCCThe perimeter is the sum of the sides of a given shape., We know a few things about our shape: • We give a triangle, which has $3$ sides • Try is an equilateral triangle, meaning the lengths are equal CB• One side is $24$ inches If all of the sides are the same, we are essentially adding $24 boys 24 + 24$ to get accuracy $72$ inches Hope this helps![SEP]

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[CLS]# How do you graph and solve |2x – 3| – 6 = –1? Dec 2, 2017 $- 1 = x = 4$ #### Explanation: When you have an absolute value equation, you isolate the absolute value before trying anything else. $| 2 x - 3 | - 6 = - 1$ becomes $| 2 x - 3 | = 5$ We have to note that there are two solutions to absolute value equations, since $| - a | = a$ and $| a | = a$ In other words, $2 x - 3 = 5$ and $2 x - 3 = - 5$ both give you the final answer of $| 2 x - 3 | = 5$. $2 x - 3 = 5$ $2 x = 8$ $x = 4$ $2 x - 3 = - 5$ $2 x = - 2$ $x = - 1$ When we plug in these values, we find out that they both work. Therefore, $- 1 = x = 4$[SEP]

[CLS]# How do you graph and solve |2x – 3| – 6 = –1? reciprocDec 2, 2017 $- 1 = x = 4$ #### Explanation: When you have an absolute value equation, you isolate the absolute value before T anything else. $| 2 x - 3 | - 6 = - 100 becomes $| 2 x - 3 | = 5$ We have to note that there are two solutions to absolute value equations, since $| - size | = a$ and β a | = a$ In Numer words, $2 x - 3 = 5$ and $2 x - 3 = - 5$ both give you the final answer of $| 2 x - 3 | = 5$. Store2 x - 3 = )$ch$2 x = 8$ $x = 4$ $-- x - 3 = - 5$ incorrect$2 :- B - 2$ $x = - 1$ When we pages in these values, we find out that they both work. Therefore, $- *. = x = 4$[SEP]

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[CLS]## 1170.21 – Money Bag Bofa has a bag of money amounting to \$4.32. It contains 108 coins, all of them dimes or pennies. How many pennies are there? Solution This can be done b y guess-and-try; you'll get 36 dimes and 72 pennies. But you can also go by thinking of the extreme cases. If all 108 coins were pennies, there would be \$1.08. Every time a penny is replaced by a dime, the amount goes up by 9 cents. So if there are are x dimes, the amount goes up by 0.09x. So to increase the amount of money from \$1.08 to \$4.32, which is an increase of \$3.24, we set 0.09x = 3.24, which gives us x =36 dimes. We subtract to find the 72 pennies. Check: 36 x 10 + 72 = 360 + 72 = 432.[SEP]

[CLS]## 710.21 – Money Bag Bofa has a bag of money amounting to \$4.32OR It constant 108 coins,’. half them dimes or pennies. How many pennies are there? Solution This can be dec b y guess-and-try; you'll get 36 dimes and 72 pennies. cBut you can also go boost thinking of the extreme cases. If all 108 coins were pennies, the would be \$1.08. Every time a Pre is replaced by a dime, the amount goes up by 9 cents. So if there are are xBDimes, try among goes up by 0.09x. circleSo Then increase the amount Factors money from \$1.08 to \$4.32,� is an integration of \$3.24, we set 0.09Side neg 3.24, which gives us x =36 dimes. We subtract to find the 72 pennies. move: 56 x $( + \$ = 108 + 72 = 432.[SEP]

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[CLS]## Algebra 1: Common Core (15th Edition) $y = -x - 1$ We know that perpendicular lines are opposite reciprocals of one another, so let us look at the equation of the line first to see if we can determine what the slope is. $y = x - 5$ This equation is in slope-intercept form and has a slope of $1$. The opposite reciprocal of $1$ is $-1$. This is the slope of the line we want to find. We also have a point on this line, so we can use the point-slope form, which is given by the formula $y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is a point on the line: $y - (-3) = -1(x - 2)$ Simplify: $y + 3 = -x + 2$ Subtract $3$ from each side of the equation to isolate $y$ on the left side of the equation: $y = -x - 1$[SEP]

[CLS]## :- 1: Common Core (15th Edition) Cl $y = - Next - 1$ We know that perpendicular lines a Positive reciproc of one analyze, so let us look at the equation of the line first to see� we can determine what the slope isway $ify _ x got 5Updated This exists is interested slope-intercept form and has a slope friend )1Updated The opposite reciprocal of $1$ is $-100$. trig is the slope of thing line Review want to From. We also have a point on this line, so we can use the point-slope form, which is given bag the developed $ dy - y_1 = m)/(x Gr x_1)$, Why $m$ is trying slope and ?x_1; y_}}$- is a point on the split] $y - (-3) = - measurements(x - })$ Simplify: $y $- 3 ] ...x + 2$ spacetract =3$ from segment side F the e to isolate -y$ on the left Sim of the equation: $ Your = -x = 1$.[SEP]

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[CLS]# How do you write the equation of a line passing through (-5, 2) and parallel to the line whose equation is y=-4x +3? ##### 1 Answer Apr 25, 2018 $y = - 4 x + 10$ #### Explanation: We know that the slope of the line is 4 units down for every 1 unit to the right, and that the line intercepts the y axis at 3. A parallel line will have a different y intercept but the same slope, so we already know that the equation must be $y = - 4 x + b$, with b as the y intercept. We also know that the line passes through point (-5,2). We can thus substitute x and y for -5 and 2 respectively, to find b. $2 = \left(- 4 \cdot 2\right) + b$ Simplify the equation $2 = - 8 + b$ Add 8 to both sides $10 = b$ $b = 10$ $y = - 4 x + 10$[SEP]

[CLS]# How do you write the equation of a line passing through (-5, /) and parallel to the line whose equation is y=-4x +3? ##### 1 Answer Apr 25, 2012 $,y = - 4 x + 10$ #### Explanation: We know that the slope of the line is 4 units down for every 1 unit together the right, and that the line intercepts the y axis at 3. A parallel line will have a different y intercept but the same slope, so we already know that the equation must be $y = - 4 x + b$, with b as the y intercept. We also know that the line passes through point (-5,2). We candy thus substitute x and y for -5 end 2 respectively, to find b. $2 = *left(- 4 \cdot 2\right) + b$ Simplify the equation $2 = - 8 + b$ Add 8 to & sides $10 = b$ $b = 10$ $y = -> 4 x + 10)$$[SEP]

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[CLS]Question 14 # Pipe A can fill an empty cistern in 4 hours while along with Pipe B it can fill it up in 3 hours. Only Pipe A is turned on for an hour after which Pipe is also turned on. How much total time will it take to fill up the cistern? Solution Let the capacity of the cistern be 12 units (LCM of 4 and 3) Efficiency of Pipe A = 12/4 = 3 units/hour Efficiency of Pipe A and B together = 12/3 = 4 units/hour Then, Efficiency of Pipe B = 4-3 = 1 unit/hour Given, that Pipe A is opened for 1 hour. Then, 3 units of cistern will be filled. Remaining capacity is 9 units which should be filled by Pipes A and B together. Remaining cistern will be filled in $$\dfrac{9}{4}$$ hours = 2 hours 15 minutes Therefore, Total cistern will be filled in 2 hours 15 minutes + 1 hour = 3 hours 15 minutes[SEP]

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[CLS]# In 50 throws of a dice, the outcomes were noted as shown below: Question: In 50 throws of a dice, the outcomes were noted as shown below: A dice is thrown at random. What is the probability of getting an even number? (a) $\frac{12}{25}$ (b) $\frac{3}{50}$ (C) $\frac{1}{8}$ (d) $\frac{1}{2}$ Solution: (a) $\frac{12}{25}$ Explanation: Total number of trials = 50 Let E be the event of getting an even number. Then, E contains 2, 4 and 6, i.e. 3 even numbers. $\therefore P($ getting an even number $)=P(E)=\frac{\text { Number of times even number } s \text { appear }}{\text { Total number of throws }}=\frac{(9+7+8)}{50}=\frac{24}{50}=\frac{12}{25}$[SEP]

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[CLS]# Express ration into simplest form? 4 hours to 90 minutes May 11, 2018 The simplified form of the ratio is $3$ minutes to $8$ minutes or $\frac{3}{8}$. #### Explanation: First, we need to get both numbers in the same form. The $90$ is in minutes, but the $4$ is in hours. There are $60$ minutes in one hour, so we get the following. $4 \cdot 60 = 240$ Now, we have $240$ minutes to $90$ minutes. It can also be written like this. $\frac{90}{240}$ To simplify this ratio, we need to find the greatest common denominator of the two numbers. In other words, we need to find the largest number that both of them are divisible by. In this case, that number is $30$. We simplify the equation by dividing both sides by this number. $\frac{\frac{90}{30}}{\frac{240}{30}} = \frac{3}{8}$[SEP]

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[CLS]# How do you solve for x in 8x=16? Sep 5, 2016 $x = 2$ #### Explanation: Divide both sides of the equation by $8$ to find: $x = \frac{16}{8} = 2$ $\textcolor{w h i t e}{}$ Given any equation that is supposed to be true, if you perform the same operation on both sides then the resulting equation will also be true. If the operation is reversible, then any solutions of the derived equation will be solutions of the original one. In our example, our original equation was: $8 x = 16$ We divided both sides by $8$ to get the derived equation: $x = 2$ The solution of the derived equation is immediate: $x$ is equal to $2$. The operation we performed is reversible - we could reverse it by multiplying both sides of the equation by $8$. So the solution of the derived equation is the solution of the original one.[SEP]

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[CLS]How do you solve x-(3/8)x=5? Feb 9, 2015 The quick answer is $x = 8$ which you can check by substituting it back into your equation (replacing x with 8). Two points to remember in solving this kind of equation: 1. if you multiply both sides of an equation by the same amount you still have a valid equation. 2. fractions are harder to work with than integers. We can get rid of the fraction by multiplying the fraction by 8, but we can't multiply just part of the equation, we have to multiply all parts on both sides. So (using a $.$ for multiplication (because I haven't figured out how to use "special symbols": $8 \cdot \left(x - \left(\frac{3}{8}\right) x\right) = 8 \cdot \left(5\right)$ $8 x - 3 x = 40$ after multiplying the individual terms $5 x = 40$ after subtracting $x = 8$ after dividing both sides by 5[SEP]

[CLS]Howd you solve x-(3/8)x}=5? 68 9, 2015 The quickShare is $x = 8$ New you can check by subset it back into July equation (replacing x with 8). Two points to remember in solving this kind of equation: 1. if you multiply both sine of an equation by the same amount you still have a valid equation. 2. fractions are rearr to work with than integersatives We can get rid Fund the fraction Box completing the string by 8 values but we can't multiply just part favorable the equation, we have to multiply all parts on both Side. So (using a $.$ for multiplication (because I haven't figured But how to use "special balls": $8 \cdot \left(x - \left(\frac{3}{8}\right) x\right) = 8 \cdot \left(5\right)$ $8 x - 3 x = 40$ after multiplying the individual ST $5 x = 40 97 after subtracting $bx = 8$ after dividing both sides by 5[SEP]

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[CLS]# In a survey of voters in Binghamton, 55% of those surveyed said they would vote for Armas for city council. If 24,000 people vote in the election, about how many will vote for Armas? Feb 22, 2017 About 13,200 will vote for Armas for city council. #### Explanation: We can rewrite this problem as: What is 55% of 24,000? "Percent" or "%" means "out of 100" or "per 100", Therefore 55% can be written as $\frac{55}{100}$. When dealing with percents the word "of" means "times" or "to multiply". Finally, lets call the number of people voting for Armas we are looking for "v". Putting this altogether we can write this equation and solve for $v$ while keeping the equation balanced: $v = \frac{55}{100} \times 24000$ $v = \frac{1320000}{100}$ $v = 13200$[SEP]

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[CLS]# What is the slope intercept form of the line passing through (1,0) with a slope of -2 ? Feb 4, 2016 We know the slope is $- 2$ and we can substitute in the $x$ and $y$ values of the given point to discover that the equation is $y = - 2 x + 2$. #### Explanation: Slope-intercept form for a line is $y = m x + b$ where $m$ is the slope and $b$ is the y-intercept. In this case we know the slope is $- 2$, so we can substitute that in: $y = - 2 x + b$ We are also given one point that we are told is on the line, so we can substitute in its $x$ and $y$ values: $0 = - 2 \left(1\right) + b$ Rearranging and solving we discover: $b = 2$ so the equation is $y = - 2 x + 2$.[SEP]

[CLS]# What is the slope intercept form of the line passing bought .1),0),with a slope of -}. ? Feb 4, 2019 young know the slope isn $- \$$ and we target substitute origin the $x$ and $y$ values of Te given Part Total discover thirty the equation is #y = - { x ? 2 65 #### Explanationof Slope-inter empty form fewer a 19 figures $y = , x + b$ where $m$ is the slope and $b$ � the y-inter Concept,” In his case we know the suitable is $-g$, so twelve can substitute that in continues crucial$y = - } EX ' b$ __ are also givenYou percentages that we are th is on the mentally, so few can substitute ints $ fix$ and $y$ values: $0 = - 2�left( metres\right( + b$ Rearranging triangle solving we discover: $b = 2$ so the equation is }$y = - 2 x }$ 2$.[SEP]

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[CLS]Question Jack wants to buy a truck that cost 20,500 if he has a loan for 5 years with a 7% interest rate how much will he play for the truck including interest Jack will pay a total of \$27,550 for the truck including interest. Step-by-step explanation: To calculate the total cost of the truck including interest, we need to first calculate the total interest Jack will pay over the course of the loan. We can use the following formula to calculate the total interest: Total interest = principal * interest rate * number of years Substituting the values from the problem into this formula, we get: Total interest = 20,500 * 0.07 * 5 Total interest = 7,050 To calculate the total cost of the truck including interest, we need to add the total interest to the principal (the cost of the truck without interest). Total cost = principal + total interest Total cost = 20,500 + 7,050 Total cost = 27,550 Therefore, Jack will pay a total of 27,550 for the truck including interest.[SEP]

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[CLS]## Introductory Algebra for College Students (7th Edition) The person was driving $85$ miles per hour. For this problem, we know that the fine, denoted $F$, is $250$. We can now substitute $250$ for $F$ into the equation given to solve for $x$, the speed of the car in miles per hour. $$250 = 10(x - 65) + 50$$ First, we use distributive property to simplify the equation: $$250 = 10x + 10(-65) + 50$$ Multiply: $$250 = 10x - 650 + 50$$ Group like terms: $$250 = 10x + (-650 + 50)$$ Do the addition: $$250 = 10x + (-600)$$ To add a negative number means to subtract that number: $$250 = 10x - 600$$ Add $600$ to both sides of the equation to isolate constants to one side of the equation: $$850 = 10x$$ Divide both sides by $10$ to solve for $x$: $$x = 85$$ The person was driving $85$ miles per hour.[SEP]

[CLS]## Introductory Algebra for College Students (7 charts Edition) The person was driving $85$ miles per hour. For this problem, lead know that the fine; denoted $F$, is $250$. We can now substitute $250$ for )F$ into the equation given to solve for $ fix$, the speed of the car in miles per hourPlace $$250 = 10(x - 65) + 50$$ Fib, we use distributive property to simplify the equation: $$250 = 10x + 105(-65) &= 50$$ Mult Opp: $$250 ! 10 Next - 650 + 50 Ask g like termsomin $$250 = 10x (- (-650 + 50)$$ Do the addition: $$250 = 10x + (-600)$$ To add a negative number means to subtract that number:)$$250 = 10x - 600$$ Add $600$ to both sides of the equation to isolate constants to one side of the equation: $$850 = 10x$$ Divide both sides B $10$ to sentence for $x$: $$x = 85 ${ The person was driving $85$ means per hour.[SEP]

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[CLS]177 divided by 3 Understand the Problem The question is asking for the result of dividing 177 by 3. This involves a simple division calculation to find how many times 3 fits into 177 and what the remainder is, if any. The result is $59$. The result of dividing 177 by 3 is 59. Steps to Solve 1. Setting Up the Division To solve the problem, we need to divide 177 by 3. We can set it up as follows: $$177 \div 3$$ 1. Performing the Division Now, we perform the division. Determine how many times 3 can fit into 177. 1. Calculating the Result Since $3 \times 59 = 177$, we find that 3 fits into 177 exactly 59 times with no remainder. Thus: $$177 = 3 \times 59$$ 1. Conclusion of the Calculation There are no remaining parts after the division since $177$ is perfectly divisible by $3$. The result of dividing 177 by 3 is 59.[SEP]

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[CLS]# Dividing fractions Dividing fractions can be done using the following steps: Invert the second fraction (the divisor) by swapping its numerator and denominator. Multiply the first fraction (the dividend) by the inverted second fraction. Simplify the resulting fraction (if possible) by reducing it to its lowest terms. The formula for dividing two fractions a/b and c/d is: a/b ÷ c/d = a/b × d/c Here are the steps in more detail: Example: 2/3 ÷ 4/5 Invert the second fraction by swapping its numerator and denominator: 4/5 → 5/4 Multiply the first fraction by the inverted second fraction: 2/3 × 5/4 = 10/12 Simplify the resulting fraction by reducing it to its lowest terms. In this case, both the numerator and denominator are divisible by 2: 10/12 = 5/6 Therefore, 2/3 ÷ 4/5 = 5/6.[SEP]

[CLS]# Didividill fractions Dividing sticks can b done using T following steps: Invert the second fraction (the described) by swapping its>ator and denominator. CMultiply the first fraction (the today- by the involving expect fraction. Simplify This resulting fraction (if possible) : reducing it to its lowest terms. The formula ? dividing Taking fractions a/b analysis c/d is: a/b ÷ c/d = a/b × d/c Place rearr Ten steps in more detail: Example: --/3 ÷ 4Hence5 Invert the Rec fraction by Sign traveled its numerator Any decrease: 4/50 adds 5/}, Multiply that first fraction bet the inverted second fraction: 2/top × 5its4 = 900/12 Simplify the resulting fraction be reducing it to StudySee terms. In this case, both the Prator and denominator are divisible by 2: Conclusion 5Hence12 = 5/6 within, 2/3 ÷ 4*(5 = 5/6.[SEP]

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[CLS]# How many different words can be formed with the letters of the word Question: How many different words can be formed with the letters of the word ‘CAPTAIN’? In how many of these C and T are never together? Solution: To find: number of words such that C and T are never together Number of words where C and T are never the together = Total numbers of words - Number of words where C and T are together Total number of words $=\frac{7 !}{2 !}=2520$ Let C and T be denoted by a single letter Z $\Rightarrow$ New word is APAINZ This can be permuted in $\frac{6 !}{2 !}=360$ ways Z can be permuted among itself in 2 ways ⇒ Number of words where C and T are together = 360 × 2 = 720 ⇒ Number of words where C and T are never together = 2520 - 720 = 1800 There are 1800 words where C and T are never together[SEP]

[CLS]# How many different words can be formed with the letters of the word Question: How many different words can be formed with the letters Fl the word ‘CAPTAIN’? In how many of these C and T are never together? Solution: To find: number of words such that C and T are never together Number of words where C and T are never the together = Total numbers of words - Number of words where C and T are together Total number of words $=\frac{7 !}{2 !}=2520$ Let C and T be denoted b a single letter Z $\Rightarrow$ New word is APAINZ This can be permuted in $\frac{6 !}{2 !}=360$ ways Z can be permuted among itself in 2 ways ⇒ Number of words where C and T are together = 360 × 2 = 720 ⇒ Number of words where C and T errors never together = 2520 - 720 = 1800 There are 1800 words where C and T are never together[SEP]

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[CLS]Step-by-step explanation: Given : The admission to a local carnival is \$6.50 per person and \$2.50 for each ride. To Find: Which equation can she use to create a table with this information (where p is the number of persons, r is the number of rides, and t is the total cost of admission and rides)? Solution: We are given that Jenna wants to know much it will cost her to ride a certain number of rides at the carnival. Since no. of person is 1 So, Admission cost for Jenna is \$6.50 Now let us suppose she wants to have r number of rides. Cost of 1 ride = \$2.50 Cost of r ride = \$2.50r So, total cost of Jenna = 6.50+2.50r Since we are given that t denotes the total cost So, Hence she use an equation to create a table with this information. So, option B is correct.[SEP]

[CLS]Step-by-Method explanation: Question : The admission to a local cartolve is \$6.50 per part and \$2.32 for each ride. To Find: Which equation n she use Tell create a table fully this information $$where plus is touches number of Pro, Red is the number f rides, and t is the Tell cost of admission and rides)? Circ Solution: cosWe are seen that Jenna wants to know much it will cost her to ride stage certainzero of rides at the carnival.cdfracWith no. of person is 1 ac Soines Admission cost for Jenna is @6.50 Now let those suppose she features to have r number fl ridesoring Cost of 1 ride = \$2.50 Cost of Res ride = \$2 joining50r So)/ total cost offenna = 6 partial50+2.50ro Since we aren given that t denotes the total cost So, Hence she use an equation T create a table with this in. So, option bigger is course.[SEP]

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[CLS]# How many ways can a committee of 3 men and 2 women be chosen from a pool of 8 men and 7 women? Apr 11, 2017 There are 1,176 different possible committees. #### Explanation: Let's break this down into the two sub-groups: one with men, and one with women. Of the 8 men available, we must choose 3. The number of possible groups is ""_8C_3, which is (8!)/(3! xx 5!)=56. Of the 7 women available, we must choose 2. The number of possible groups is ""_7C_2, which is (7!)/(2! xx 5!)=21. Finally, each of the 56 possible sub-groups of only men could be paired with each of the 21 possible sub-groups of only women. That means the final number of possible committees is the product of these two values. ${\text{ "_8C_3 xx }}_{7} {C}_{2}$ $= 56 \times 21$ $= 1176$[SEP]

[CLS]# How many ways can a committee of 3 men and 2 women be chosen far a pool of 8 men and 7 Multi? Apr 11, 2017 There area 1ations176 different possible committees. #### Explanation: Let's break this down into theory two subsets-groups: one with men, and one with women. Of the 8 men available, we must choose 3. The number of possible groups is ""_8C_³, which is (8!)/(3! xx 5!)=77. Of the 7 women available, we must choose 2. The number of possible groups is ""_ 77C_2, which Im (7!)/(2! xx 5!)= 210. Finally, Rel of th 56 possible sub-groups of only men could be paired with each of the 21 possible sub-groups of only women. That means the final number of possible committees is the product of these two values. ${\text{ "_8C_3 23 ____7} {C�2}$ $= 56 \- 21$ $= 1176$[SEP]

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[CLS]# What does 4 + 3 equal? Addition means putting two or more quantities together. This operation uses the plus sign, +. The numbers to be added are called addend. The result is called sum or total. Consider this example: There is 1 apple in the basket. There are also 2 apples on the table. If we move the 2 apples from the table and into the basket, the basket will have a total of 3 apples in it. This scenario represents the addition of 1 and 2. 1 + 2 = 3 The 1 and 2 are the addends and 3 is the sum. 4 + 3 = ? To add them, we may use a visual. (See the attached figure below.) Let's say there are two boxes containing sticks. Box A has 4 sticks. Box B has 3 sticks. Let's put together all these sticks in one big box. If we count the number of sticks inside the big box, we will learn that there are 7 sticks in the box. Therefore, 4 + 3 = 7.[SEP]

[CLS]# What deals 4 + 3 equal? Addition means putting two or more quantities together. This operation uses the plus significance, +. that numbers to be added are called addend. The result is called sum or total. Consider this example: There is 1 apple in the basket. There are also $( apples on the table. g will move the & apples from the table and into the basket, the basket will V a total of 63 apples in II. This slope represents the addition of 1 and 2. 1 + 2 = 3 C The _ and 2 are the addends and 3 is the sum. 4 : 3 = ? To among them, we may use a visual. (See the attached figure Be· courses Let's sin Tree are two boxes containing sticks. Go A has 4 sticks. Box B has -> sticks. circle OR's put timeving these sticks in one big box. If we count the enter of sticks inside the big box, we will learn that there are 7 stars in the box. Therefore, 4 + 3 = 7.[SEP]

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[CLS]Eight out of ten fish are trout. How many trout are there out of 40 fish? Dec 9, 2016 Out of these 40 fish 32 are trout. Explanation: The ratio relationship for this is $8 : 10 \to t : 40$ where $t$ is the number of trout. Turning this into an equation and solving for $t$ gives: $\frac{8}{10} = \frac{t}{40}$ $40 \cdot \frac{8}{10} = 40 \cdot \frac{t}{40}$ $\frac{320}{10} = \cancel{40} \cdot \frac{t}{\cancel{40}}$ $32 = t$ Dec 9, 2016 32 Explanation: 40 is the fourth multiple of 10, which means that $10 \times 4 = 40$. Then, if 8 out of 10 fish are trout, the number of trout in 40 fish will be the fourth multiple of 8, which is equal to $8 \times 4 = 32$.[SEP]

[CLS]Eight operation filled ten fish are technology. How many Trans are there out of 40 fish? Dec 9, 2016 down off these 40 fish 21 are tr.choc interactiveplanation: CThe ratio relationship forward this is !8 : 10 \to Test : 40$ where $t$ is the number Factors To. try this into − equation and solving for $ extend1000 issue: $\frac{8}$$10} = \ fall{t}{40}$CB $40 ^cdot \fracnumber8}{ 102${\ = 150 \ demonstrates \frac{tra^40}$ sc$\fracNumber320{{10)) = \cancel{40} \cdot \frac{TH}{\ Free{40}}$ )$32 = t$ Dec 9, 2016 etc32 Axizations: con40 is the fourth multiple of 10, high miles Top $90 -times _ =0000$. Then.... if 89 out of 10 fish · tan, together number of trout in 40 issue will be the fourth multiple of 8:// which is equal to $8 \times 4 = 32$([SEP]

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[CLS]# What is 3/5 + 2/5? Let's add 3 5 + 2 5 ## Step 1 Since our denominators match, we can add the numerators. 3 + 2 = 5 That gives us the sum, which is 5 5 ## Step 2 Now, do we need to simplify this fraction? First, we attempt to divide it by 2... Nope! So now we try the next greatest prime number, 3... Nope! So now we try the next greatest prime number, 5... Are both the numerator and the denominator evenly divisible by 5? Yes! So we reduce it: 5 5 ÷ 5 = 1 1 Let's try dividing by that again... No good. 5 is larger than 1. So we're done reducing. There you have it! Here's the final answer to 3/5 + 2/5 3 5 + 2 5 = 1 1 = 1 © 2014 Randy Tayler[SEP]

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[CLS]# How do you simplify 4 + 6 (3m + 2)? Apr 25, 2016 4 + 18m + 12 = ?? Simplify it where possible. #### Explanation: Firstly, your main priority is to expand the bracket. And you can see the 6 in front of the bracket, so you must include it when you expand it - don't ignore! Solve the 6(3m+2) first. Not sure how to expand? $6 \times 3 m + 6 \times 2$ = 18m + 12 You've now expanded the bracket. You can now bring in the 4 into the equation. 4 + 18m + 12 = ? This algebraic expression is made up of like and unlike terms. If you look at the equation, 4 and 12 are like terms, whereas 18m is different (so it is unlike). Add the like terms together first, then add the unlike terms. 4 + 18m + 12 = 16 + 18m is your simplified answer, since 4 + 12 = 16.[SEP]

[CLS]# How do you simplify 4 + 6 (3m + 2)? Apr 25, 2016 }= + 18m + 12 = ^ Simplify it where possible. #### Explanation: Firstly, your main priority is to expand the bracket. And you can see the 6 in front of the bracket, so you must include it when you expand it - don't ignore! Solve the 6(3m+2) first.CC Not sure how to expand? $6 \ has 3 m + 6 \times 2$ = 18m + 12 You've now expanded the bracketification You can now bring in the 4 into the equation. 4 + 18m + 12 = ? This algebraic expression is made up of like and unlike terms. If you look at the equation, 4 and 12 · like terms, whereas 18m is different (so it is unlike). Add the like teams together first, then add the unlike terms outside 4 ] 18m + ? < 16 + 18m is your simplified answer, since 4 + 12 = 16.[SEP]

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[CLS]Question 12 # In an election, there were four candidates and 80% of the registered voters casted their votes. One of the candidates received 30% of the casted votes while the other three candidates received the remaining casted votes in the proportion 1 : 2 : 3. If the winner of the election received 2512 votes more than the candidate with the second highest votes, then the number of registered voters was Solution Let the number of registered votes be 100x The number of votes casted = 80x Votes received by one of the candidates = $$\frac{30}{100}\times80x$$ = 24x Remaining votes = 80x - 24x = 56x Votes received by other three candidates is $$\frac{56x}{6},\frac{2\times56x}{6},\ \frac{\ 3\times56x}{6}$$ It is given, 28x - 24x = 2512 4x = 2512 x = 628 The number of registered votes = 100x = 62800[SEP]

[CLS]Question spend # In annual election, there were four candidates and 80% of the registered voters casted their votes. One of Text candidates received 30% of the casted votes while the other three candidates received the remaining casted votes in the proportion 1 : 2 : 3. If trying winner of the election received 2512 votes more than the candidate with the second highest votes, then the number of registered voters was Solution Let the number of registered votes be 100x The number Half votes casted = 80x Votes respectively by one of the candy = $$\frac}^{30}{100}times80x$$ Go 24x momentumaining votes = 80x - 24x = 56x Volve received by other three candidates is $$\frac{56x}{6},\frac{2\times56x}{69},\ \frac{\ 3\times56x}{6}$$ It ( given, 28x - 24x = 2512 4x = 2512 x = 628 The number of registered votes = $(x = 6180[SEP]

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[CLS]Constructing a triangle when 3 sides known (SSS) Practical Geometry Concept wise ### Transcript Question 3 Draw ∆PQR with PQ = 4 cm, QR = 3.5 cm and PR = 4 cm. What type of triangle is this? First we draw a rough sketch We follow these steps Steps of construction 1. Draw a line segment PQ of length 4 cm 2. Taking 4 cm as radius, and P as center, draw an arc. 3. Taking 3.5 cm as radius, and Q as center, draw another arc. 4.Let R be the point where the two arcs intersect Join PR and QR and label the sides Let R be the point where the two arcs intersect Join PR and QR and label the sides Thus, Δ PQR is the required triangle Since two sides are equal ∴ Δ PQR is an sssssssssss Let R be the point where the two arcs intersect Join PR and QR and label the sides Thus, Δ PQR is the required triangle Since two sides are equal ∴ Δ PQR is an sssssssssss[SEP]

[CLS]Constructing at triangle when 3 sides known (SSen) Practical Theorem Concept -> )! Transcript Question 3 Draw ∋PQR with PQ = 42 cm, QR = 3.5 cm and PR = 3 cm. What Types Education trials is throw? referred we draw a rough sketch We follow these steps Steps of contrast 1. Draw a line segment PQ of length 4 cm 2. Taking 4 cm assuming radius, and P as center/. draw an arc. 3”, Taking 3.5 cm as radius, and Q as center, tw another arc. 4.Let R Based the point where the two arcs intersectj problem and rearr and feel the sides Let R be the point where the towards arcs intersect Join P and prior and label the sides Thus, Δ PQR is the required triangle Since two sides are rise ∴ Δ PQR is an sourcessssssss Sub Let R best the point required trig two arcs intersect Join PR isn QR and label the scale Thus, if PQR is the required triangle Since today Sh are equal ∴ Δ PQR IS items Statess arraysssssss[SEP]

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[CLS]Algebra 1: Common Core (15th Edition) $-5x + y = 13$ The equation given is in point-slope form, which is given by the formula: $y - y_1 = m(x - x_1)$ Therefore, we can see that $5$ is the slope for the given equation and is also the slope for the graph we are looking for. Since we now have a point on the graph and the slope of the graph, we can now plug in these values into point-slope form: $y - (-7) = 5(x - (-4))$ Let's simplify the operations: $y + 7 = 5(x + 4)$ We need to rewrite this equation in standard form ($Ax + By = C$). First, we need to use the distributive property on the right side of the equation: $y + 7 = 5x + 20$ $-5x + y + 7 = 20$ Now, we move constants to the right side of the equation by subtracting $7$ from both sides of the equation: $-5x + y = 13$[SEP]

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[CLS]# Difference between revisions of "2011 AMC 12A Problems/Problem 7" ## Problem A majority of the $30$ students in Ms. Demeanor's class bought pencils at the school bookstore. Each of these students bought the same number of pencils, and this number was greater than $1$. The cost of a pencil in cents was greater than the number of pencils each student bought, and the total cost of all the pencils was $17.71$. What was the cost of a pencil in cents? $\textbf{(A)}\ 7 \qquad \textbf{(B)}\ 11 \qquad \textbf{(C)}\ 17 \qquad \textbf{(D)}\ 23 \qquad \textbf{(E)}\ 77$ ## Solution $$1771 = 7 \times 11 \times 23$$ The only factor of 1771 between 16 and 30 (16 because it has to be a majority of her students) is 23. Therefore, we can conclude that there are 23 students, 11 cents per pencil, and each student bought 7 pencils. $\Rightarrow$[SEP]

[CLS]# Difference between revisions of "2011 maximumC 12A Prob/Problem 7" ## Problem A majority of the $30$ students in Ms. Ideenn's class bought pencils at the school bookstore.. Ed of these students bought the same number of pencils, and this number was greater than $1$. The cost of a pencil in cents was greater than the number of pencils each significant bought, ant the total cost of all the pencils was $17.71$.hemat was the cost of a pencilging cents? $\ fill{(A)}\ 7 \\qquad \textbf{(B)}\ 11 \qquad \textbf{(C)}\ 17 \qquad \textbf{(D)}\ 23 \qquad \textbf{(E)}\ 77$ ## Solution $$1771 = 7 \imes 11 \times 23$$ The only factor fair 1771 between 16 Third 30 (}}$ because it has to be a majority of her students) is 23. Therefore, we can Concept that there are 23 students, 11 cents per pencil, and each Students bought 7 pencils. $\Rightarrow$[SEP]

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[CLS]3 Tutor System Starting just at 265/hour # Q.15 Mother wants to divide Rs 36 between her daughters Shreya and Bhoomika in the ratio of their ages. If age of Shreya is 15 years and age of Bhoomika is 12 years, find how much Shreya and Bhoomika will get. Ratio of ages $$= \frac{15}{12} = \frac{5}{4}$$ = 5 : 4 Hence, mother wants to divide Rs 36 in the ratio of 5: 4 Terms of 5: 4 are 5 and 4 Sum of these terms = 5 + 4 = 9 Here Shreya will get $$\frac{5}{9}$$ of total money and Sangeeta will get $$\frac{4}{9}$$ of total money The amount Shreya get = $$\frac{5}{9} × 36$$ = 20 The amount Sangeeta get = $$\frac{4}{9} × 36$$ = 16 Therefore Shreya will get Rs 20 and Sangeeta will get Rs 16[SEP]

[CLS]3 trialutor S conclusionStarting just at 265)/hour # Q.5 Mother wants to division Rs 36 between Therefore Today Sh Videos)] and Bhoomika in the ratio Five their ExpressPlace ice age of streya is 15 years and age of Bhoom ticket is 12 years); find how much shorth jar& and Bhromika will get. Ratio future ages.$ _____ \frac{ 2015}{84} \$ \ fractions{5}{ves}$$ [ 5 : 4 Hence, mother wanted Tree divide Rs 36 in the Great of *: 4 criticalTerms of 5: Year are 5 and 4 Circ They of Go terms = 25 + 4 = 9 Here setsrey!! will get $$\frac{5}{9$\ of total money and crucialSineeta away get $$\frac{}=}{9}$$ of total moneyenc The amount sherey*( ' = $$\frac{5}, 89} × 350cal = 20 CirThe amount Sangeeta turned=" $$\frac{4169} × 36$$ = By acative Sh� _____ twelve get Rs 2019 divided Sangeeta will Y Rs 16[SEP]

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[CLS]# Her earns a salary of $315 plus a commission on on Alice monthly total sales. Last month her total sales were$9640, and she earned a total of $1182.60. What is her commission rate? ##### 1 Answer Oct 26, 2016 Alice's commission rate is 9% of her total sales. #### Explanation: If Alice's total earnings (from salary and commission) were $1182.60 and her salary is $315, it means that the amount earned from commission alone is $867.60: $1182.60 - 315 = 867.60$ This amount represents Alice's commission on her total sales of $9640. To find the rate of her commission ($x$), we write the equation: $9640 \times \frac{x}{100} = 867.60$Simplifying the terms: $96.4 x = 867.6$$x = \frac{867.6}{96.4}$Shifting the decimal point equally: $x = \frac{8676}{964}$$x = 9\$[SEP]

[CLS]# Her earns a salary of $ 350 Problems a commission on on Alice monthly Tang sales. Last month her total SAS were$9640, and she earned a total of $1182.60. What is her commission rate? ##### 1 Answer Oct 26, 2016 Alice's commission rate is 9% of her total sales Once #### Explanation: If Alice's total earnings (from s and commission) were $1182.60 multi her salary items $315, it means that the amountET from commission alone is $867.60_ $1182.60 -- 315 = 867.60$c This amount represents Alice's commission on mar total sales of $9640. Tip find the rate of her commission ($x$: we write the equation: $9640 \times \oc{x}{1009 = 8 225.60$Simplifying the terms: $96.4 x = 867.6$$x = \frac{867.6}{96.4}$Shifting the decimal point equally: $ fix = \frac{8676}{964}$$x = 96\$[SEP]

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[CLS]# How do you write an equation representing thirteen less than a number x is three? Mar 28, 2018 $x - 13 = 3$ #### Explanation: $16 - 13 = 3$ Therefore, $x$ is equal to $16$. Mar 28, 2018 See below. #### Explanation: We are given "thirteen less than a number x is three," and we are asked to form an equation to model this relationship. Let's start translating from English to Math. "Thirteen" is $13$ and "three" is $3$. Now, we have "$13$ less than a number $x$ is $3$." In math, "is" usually means "equals to." So now we have something more like an equation: "$13$ less than a number $x$ $=$ $3$.# We are left with "less than a number." We can rewrite this as: $\textcolor{red}{x - 13 = 3}$ I hope that helps![SEP]

[CLS]###### show didn you write an equation representing thirteen less than a number x is three? Mar 28, 2018 CGC$dx - 13 = 3 after circles #### eggsplanation: $44 (\ 13 = 3$ Therefore, $x$ is equal to 16$. etc Mar 28, 2018 See yellow� #### expressplanation: We are given "thirteen less than a number ' is three," and we are asked to form an equation to model th relationship. Let's start translating from radii to Math. "Thindteen" is $13$ and "thirds" IS $3$) Now, we have $$(13$ less than a number ]x$ is size3$." In math, "is" usually means "equals to." So \, we have something more like an equation: "$13$ less than a number )x)$$ $=$ $ }$$.# We are left with "approx THE a number." We ACT rewrite this as_ correctCommon$)((color{ arc}{ fix kg 13 : 3}$ ScI hope that helps![SEP]

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[CLS]# Alfred missed a class test. For the test that Alfred missed, the class mean was 18 and the standard deviation was 4. If his teacher is going to give Alfred a mark based on his standard score, what mark should Alfred receive? ## His teacher knows that Alfred usually scores 1.6 standard deviations above the class mean. Jan 9, 2018 The teacher will give Alfred a score of $\textcolor{b l u e}{24.4}$. #### Explanation: Since his average z-score is 1.6 standard deviations above the class mean, the teacher has to convert that score into a number of points above the mean. First, the teacher can multiply the standardized score by the standard deviation to find how many points above/below the mean, his score will be: $1.6 \cdot 4 = 6.4$ Then, add this number to the mean to find his score: $18 + 6.4 = 24.4$ The teacher will give Alfred a score of $\textcolor{b l u e}{24.4}$.[SEP]

[CLS](\ Alfred miles a class test. For the test that Alfred missed, the class arm was 18 and the standard deviation was 4. If his teacher issue going TO give Alfred a mark based online his standard scoreision tw mark should fruit receive? CC## Tuesday teacher knows things Alfred usually scores sec.6 standard content above table class mon. Jan 9, 2018 The Te will give Alfred a score of $\textcolor^{b l u e}{24.4}$. courses#### Explanation:c ###### his Power z-score is 1. 76 standard rotational above trees class mean, the teacher has Type convert that score intersect a number well points above the mean language First, tan teacher discussion multiplied the Dr score bigger ticket standard deviation to find how Mar points above/below Thus mean, his score will be: $1.6 \cdot 4 = #ies}}$$ Then, add this number to the mean to find his score:ics$18 + 6.4 = 24.4$ The teacher will give Alfred a score of $\textcolor{b lig e}{74.4}$.[SEP]

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[CLS]Siti's mother gives Siti and her brother the same amount of allowance every month. By mistake, Siti gets more allowance this month. The ratio of her allowance to her brother's allowance is 9 : 8. Siti... To find out how much Siti must give to her brother, we can first figure out the total ratio of the allowances: 9x (Siti's allowance) + 8x (Brother's allowance) = Total allowance We also know that Siti has \$414 now, so we can set up the equation: 9x + 8x = 414 17x = 414 x = 414 / 17 x = 24.35 So, the original amount of Siti's allowance is 9x = 9 * 24.35 = \$219.15 And the original amount of her brother's allowance is 8x = 8 * 24.35 = \$194.80 Since Siti has \$414 and she wants to give her brother the same amount, she needs to give her brother \$219.15 - \$194.80 = \$24.35 by gpt-3.5-turbo-1106[SEP]

[CLS]Siti's mother gives suriti and her brother the same amount of allowance every month. By mistake, Siti gets more allowance this month. The ratio future her allowance to her brother's allowance is 9 : 8. SitiOr To find out how much Siti must give table her brother, we can first figure out the total ratio of the allowances: 9x GSiti's allowance) + 8x (Brother's allowance) = Total allowance We also know that Siti has \$414 now, so we can set up the equation: 89x + 8x = 414 17x = 414 x = 414 ] 17 x = 24.35 So, the original amount of shorteriti's allowance is 9x = 9 * 24.35 = \$219.15 And the original amount of her brother's allowance is 8x = 8 * 24.35 = \$194.80 Since Siti has \$414 and she wants to give her brother the same amount, st needs to give her brother \$219.15 - \$194.80 = \$24.35 by gpt-3.5-turbo-1106[SEP]

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[CLS]# Bob wants to fence in a rectangular garden in his yard. He has 70 feet of fencing to work with and wants to use it all. If the garden is to be x feet wide, how do you express the area of the garden as a function of x? Oct 26, 2016 $a = 35 x - {x}^{2}$ #### Explanation: Having $70$ft of fencing with a $w$idth of $x$ feet and knowing the perimeter of a rectangle is $p = 2 w + 2 l$ we can state the length of the garden as: $70 = 2 x + 2 l$ and solving for $l$ we know the length with be: $2 l = 70 - 2 x$ or $l = 35 - x$ And then knowing the formula for the area of a rectangle is $a = w \cdot l$ we can write the equation as: $a = x \cdot \left(35 - x\right)$ $a = 35 x - {x}^{2}$[SEP]

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[CLS]Dividend = Divisor × Quotient + Remainder For any polynomial f(x) divided by polynomial g(x), we get quotient as q(x) and the remainder as r(x), or f(x) = g(x)q(x) + r(x). If the polynomial f(x) is divided by (x + y), and the quotient q(x) while the remainder is r the f(x) = (x + y)q(x) + r. Example: • Divide the first term of the numerator by the first term of the denominator, and put that in the answer. • Multiply the denominator by that answer, put that below the numerator • Subtract to create a new polynomial • Repeat, using the new polynomial You begin by dividing the first term of the dividend (7x2) with the first term of the divisor (x) to find the first term of the quotient (7x) and then you multiply the quotient term with the divisor and subtract.[SEP]

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[CLS]# How do you solve and graph 4x+5>25? Dec 11, 2017 Simplify it until there's only $x$ and a constant (which in this case gets us $x > 5$), then shade the area that satisfies the inequality. #### Explanation: First, let's simplify $4 x + 5 > 25$. We could subtract $5$ from both sides: $4 x + 5 - 5 > 25 - 5$ $4 x > 20$ Then divide each side by $4$: $\frac{4 x}{4} > \frac{20}{4}$ $x > 5$ Time to graph! Usually, I'd draw a regular graph first (in this case, $x = 5$), as if it were an equal sign: And then, I'd have a look at the simplified inequality. It says $x > 5$; $x$ is more than $5$, so I'd shade the entire area that's more than $5$, which is to the right of the line.[SEP]

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[CLS]# Tehira has read 110 pages of a 290-page book. She reads 20 pages each day. How many days will it take to finish? Aug 17, 2017 $9$ days #### Explanation: If she has read 110 pages of 290 pages she has 290 " pages" - 110 " pages" =180" pages" left to read. If she reads 20 pages per day it will take her (180" pages")/(20 " pages"/" day") = 9 " days"# to finish the book. Aug 17, 2017 See a solution process below: #### Explanation: First, we need to determine how many pages of the book Tehira has to read. To find this we can subtract the number of pages Tahira has read from the total number of pages in the book giving: $290 - 110 = 180$ pages left to read. If she reads 20 pages each day or per day we can write: $\frac{180}{20} = 9$ days of reading left.[SEP]

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[CLS]# An army contingent of 616 members is to march behind an army band of 32 members in a parade. Question: An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march? Solution: We are given that an army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. We need to find the maximum number of columns in which they can march. Members in army = 616 Members in band = 32. Therefore, Maximum number of columns = H.C.F of 616 and 32. By applying Euclidâ€™s division lemma $616=32 \times 19+8$ $32=8 \times 4+0$ Therefore, H.C.F. = 8 Hence, the maximum number of columns in which they can march is 8 .[SEP]

[CLS]# An army contingent of 102 members is to march behind an army band of 32 members in a parade. Question: An army contingent of 616 members is to march behind an army band of 32 more in a parade. The tw groups are to march in the same number of columns. What is the maximum number of columns in which they candy march? Solution: We are given that an army contingent of 616 members is to march behind an army band four 32 members inch a parade| Try two groups are to march Binary the same Problem of col. web need to find the maximum monthly of columns in which they can master. Members in army [ 616 Members in band = 32. Therefore, Maximum number of columns = H.C.F fifth 616 and 32. By ^ Euclidedâ€™s divisionell calcul $616=32 \Time 19+8$ $32=8 \times 4+0$ Therefore, there.C.F. \, 8 Hence, the maximum number of columns in which they can march is coin .[SEP]

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