Mathematics College

The graph shows a relationship between the size of 18 households and the average amount of time, in hours, each member of the household spends on chores per week. Which equation best models this data set?

A. y = 0.34x + 5.19
B. y = -0.34x - 5.19
C. y = 0.34x - 5.19
D. y = -0.34x + 5.19

The Graph Shows A Relationship Between The Size Of 18 Households And The Average Amount Of Time, In Hours,

Answers

Answer 1

Answer:

Option (D)

Step-by-step explanation:

Equation to represent the household expenditure per week will be in the form of,

y = mx + b

Where m = slope of the line

b = y-intercept

From the graph attached,

Since, line of best fit touches the positive side of the y-axis, y-intercept will be positive.

Since, y-values on the graph are decreasing with the increase in the x-values,

Slope of the graph will be negative.

[Slope = [tex]\frac{\text{Rise}}{\text{Run}}[/tex], Since rise of the line is negative and run is positive, slope will be negative]

By these properties equation of the linear graph will be,

y = -0.34x + 5.19

Option (D) will be the correct option.

Answer 2

The equation that best models this data set is y = -0.34x + 5.19

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the slope of the line and b is the y intercept.

Let y represent the time spent on chores for x household members.

From the graph, the line passes through (3, 4.25) and (8, 2.5). Hence:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-4.25=\frac{2.5-4.25}{8-3}(x-3) \\\\y-4.25=-0.35(x-3)\\\\y=-0.34x+5.2[/tex]

The equation that best models this data set is y = -0.34x + 5.19

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Related Questions

A rectangle has a length of 12 yards less than 3 times its width. If the area of the rectangle is 135 square yards, find the length of the rectangle.

Answers

Answer:

The length is 15 yards

Step-by-step explanation:

Given

Represent the width with W and length with L: So

[tex]Area = 135yd^2[/tex]

[tex]L=3W - 12[/tex]

Required

Determine the length of the rectangle:

Area is calculated as thus:

[tex]Area = L * W[/tex]

Substitute 3W - 12 for L and 135 for Area

[tex]135= (3W - 12) * W[/tex]

[tex]135= 3W^2 - 12W[/tex]

Reorder:

[tex]3W^2 - 12W - 135= 0[/tex]

Divide through by 3

[tex]W^2 - 4W - 45 = 0[/tex]

Expand:

[tex]W^2 - 9W + 5W - 45 = 0[/tex]

[tex]W(W - 9) + 5(W - 9) = 0[/tex]

[tex](W + 5)(W-9) = 0[/tex]

[tex]W + 5 = 0[/tex] or [tex]W - 9 = 0[/tex]

[tex]W = -5[/tex] or [tex]W = 9[/tex]

But width can't be negative

So:

[tex]W = 9[/tex]

Recall that: [tex]L=3W - 12[/tex]

[tex]L = 3 * 9 - 12[/tex]

[tex]L = 15[/tex]

Hence, the length 15 yards

A basketball team played six games. In those games, the team won by 7 points, lost by 20, won by 8, won by 11, lost by 3, and won by 9. What is the mean amount by which the team won or lost over the six games?

Answers

Answer:

2

Step-by-step explanation:

A rancher has a square cow pen with side length x. He decides to change the shape

of the pen while still using the same amount of fencing materials. The equation

(x + 10)(x - 10) = 300 represents the relationship of the new side lengths (in feet)

of the pen and its area (in square feet).

a. If 300 represents the area of the new cow pen, what do the expressions

(x + 10) and (x - 10) each represent?

b. Find x, the original side length (in feet) of the square pen. Show your reasoning.

Answers

Answer:

a) x+ 10 is the length of the ranch

x - 10 is the width of the ranch

b) 20 feet

Step-by-step explanation:

Area of the square ranch = L²

L is the side length of the ranch

If the equation

(x + 10)(x - 10) = 300 represents the relationship of the new side lengths (in feet)

Then we can find x where;

x + 10 is the new length of the ranch

x - 10 is the new width of the ranch

Open the parenthesis

equation

(x + 10)(x - 10) = 300

x²²-10x + 10x - 100 = 300

x² - 100 = 300

x² = 300+100

x² = 400

x = √400

x = 20

Hence the original length of the square pen is 20 feet

The values (x + 10) and (x - 10) represents the length and width of the new pen.

The value of x, the original length of the pen is 20 cm

How to find the side of a square?

The pen is a square. It was later reconstructed to form the following expression.

(x + 10)(x - 10) = 300

where

area = 300  feet squared

Therefore,

(x + 10)(x - 10) = 300

x² - 10x + 10x - 100 = 300

x² - 100 = 300

x² = 300 + 100

x² = 400

x = √400

x = 20 ft

Therefore, the original side length of the square pen is 20 ft.

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What's 84 divided by 10 1/5? Thanks.

Answers

Answer:

8.23529412

Step-by-step explanation:

Do long division to get the answer as simple as that!

Answer:

168

Step-by-step explanation: (10 1 ÷5)  ÷ 84

All changes saved
4. Calculate the federal income taxes. In 1862, the federal income tax was 3 percent on incomes between $600 and $10,000 per year and 5 percent on incomes
over $10,000 per year. In 1862, you made $750. How much did you pay in income taxes?
O $37.50
O $225
O $22.50
$2,250

Answers

Answer:

$22.50

Step-by-step explanation:

My bad lol, I posted the answer under the wrong thing.

2 4/5 ___ 2.45
(>,<,=)

Answers

Answer:

2 and 4/5 > 2.45

Step-by-step explanation:

2.8 is greater than 2.45

Answer:

2 4/5 is equal to 2.8 so 2 4/5 > 2.45

Step-by-step explanation:

If f(x) = (2x^3 − 4)^6, then what is f '(x)?

21x^2(x^3 − 4)^5
21x^8
6(2x^3 − 4)^5
6(2x^3 − 4)^5(6x^2)

Answers

The correct answer is:

6(2x^3-4)^5(6x^2)

Explanation:

That is the derivative after you differentiate using the Chain Rule.

GIVING OUT BRAINLIEST TO FIRST ✅CORRECT✅ ANSWER

Answers

Answer:

1,-5 and -1,-3

Step-by-step explanation:

is 9pi > 27 a true inequality?

Answers

yes it is a true inquation.

You spend half of your money on a movie ticket. Then you spend half of what you have left to buy a large popcorn. Then you spend half of what remains to buy a small drink. Which expression equals the fraction of money you have left?​

Answers

Answer:

1/8

Step-by-step explanation:

1 divided by 2 = 1/2

1/2 divided by 2 = 1/4

1/4 divided by 2 = 1/8

Describe the shape of the distribution

Answers

Answer:

it is bimodal

Step-by-step explanation:

pls make me ur brainliest

Answer:

it is skewed

Step-by-step explanation:

When testing for current in a cable with eleven color-coded wires, the author used
required for every possible pairing of two wires?
meter to test two wires at a time.
The number of tests required is

Answers

Answer:

The number of test required is: 55

Explanation:

Using combination formula:

n!/x!(n-x)!

= 11!/2!(9)!

= 55

The rectangle shown as a perimeter of 70 cm and the given area. It’s length is 8 more than twice it’s width. Write and solve a system of equations to find the dimensions of the rectangle.

The length of the rectangle is ___cm and the width of the rectangle is ___cm.

Answers

width of the rectangle = b = x

length of the rectangle = l = 8 + 2x

Perimeter of the rectangle = 70cm

Also, perimeter of the rectangle = 2(l + b)

70 = 2[x + (8 + 2x)]

70 = 2(x + 8 + 2x)

70 = 2(3x + 8)

70 = 6x + 16

70 - 16 = 6x

54 = 6x

54/6 = x

9 = x

Therefore, b = x

b = 9cm

l = 8 + 2x

I = 8 + 2×9

I = 8 + 18

I = 26cm

Given Z1 and Z2, find the
distance between them.
Z1 = 2 – 3i and Z2 = 4 + i

Answers

Answer:

The distance between given points is: √20

Step-by-step explanation:

The given numbers are complex numbers. In order to find the distance between two numbers in complex plain, their difference is taken and then modulus is applied.

Given numbers are:

[tex]z_1 = 2-3i\\z_2 =4+i[/tex]

The difference will be calculated as:

[tex]z_2-z_1 = (4+i)-(2-3i)\\= 4+i-2+3i\\=2+4i[/tex]

The distance will be:

[tex]d = \sqrt{(2)^2+(4)^2}\\= \sqrt{4+16}\\=\sqrt{20}[/tex]

Hence,

The distance between given points is: √20

what is 0.125 in a percent

Answers

12.5% hope this helped mark as brainliest pls?
12.5 percent because there behind the decimal

1. Here is a number line. Write the two missing numbers in the boxes.
0
2

Answers

Answer:

The box on the left is 0.4 and the box on the right is 1.8

a delivery person uses a service elevator to bring boxes of books up to an office. the delivery person weighs 160 lb and each box of books weighs 50 lb. the maximum capacity of the elevator is 1400 lb. how many boxes can the delivery person bring up at one time?

Answers

He can carry around 6 boxes. How? So add one box of books and himself. You should get 210 lb. Afterwards, do 1,400 lb / 210 lb, since the max capacity of the elevator is 1,400 lb. You will get 6.666 and repeating. It will only be 6 boxes at one time. Do NOT round the decimal. The elevator will not be able to take 7 boxes PLUS himself. Otherwise the elevator will crash and fall. Hope this helped!

7. 21 is what percentage of 30? *

Answers

Answer:

70

Step-by-step explanation:

21/70 is .7 move to the right 2 times so 70%

Answer: 70

:D.............

Roxanna has a collection of silver spoons from all over the world.
- If the spoons are arranged in sets of 7, there are 5 left over.
- If the spoons are arranged in sets of 8, there is 1 left over.
- If the spoons are arranged in sets of 15, there are 14 left over.

If she has at least 50 spoons, what is the smallest possible number of spoons in her collection?

Answers

50 because spoons 15 so desk 14 seat 10

Which of the following is a rational number? A.102 B.144 C.21 D.29

Answers

Answer:

I'm pretty sure they're all rational numbers since they're all whole numbers.

PLEASE HELP!! I’L MARK AS BRAINLIEST!!
The flow of water out of a bathtub would best be described as which type of data?
A. Discrete
B. Continuous
C. Linear

Answers

It’s continuous:)
Hope this helps!

If he saves $50 a week , about how many months will it take to have enough to buy the motorcycle

Answers

Answer:

Step-by-step explanation:

There is not enough info.

But you would take-

price of the motorcycle=50(x)  x is the number of months. I can't give the exact amount without the price of the bike.

Each of the points $A, B, C, D, E,$ and $F$ in the figure below represents a different digit from 1 to 6. Each of the five lines shown passes through some of these points. The digits along each line are added to produce five sums, one for each line. The total of the five sums is 47. What is the digit represented by $B$ ?

Answers

Answer:

(E) 5

Step-by-step explanation:

Refer to picture

Calculating sums, we get a result of:

2A + 3B + 2C + 2D + 2E + 2E = B + 2(sum of all digits) = 47

Sum of all digits is:

1 + 2 + 3 +4 + 5 + 6 = 1/2*6*(1 + 6) = 21

Considering this in the equation above, we get:

B + 2*21 = 47B = 47 - 42B = 5

Correct answer is (E) 5

Which statements are TRUE? Select all that apply.

A. Marisa drives 112 miles in 1 hour and 45 minutes, which means her speed is 64 miles per hour.
B. If 6 pens cost $7.74, then 7 pens cost $9.03.
C. If Raymond drives at a speed of 57 miles per hour, then it takes him 4 hours and 10 minutes to drive 256.5 miles.
D. If 17 identical cans of soup cost $38.59, then 3 of the cans must cost $6.81.
E. Mr. Mayes buys two dozen eggs for $8.40, which means that he pays 70 cents per egg.

Answers

Answer:

A, B, D are true

Step-by-step explanation:

A)  Speed = Distance travelled ÷ time taken

                 = 112 ÷ 1.75

                  = 64 miles per hour

True

B) Cost of 6 pens = $7.74

   Cost of 1 pen    = 7.74 ÷ 6 = $ 1.29

   Cost of 7 pens = 1.29 * 7   = $ 9.03

TRUE

C) Speed = 57 miles per hour

4 hour 10 minutes = 250 minutes

Distance traveled in an hour  = 57

Distance traveled in 250 minutes = (57* 250)   ÷ 60 = 237.50 miles

FALSE

D) Cost of 17 cans = $ 38.59

   Cost of 1 can      = 38.59 ÷ 17 = $2.27

   Cost of 3 cans    = 2.27 * 3 = $ 6.81

TRUE

e) Cost of two dozen eggs = $ 8.40

    Cost of an egg                = 8.40 ÷  24  =   $ 0.35

FALSE

PLEASE HELP!!

The blue dot is at what value on the number line?

Pictrure Below:

Answers

the blue dot value on the number line is 3

What is the slope of the line that passes through the points (2, -3) and (2, 13)
Write your answer in simplest form.

Answers

Answer:

The answer is undefined

Step-by-step explanation:

The slope of the line that passes through points (2, -3) and (2, 13) is not defined.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The line that passes through points (2, -3) and (2, 13)

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Plug the values to find the slope of the line:

m = (13 + 3)/(2-2) = 16/0 = not defined

Thus, the slope of the line that passes through points (2, -3) and (2, 13) is not defined.

Learn more about the linear equation here:

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Need this to be solved thanks

Answers

Answer:

The answer is B

Is it possible for you to get brainliest if correct?

Step-by-step explanation:

pear+apple=3

3pear+3apple=9

10.50-9=1.50

apple = 1.50

Khan Academy
Factor using polynomial division
The polynomial p(x) = x3 + 7x2 – 36 has a known factor of (x + 3).
Rewrite p(x) as a product of linear factors.
p(x)=

Answers

Answer:

p(x) as a product of linear factors. [tex]p(x)=(x+3)(x-2)(x+6)[/tex]

Step-by-step explanation:

(x+3) is the factor of polynomial [tex]p(x) = x^3 + 7x^2 - 36[/tex]

So, we can divide [tex]p(x) = x^3 + 7x^2 - 36[/tex] by (x+3) to find other factors

The division is shown in figure attached.

The quotient is: x^2+4x-12

Now factoring the quotient to find linear factors

[tex]x^2+4x-12\\=x^2+6x-2x-12\\=x(x+6)-2(x+6)\\=(x-2)(x+6)[/tex]

The factors are [tex](x+3)(x-2)(x+6)[/tex]

So, p(x) as a product of linear factors. [tex]p(x)=(x+3)(x-2)(x+6)[/tex]

-2/3 x 3/4
Please help!

Answers

Answer:

-1/2

Step-by-step explanation:

Answer:

-9/8.

Step-by-step explanation:

-3/2 * 3/4

= -3*3 / 2*4

= -9/8.

What is 5-4 in the quadratic

Answers

Answer:

1

Step-by-step explanation:

The point is located in the first quadrant because x and y are both positive. The quadrants are labeled in counter-clockwise order, starting in the upper-right.

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