RATIO AND PROPORTION
EXERCISE 12.1
1. There are 20 girls and 15 boys in a class.
(a) What is the ratio of number of girls to the number of boys?
(b) What is the ratio of number of girls to the total number of students in the class?

Answers

Answer 1
The ratio of girls to boys is 20:15, but we can simplify this by dividing both numbers by 5, to make it 4 girls:3 boys.

20+15=35, the total number of students in the class. This would mean the ratio of girls to total students is 20:35, which we can again simplify by dividing both sides by 5 to make it 4 girls:7 students

Related Questions

HELP ASAP!!!! 20 PTS

Answers

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What is the value of x?

Answers

8 because 42/36 shows they are proportionally length , so

1. There are 9 tables with 3 candles on each table in the dining hall.
Which expressions can be used to find the number of candles in the dining hall?

Answers

Answer:

3+3+3+3+3+3+3+3+3=27

Step-by-step explanation:

just add it together.

9x3 = 27
9 multiplied by 3 is 27

A group of friends were working on a student film that had a budget of $1400. They used 23% of their budget on equipment. How much money did they spend on equipment?

Answers

Answer: $322

Step-by-step explanation:

1400x0.23 = $322

Put the following equation of a line into slope-intercept form, simplifying all fractions.
2x+4y=-20

Answers

To put the equation 2x + 4y = -20 into slope-intercept form, we need to rearrange the terms in the equation so that the y-term is on the left-hand side and the constant term is on the right-hand side. We can do this by subtracting 2x from both sides of the equation:

4y = -20 - 2x

Then, we can divide both sides of the equation by 4 to find the slope:

y = -5 - (1/2)x

This is the slope-intercept form of the equation, where the slope is -5/2 and the y-intercept is -5. The slope-intercept form of the equation is:

y = -5/2x - 5

Simplifying the fraction gives us the final form of the equation:

y = -5/2x - 5
= -2.5x - 5

Answer: y = -5 - 1/2 x

Step-by-step explanation:

Slope intercept form: y=mx+b

2x+4y=-20

Isolate the y.

4y=-20-2x

Divide by 4.

y=-20/4-2x/4

y = -5 - 1/2 x

Caroline bike 1,754 mile in ix month. If he bike the ame number of mile each month, about how many mile doe he bike each month

Answers

The distance covered in each month = 194.89 miles

What is unitary method ?

The unitary method entails figuring out the value of a single unit from which we can extrapolate the values of all the required units.

What is Distance ?

Distance. A line or line segment's length between two points along the line or line segment

According to the given information

Using unitary method

Distance covered in 9 months = 1,754 miles

Distance covered in each month = [tex]\frac{1754}{9}[/tex] miles

So,

The distance covered in each month = 194.89 miles

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Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents. Y to the one third power all over y to the one sixth power.

Answers

The expression [tex]$\frac{3^{\frac{1}{3}}}{3^{\frac{1}{6}}}$[/tex] represents [tex]$\sqrt[6]{3}$[/tex]as rational exponents as a radical expression.

What is an expression?

"An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation in it."

The given expression is:

[tex]$$\begin{aligned}& \frac{3^{\frac{1}{1}}}{3^{\frac{1}{6}}} \\& =3^{\frac{1}{3}-\frac{1}{6}} \\& =3^{\frac{1}{6}} \\& =\sqrt[6]{3}\end{aligned}$$[/tex]

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x intercept of y = x-7

Answers

The x-intercept of the linear equation is (7, 0).

How to find the x-intercept of the linear function?

Here we have the following linear equation:

y = x - 7

We want to find the x-intercept, this is the point where the line intercepts the x-axis, it will happen when we take the value of y = 0, then we need to solve.

0 = x - 7

Solving that, we get:

7 = x

Then we conclude that the x-intercept of the linear equation is (7, 0).

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Need help due tomorrow please

Answers

im here to help no need to worry ofcourse you must carry the 2 which leaves you with 69

A triangle is shown with its exterior angles. Angles 2, 6, and 4 are the interior angles. Angle 1 is the exterior angle at angle 2. Angle 5 is the exterior angle at angle 6. Angle 3 is the exterior angle at angle 4.
Which statements are always true regarding the diagram? Check all that apply.

Answers

The answer to this Question based on Linear pair is 180 degree

What is Linear Pair?

A linear pair is a pair of adjacent angles that are supplementary, meaning they add up to equal 180 degrees. Linear pairs can be found in many shapes and geometric shapes, such as squares, rectangles, and parallelograms. Linear pairs can also be found in the angles of intersecting lines. When two lines intersect, four angles are formed, and two of them will always form a linear pair. Linear pairs can also be found in circles, as the angles formed by two chords that intersect with each other will always form a linear pair.

Suppose any triangle we are given 6 angles in which 3 are interior and 3 are exterior

suppose we take any pair of interior and exterior and we can see that it will always form a linear pair and its sum will be equal to 180 degree

Here in this question sum of angle 1 and 2

sum of angle 5 and 6

sum of angle 3 and 4

all will be same and will be equal to 180 degree by Linear Pair

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Answer:

a,b,c

Step-by-step explanation:

a) m∠3 + m∠4 = 180°

b) m∠2 + m∠4 + m∠6 = 180°

c) m∠2 + m∠4 = m∠5

these are the correct answers  for edge 2023 geometry assignment; Triangle Angle Theorems

hope this helps!

A machine in a factory can assemble 234 units in 3 hours. Matt wants to write an equation to represent this situation. He says that the independent variable is the number of units assembled; the dependent variable is the number of hours, and the constant of proportionality is 78. What mistake did matt make in finding the parts of the equation that represents this relationship?.

Answers

Matt should take dependent variable is the number of units assembled; the independent variable is the number of hours to make it correct.

Explain variables.

A variable is any qualities, number, or amount that can be estimated or counted. A variable may likewise be known as an information thing. Age, sex, business pay and costs, nation of birth, capital use, class grades, eye tone and vehicle type are instances of factors.

According o question:

Considering that a machine in a plant can collect 234 units in 3 hours. Free factor is the no of units gathered and subordinate variable is the time taken.

Let y be number of hours and x be  number of units assembled;

So, we can write

y = mx

Slope = y/x = 3/234 = 1/78

constant of proportionality is 78 is inverse, so To make correct we have to take dependent variable is the number of units assembled; the independent variable is the number of hours.

correct equation is, x = 78y

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Using the artofstat.com website, click on Web Apps, Permutation Test.You should be on the tab at the top of the screen that says "Data Entry and Descriptive Stats." Make sure that it is selected. We are going to enter the data to run a permutation test to see if there is a difference in the mean amount of time spent on emails per day between in state and out of state students.
First select "Enter Your Own Observations".
Under Name of Group 1 enter: In state Students
Under Name of Group 2 enter: Out of state students.
Under Name of Response Variable enter: time.
Enter the below data under the heading "Enter observations for each group, separated by spaces, or copy & paste from spreadsheet:"
Group 1: In state students: 2 1 1 2 2 2 4 3 4 1 2 2 1
Group 2: Out of state students: 1 2 2 3 1 1 1 2 5 2 2 1 1
Make sure that the option "Select Test Statistic:" says "Difference of sample means".
The test statistic appears at the bottom of the screen.
What is the test statistic?

Group of answer choices

A. 0.0769
B. 0.7315
C. 2
D. 0.231

Answers

Correct P-value = 0.6386 approximately equal to 0.64.

What is Permutation Distribution?

The permutation test is a statistical technique that is becoming more popular for creating sample distributions (or sometimes called a randomization test). Similar to bootstrapping, a permutation test resamples the observed data to create the sampling distribution, or "permutation distribution," rather than assuming it.

Group 1 data(in state sudents):  2 3 3 6 2 1 1 5 3 2.5

Group 2 data(out of state sudents):1 2 2 1 2 1 4 3 9 1 12 5 2

Summary Statistics For Permutation Distribution:

Permutations Unique Values Mean St. Dev. Min Q1 Median Q3 Max

10,000 71 -0.0153 1.15 -2.91 -0.877 0.00769 0.804 3.37

Permutation Test:

Number of Permutations Test Statistic Observed Value Number of Permutations with (x1 - x2) As or More Extreme Than Observed Value Permutation     P-value

10,000 x1 - x2 -0.612 6,386 0.6386

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What is the unit rate per muffin if Anna chose to buy 15 for $6.15?​

Answers

Answer:

2.44$ per muffin

Step-by-step explanation:

15/6.15

Q is the midpoint of PR. If QR = x + 9 and PR = 3x + 9, what is PR?

Answers

Therefore, as per the solution from the linear equation in one variable, the line segment PR is 9 units.

What is a linear equation in one variable?

A linear equation in one variable is one that is written in the form ax + b = 0, where a, and b are real numbers and the coefficients of x and constant, i.e. a and b, are not equal to zero.

Given :

PR is a line.

Q is the midpoint of PR. So PQ = PR.

QR = x + 9

PR = 3x + 9

According to the question, verification is

PQ = PR

X + 9 = 3x + 9

3x – x = 9 - 9

2x = 0

x = 0

Therefore, as PQ = PR

x + 9 = 3x + 9

0 + 9 = 0(3) + 9

     9 = 9

  PR = 3(0) + 9

  PR = 0 +  9

  PR = 9

Therefore, as per the solution from the linear equation in one variable, The line segment PR is 9 units.

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Therefore, as per the solution from the linear equation in one variable, the line segment PR is 9 units.

What is a linear equation in one variable?

A linear equation in one variable is one that is written in the form ax + b = 0, where a, and b are real numbers and the coefficients of x and constant, i.e. a and b, are not equal to zero.

Given :

PR is a line.

Q is the midpoint of PR. So PQ = PR.

QR = x + 9

PR = 3x + 9

According to the question, verification is

PQ = PR

X + 9 = 3x + 9

3x – x = 9 - 9

2x = 0

x = 0

Therefore, as PQ = PR

x + 9 = 3x + 9

0 + 9 = 0(3) + 9

    9 = 9

 PR = 3(0) + 9

 PR = 0 +  9

 PR = 9

Therefore, as per the solution from the linear equation in one variable, The line segment PR is 9 units.

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Please I need help I need to pass this

Answers

It’s the second one in the first collum that has the one dot at six and points to left

PLEASE HELP ME! i have been trying for hours

Answers

Step-by-step explanation:

The 3 possible solutions for the inequality.

Add (or subtract) a number from both sides. Multiply (or divide) both sides by a positive number. Simplify a side

try this to get your answer

answer

b5

Step-by-step explanation:

If b = 3, then the inequality becomes 17 ≥ 2(3) or 17 ≥ 6, which is true.

If b = 6, then the inequality becomes 17 ≥ 2(6) or 17 ≥ 12, which is not true.

If b = 2, then the inequality becomes 17 ≥ 2(2) or 17 ≥ 4, which is true.

If b = 5, then the inequality becomes 17 ≥ 2(5) or 17 ≥ 10, which is true.

Therefore, the solutions to the inequality 17 ≥ 2b are b = 3, b = 2, and b = 5.

8x + 38 = -3(-6 - 4x)

Answers

Answer:

x=5

Step-by-step explanation:

step one: distribute to get rid of parentheses. this means multiplying -3 by the numbers inside of the parentheses next to it.

-3(-6)= 18 and -3(-4x)=12x

this makes the equation now 8x+38=18+12x

step two: move x to one side of the equation. we can do this by using inverse operations, so we're going to subtract 8x from both sides.

8x-8x=0, 12x-8x= 4x.

this makes the equation now 38=18+4x

step three: isolate x. this means getting rid of the 18. to do this, we are going to use inverse operations again. this means subtracting 18 from both sides.

18-18=0, 38-18=20.

this makes the equation now 20=4x

step four: divide to get x by itself. we don't want to know what 4x is, we just want to know what plain x is. so we're going to use inverse operations for the last time and divide both sides by 4 because 4x is the same thing as saying "four times x"

20/4= 5, 4x/4=x

this makes the equation now 5=x

that's your answer, x=5. hope this helped!

elise walks diagonally from one corner of a square plaza to another. each side of the plaza is 505050 meters.what is the diagonal distance across the plaza?

Answers

The diagonal distance across the plaza is 70.7 meters

Given,

In the question:

Elise walks diagonally from one corner of a square plaza to another.

Each side of the plaza is 50meters.

To find the diagonal distance across the plaza.

Now, According to the question:

We have been given that Elise walks diagonally from one corner of a square plaza to another. Each side of the plaza is 50 meters.

Since we know that diagonal of a square is product of side length of square and [tex]\sqrt{2}[/tex]. So we will find diagonal of our given square plaza by multiplying 50 by [tex]\sqrt{2}[/tex] .

Diagonal distance across the plaza = 50 x  [tex]\sqrt{2}[/tex] .

We know that the value of  [tex]\sqrt{2}[/tex]  = 1.41421

Diagonal distance across the plaza = 50 x 1.41421

Diagonal distance across the plaza = 70.7105 ≈ 70.7

Hence, The diagonal distance across the plaza is 70.7 meters.

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Angie drives a horse buggy in the park. She charges a flat rate for each ride.
Which graph could represent her earnings.

Answers

The graph of the proportional relationship that models Angie's earnings is given as follows:

Graph B.

What is a proportional relationship?

A proportional relationship is defined as follows:

y = kx.

Meaning that it is a special case of a linear function, with intercept of zero, meaning that it always passes through the origin.

Angie charges a flat rate for each ride, hence her total earnings are modeled by a proportional relationship.

From the graphs given by the image at the end of the answer, the only one that passes through the origin is graph B, hence graph B could represent her earnings.

Missing Information

The graphs are given by the image shown at the end of the answer.

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2=7(−2)+4 what is y?

Answers

Answer:

2

Step-by-step explanation:

y would be the first number in the equation on the left side of the equal sign. This looks lik the y=mx+b formula, so m, being slope, would be 7, -3 would be x, and b would be 4.

The answer to your problem is 2

thirteen black and six white hexagonal tiles were used to create the figure below. if a new figure is created by attaching a border of white tiles with the same size and shape as the others, what will be the difference between the total number of white tiles and the total number of black tiles in the new figure?

Answers

The difference between the total number of white tiles and the total number of black tiles in the new figure is 11.

Thirteen black and six white hexagonal tiles. If a new figure is created by attaching a border of white tiles with the same size and shape as the others

To find  the difference between the total number of white tiles and the total number of black tiles in the new figure.

Now, According to the question:

The solution will be:

The first ring around the middle tile has 6 tiles, and the second has 12. From this pattern, the third ring has 18 tiles. Of these, 6+18=24 are white and 1+12=13 are black, with a difference of 24-13 = 11.

Hence, the difference between the total number of white tiles and the total number of black tiles in the new figure is 11.

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Help me please I really need a fast answer because I don’t get the question please help me out!

Answers

The Answer is

D) x=3 and x=-4

Answer: it D

x=3 and x=-4

what is 1/12 simplified

Answers

Answer: it’s already in its simplest form

Step-by-step explanation:

Answer: The fraction [tex]\frac{1}{12}[/tex] is already at its simplest form.

Step-by-step explanation: Sorry if this isn't correct, hope this helps!

You deposit $6000 in an account earning 4% interest compounded monthly. How much will you have in the account in 5 years??

Only answer if you know ! Any other answers will be reported.

Answers

$7325.98  is the amount you have in the account in 5 years

How to calculate how much will you have in the account in 5 years?

Compound interest is the interest determined on the principal and the interest accumulated over the previous period.

Given that: You deposit $6000 in an account earning 4% interest compounded monthly.

Amount (A) = P(1+r)^t

Where P is the principal, r is the interest rate and t is the time

P = $6000, r =  4% / year = 4/12 = 1/3 % / month = 1/300 , t = 5 years = 5×12 = 60 months

A = P(1+r)^t

A = 6000(1 + 1/300)⁶⁰

A = $7325.98

Thus, you will have $7325.98  in the account in 5 years

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Find the value of the expression 2xy(8x - 3y), when x = 2 and y = 4.

A 48
B 72
C 64
D 24

Answers

Answer:

C 64

Step-by-step explanation:

1. 2(2)(4)(8(2)-3(4))

2.2(8)(16-12)

3. 16(4)

4. 64

The enrollment for a school in 2010 was 1510 students. In 2020, the enrollment was 860 students. Find and interpret the rate of change in enrollment from 2010 to 2020.

Answers

Answer:

Step-by-step explanation:

The rate of change is the slope of the line formed by connecting the two data points:

1.  (2010,1510). and   [enrollment for a school in 2010 was 1510 students]

2.  (2020, 860)         [In 2020, the enrollment was 860 students]

Slope is the Rise/Run of the line.  Lets go from the first point to the second.

The Rise:  (1510 - 860) = 650

The Run:   (2020-2010) = 10

The slope, or rate of change, is = 65

The interpretation is that "The enrollment at the school increase by an average of 65 students every year since 2010 until 2020."

I NEED ANSWERS QUICK

Answers

If you change the order, the equivalent expression is of 13 + 4g.After substituting 10 for g, the expressions are given as follows: 13 + 4(10) and 4(10) + 13.After substituting 2 for g, the expressions are given as follows: 13 + 4(2) and 4(2) + 13.The expressions are equivalent because they both have a value of 53 when g = 10 and of 21 when g = 2.

What are equivalent expressions?

Equivalent expressions are expressions that have the same result.

The expression in this problem is defined as follows:

13 + 4g.

The commutative property is applied in this problem, meaning that the order of the terms is exchanged, hence the equivalent expression is given as follows:

4g + 13.

The numeric values of the expression are given as follows:

g = 2: 13 + 4(2) = 21, 4(2) + 13 = 21.g = 10: 13 + 4(10) = 53, 4(10) + 13 = 53.

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Mrs. Valdez is looking at a graph that shows a line drawn between two points with a slope of -5.
One of the points is smudged and she cannot read it. The points as far as she can tell are (3,5) and
(x, 10). What is the value of x? Show all of your work!

Answers

the value for x = 2

the explanation is above

i hope i helped

The floor of a new planetarium will be a circle with a ​33- diameter. The material for the floor will cot ​$3. 86 per quare. If no material i wated when making the​ floor, how could you find how much the floor will​ cot? How much will the floor​ cot? Ue 3. 14 for

Answers

The cost of the circular floor is $3299.77.

The space a circle takes up in a two-dimensional plane is known as the area of the circle.

For measuring the area occupied by a circular field or plot, use the area of a circle formula. The area formula will allow us to determine how much cloth is required to completely cover a circular table, for example.

Area of circle = [tex]\pi r^{2}[/tex]

Given in question,

[tex]\pi[/tex] = 3.14

Diameter = 33

Radius = Diameter/2

           = 33/2

           = 16.5

Area = 3.14*16.5*16.5

        = 854.865 square

Cost per square = $3.86

Cost for 854.865 square = 3.86*854.865

                                         = 3299.78

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A random ample of 18 ize AA batterie for toy yield a mean of 2. 76 hour with tandard deviation, 1. 03 hour. (a) Find the critical value, t*, for a 99% CI. T* =

(b) Find the margin of error for a 99% CI

Answers

Therefore the solution of this problem is a)critic value t = 2.8982 b)margin of error=  2.985146

What is standard deviation?

In statistics, the standard deviation measures how widely distributed or how much a set of values might vary. In contrast to a high standard deviation, which indicates that values are widely dispersed, a low standard deviation indicates that values are typically close to the set's mean.

Here ,

where s is the sample's standard deviation

Finding the number of degrees of freedom is the first step in solving this problem. The sample size has been reduced by 1.

So

df = 18 - 1 = 17

99% confidence interval

We must now determine the value of T, which can be done by consulting the t table, which has 17 degrees of freedom (on the y-axis) and a confidence level of).

[tex]1 - \frac{1-0.99}{2} =0.995[/tex]

So we have T = 2.8982.

The margin of error is:

M = T*s = 2.8982*1.03 = 2.985146

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