A solid with the volume 100 cubic units is is dilated by a scale factor of k find the image for each given value of k

The correct statement regarding whether there are two parallel lines is given as follows:

C. Yes, lines n and p are parallel because corresponding angles are congruent.

When two parallel lines are cut by a transversal, corresponding angles are pairs of angles that are in the same position relative to the two parallel lines and the transversal. Corresponding angles are always congruent, which means that they have the same measure.

The angles in the same position for this problem are given as follows:

1 and 2.

The parallel lines relative to which these two angles are at the same position are given as follows:

n and p.

Hence the correct option is given by option c.

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Hence, we may conclude that function(x) behaves as though it will eventually approach infinity as x approaches infinity and will eventually approach negative infinity as x approaches negative infinity.

Mathematicians research numbers, their variants, equations, associated structures, forms, and possible configurations of these. The word "function" describes the connection between a group of inputs, each of which has a corresponding output. A function is a connection between inputs and outputs where each input results in a single, distinct outcome. Each function has a domain, codomain, or scope assigned to it. Functions are usually denoted by the letter f. (x). An x is entered. On functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions are the four main categories of accessible functions.

F(x) also approaches positive infinity as x gets closer to infinity.

F(x) also approaches negative infinity as x gets closer to its opposite.

This is due to the fact that as x increases or decreases in value, the term with the largest x power determines how the function behaves.

Hence, we may conclude that f(x) behaves as though it will eventually approach infinity as x approaches infinity and will eventually approach negative infinity as x approaches negative infinity.

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Answer: AD/DB = {AB/BD} = {DA/DB}

AD/AB = {DB/AB} = {DA/DB}

DB/AB = {AD/AB} = {BD/DA}

The graph and the table show the high temperatures in a city over a 10-day period. here are the right answer:

a. 60, b. 2, 4, and 6 days

c. Yes, the high temperature is a function of the day.

The following group is shows a the high temperatures in a city for 10 -days. Where height temperature is on day 9, lowest temparature in day 7. Here the high temperature is a function of the day.            

Here we have

The graph and the table show the high temperatures in a city for 10-days    

From the table,

The high temperature on Day 7 = 60      

The high temperature 61 degrees on 2, 4, and 6 days

Since the graph shows the change in temperature as well as the change in the number of days the high temperature is a function of the day  

Therefore,

The answer are

a. 60, b. 2, 4, and 6 days

c. Yes, the high temperature is a function of the day.

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The pair of expressions which represents the price of an order that was originally x dollars are x - 0.15x and 0.85x

Percentage discount = 15%

Original price of an order = x dollars

New price = Original price of an order - (Percentage discount × Original price of an order)

= x - (15% of x)

= x - 0.15x

= 0.85x

Therefore, x - 0.15x and 0.85x are the expressions which represent the price of an order that was originally x dollars

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the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{8}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{2}}} \implies \cfrac{ -4 }{ 3 } \implies - \cfrac{4 }{ 3 }[/tex]

According to the question the standard deviation is approximately $9,400.

Standard deviation is a measure of variability or dispersion in a data set. It is a measure of how much the individual data points within a set deviate from the mean. The standard deviation is calculated by taking the square root of the variance and is expressed as the same unit of measurement as the data set.

The standard deviation of pre-tax family incomes when the head of the household has a university degree can be computed using the empirical rule. According to the empirical rule, approximately 68% of the data lies within one standard deviation of the mean, 95% of the data lies within two standard deviations of the mean, and 99.7% of the data lies within three standard deviations of the mean.

Given that 70% of the pre-tax family incomes when the head of the household has a university degree are between $76,300 and $95,100,
we can calculate that the standard deviation is approximately ($95,100 - $76,300) / 2.66 ≈ $9,400.

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The value of the missing sides using Pythagorean theorem are;

1.  15. 81m

2. 24. 08cm

3. 12. 85 ft

4. 4. 58 in

5. 27. 02 yd

6.  18. 14 mm

7. 16. 58 km

8. 6. 24m

9. 9. 85 miles

10. 14.14 feet

11. 14.14 feet

12. 13. 78  feet

Using the Pythagorean theorem, which states that the square of the longest side of a triangle which is the hypotenuse leg is the sum of the squares of the other two sides of the triangle, that is, the opposite and adjacent.

Then, we have;

x² = y² + z²

Where the parameters are;

From the figures shown, we have that;

1. Adjacent side = 8m

Opposite side = 9m

Using the Pythagorean theorem, we have;

x² = 13² + 9²

Find the squares and substitute

x² = 169 + 81

x² = 250

find the square root

x =√250 = 15. 81m

2. For the triangle, we have;

x² = 16² + 18²

x² = 256 + 324

x = √580 = 24. 08cm

3. For the third triangle:

y² = 19² - 14²

y² = 361 -196

y = √165 = 12. 85 ft

4. For the fourth triangle

z² = 11² - 10²

z² = 121 - 100

z = √21 = 4. 58 in

5. x² = 21² + 17²

x² = 441 + 289

x = 27. 02 yd

6. z² = 27² - 20²

z² = 729 - 400

z = √329 = 18. 14 mm

7. z² = 30² - 25²

Find the squares

z² = 900 - 625

z² = 275

z = √275 = 16. 58 km

8. y² = 8² - 5²

find the squares

y² = 64 - 25

y = √39 = 6. 24m

9. x² = 9² + 4²

Find the squares

x² = 81 + 16

x = √97 = 9. 85 miles

10. Length of the diagonal is the hypotenuse side

x² = 10² + 10²

x² = 100 + 100

x = √200 = 14.14 feet

11. The height of the pole is the opposite side

y² = 15² - 5²

y² = 225 -25

y = √200 = 14. 14 feet

12. the height of the pole is the opposite side

y² = 14² - 4²

y² = 196 - 16

y = √190 = 13. 78  feet

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The variation equation if y varies jointly with x and z and y = 360 when x =12 and z = 15 is y = 2xz.

The variation equation for this situation can be represented as the equation y = kxz, where k is the constant of variation, since y varies jointly with x and z.

We can find the value of k by plugging in the given values of x, y, and z into the equation and solving for k:

360 = k(12)(15)

360 = 180k

2 = k

So, the constant of variation is 2. Hence, the variation equation is y = 2xz. This equation can be used to find the value of y for any given values of x and z. For example, if x = 4 and z = 10, then y = 2(4)(10) = 80.

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To prove that |z+w| ≤ |z| + |w| for two complex numbers z and w, we can use an algebraic proof.

First, let's rewrite z and w in terms of their real and imaginary parts:

z = a + bi

w = c + di

Now, we can use the definition of the absolute value of a complex number to write:

|z+w| = |(a+c) + (b+d)i|

= √((a+c)² + (b+d)²)

Similarly, we can write:

|z| = |a + bi| = √(a² + b²)

|w| = |c + di| = √(c² + d²)

Now, we can use the triangle inequality to prove that |z+w| ≤ |z| + |w|:

√((a+c)² + (b+d)²) ≤ √(a² + b²) + √(c² + d²)

Squaring both sides of the inequality gives us:

(a+c)² + (b+d)² ≤ (a² + b²) + (c² + d²) + 2√((a² + b²)(c² + d²))

Expanding the left-hand side of the inequality gives us:

a² + 2ac + c² + b² + 2bd + d² ≤ a² + b² + c² + d² + 2√((a² + b²)(c² + d²))

Simplifying and rearranging terms gives us:

2ac + 2bd ≤ 2√((a² + b²)(c² + d²))

Dividing both sides of the inequality by 2 gives us:

ac + bd ≤ √((a² + b²)(c² + d²))

Squaring both sides of the inequality again gives us:

(a² + b²)(c² + d²) - (ac + bd)² ≥ 0

Expanding and simplifying gives us:

a²c² + a²d² + b²c² + b²d² - a²c² - 2abcd - b²d² ≥ 0

a²d² + b²c² - 2abcd ≥ 0

(a²d² - 2abcd + b²c²) ≥ 0

(a² - 2ab + b²)(d² - 2cd + c²) ≥ 0

(a - b)²(d - c)² ≥ 0

Since the square of any real number is always greater than or equal to zero, this inequality is always true. Therefore, |z+w| ≤ |z| + |w| for any two complex numbers z and w. This completes the algebraic proof.

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After building 18 shelves and 24 tables, the carpenter will have 9 boxes of screws, 80 2x4s, and 39 sheets of plywood leftover.

To find the leftover materials, we need to calculate the total materials used to build 18 shelves and 24 tables, and then subtract that from the total materials the carpenter had on hand.

For 18 shelves, the carpenter used 18 boxes of screws, 36 2x4s, and 72 sheets of plywood. For 24 tables, the carpenter used 48 boxes of screws, 48 2x4s, and 72 sheets of plywood.

So, the carpenter used 66 boxes of screws, 84 2x4s, and 144 sheets of plywood in total.

Subtracting this from the materials on hand, we get 9 boxes of screws, 80 2x4s, and 39 sheets of plywood leftover.

Therefore, the carpenter can potentially use these leftover materials for future projects or sell them to recoup some of their costs.

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99 as a product of primes is, 99 = 3² * 11

What is  multiplication?

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

To Write 99 as a product of primes,

we get,

99 = 3 * 3 * 11

99 = 3² * 11

Hence, 99 as a product of primes is, 99 = 3² * 11

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The vertices of the image of the triangle BCD are B'(x, y) = (- 3, 13), C'(x, y) = (0, 19) and D'(x, y) = (18, 10). The representation of the resulting figure is in the image attached below.

Herein we find the representation of a triangle on Cartesian plane, whose image, that is, the result of a dilation, must be found. The formula to be used is introduced below:

P'(x, y) = P(x, y) + k · [P(x, y) - O(x, y)]

Where:

If we know that B(x, y) = (- 3, 7), C(x, y) = (- 2, 9), D(x, y) = (4, 6), O(x, y) = (- 3, 4) and k = 2, then the coordinates of the vertices of the image are listed below:

B'(x, y) = (- 3, 7) + 2 · [(- 3, 7) - (- 3, 4)]

B'(x, y) = (- 3, 7) + 2 · (0, 3)

B'(x, y) = (- 3, 7) + (0, 6)

B'(x, y) = (- 3, 13)

C'(x, y) = (- 2, 9) + 2 · [(- 2, 9) - (- 3, 4)]

C'(x, y) = (- 2, 9) + 2 · (1, 5)

C'(x, y) = (- 2, 9) + (2, 10)

C'(x, y) = (0, 19)

D'(x, y) = (4, 6) + 2 · [(4, 6) - (- 3, 4)]

D'(x, y) = (4, 6) + 2 · (7, 2)

D'(x, y) = (4, 6) + (14, 4)

D'(x, y) = (18, 10)

Now we proceed to plot the image by means of a graphing tool.

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The best method to use to solve the system of equation will be Elimination method.

According to the description of the elimination approach, it involves removing a phrase that contains any of the variables from the equation in order to simplify the computations. To achieve this, multiply or divide a number by the equation(s) until all of the variable terms' coefficients are the same. The term is then eliminated or removed from the result by adding or subtracting from both equations. Because of this, the addition technique is another name for the elimination approach. For illustration, let's use the elimination approach to resolve two linear equations with two variables.

The two equations are:

3x+7y=-19

-3x+4y=12

From the above equations we can observe that the value of the coefficient of x is same, as well as, they have opposite sign.

Hence, the best method to use to solve the system of equation will be Elimination method.

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The option E. (3/2, - 1/2, - 3) is not a solution to the system of linear equations.

The system of linear equations given is:

3x + y + z = 1
2x + y - 4z = 2

The answer that is not a solution to this system is option. To check this, we can substitute (3/2, - 1/2, - 3) into the system and solve:
3*(3/2) + (-1/2) + (-3) = 1
2*(3/2) + (-1/2) - 4*(-3) = 2

After simplifying, we get 9/2 - 1/2 + 9/2 ≠ 1 and 9 - 1 - 12 ≠ 2, so option E. (3/2, - 1/2, - 3) is not a solution to the system of linear equations.

A system of equations is a set of two or more equations in which we will find unknowns.

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The linear transformation T is defined as:

[tex]\( T(x) = \left[\begin{array}{c}-6x_{1}+x_{2}+180 \\ 24x_{1}-4x_{2}-720\end{array}\right] \)[/tex]

The linear transformation T is defined as T(x) = Ax+b, where A is a matrix and b is a vector. In this case, we have

[tex]\( A=\left[\begin{array}{cc}-6 & 1 \\ 24 & -4\end{array}\right] \)[/tex]  and  [tex]\( b=\left[\begin{array}{c}180 \\ -720\end{array}\right] \).[/tex]

So, for any vector   [tex]\( x=\left[\begin{array}{c}x_{1} \\ x_{2}\end{array}\right] \)[/tex] , we have:

[tex]\[ T(x) = \left[\begin{array}{cc}-6 & 1 \\ 24 & -4\end{array}\right]\left[\begin{array}{c}x_{1} \\ x_{2}\end{array}\right] + \left[\begin{array}{c}180 \\ -720\end{array}\right] \][/tex]

[tex]\[ T(x) = \left[\begin{array}{c}-6x_{1}+x_{2} \\ 24x_{1}-4x_{2}\end{array}\right] + \left[\begin{array}{c}180 \\ -720\end{array}\right] \][/tex]

[tex]\[ T(x) = \left[\begin{array}{c}-6x_{1}+x_{2}+180 \\ 24x_{1}-4x_{2}-720\end{array}\right] \][/tex]

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Answer:

the answer in this is letter A

Kevin buys a motorcycle for $11,000 with an annual interest rate of 10.75% and a 108-month term, his monthly payments will be $200.39 if he makes a down payment of $2,300.

The monthly payment for a $11,000 loan with an annual interest rate of 10.75% and a 108-month term can be calculated using the formula for the present value of an annuity:

[tex]PV = PMT * (1 - (1 + r/n)^{-n*t}) / (r/n)[/tex]

where PV is the present value of the loan, PMT is the monthly payment, r is the annual interest rate, n is the number of compounding periods per year, and t is the loan term in years.

With a down payment of $2,300, the loan amount is reduced to $8,700 ($11,000 - $2,300). Plugging in the values, we get:

PV = $8,700

r = 0.1075

n = 12 (since payments are monthly)

t = 9 (108 months / 12)

PMT = $200.39 (rounded to the nearest cent)

Kevin needs to pay off a loan of $11,000, which he plans to do over a period of 108 months with an annual interest rate of 10.75%. However, if he makes a down payment of $2,300, his loan amount will be reduced to $8,700. Using the formula for the present value of an annuity, we can calculate his monthly payments, which come out to be $200.39. Therefore, his monthly payments will be $200.39 if he makes a down payment of $2,300.

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The measure of arc ED is 78.7°

An arc of a circle is a portion of the circumference of a circle. It is defined by two endpoints and the arc itself.

The measure of an arc is given in degrees or radians, and it is determined by the angle that it subtends at the center of the circle.

Since FC is the diameter and arc FB is equivalent to arc BC. We can say:

arc FB + arc BC = 180°

arc FB = arc FB = 90°

Also, arc ED is twice the measure of arc CD. We can write:

arc ED = 2 * arc CD

arc CD =  (arc ED)/2

Since the sum arc FB and arc BC is 180°. We can say:

arc FE + arc ED + 0.5(arc ED) = 180°

62° + arc ED + 0.5(arc ED) = 180°

62° + 1.5(arc ED) = 180°

1.5(arc ED) = 180 - 62

1.5(arc ED) = 118

arc ED = 118/3

arc ED =78.7°

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Answer:

1/4

Step-by-step explanation:

you can plug it into a calculator

1/4

First rewrite the - as 1/2^2 , then 2^2=4 so answer is 1/4

Answer:

5,100

Step-by-step explanation:

850(6)= 5,100

Response to the given question would be that Hence, the surface area rectangular box has a surface area of 592 square cm.

Surface area is a measure of how much space an object's surface takes up overall. The total area of a three-dimensional shape's surroundings is its surface area. Surface area refers to the total surface area of a three-dimensional form. You may compute the surface area of a cuboid with six rectangular sides by adding together their individual areas. Instead, you may use the following formula to name the box's dimensions: Surface (SA) = 2lh plus 2lw plus 2hw. A three-dimensional shape's surface area is calculated as the total amount of space it occupies (a three-dimensional shape is a shape that has height, width, and depth).

Size (l) equals 10 cm

Height (h) = 8 cm

Size (h) equals 12 cm

We may use the following formula to get the box's surface area:

Surface Area = 2(lh, lw, and wh)

Inputting the values provided yields:

Surface Area equals 2 (10 x 8, 10 x 12, and 8 x 12) square centimetres.

Surface Area is equal to 2 (80, 120, and 96 square cm).

Surface Area: 2(296) square centimetres

592 square cm is the surface area.

Hence, the rectangular box has a surface area of 592 square cm.

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(A) The equation relating fare to number of miles traveled, m, is y = 0.50 + 0.80m

(B) The equation for earnings, E, in terms of sales volume, V, is E = 50 + 0.10V. The slope of this line is called marginal revenue.

A) The taxi fare starts at 50 cents and increases by 20 cents for every quarter mile traveled. This means that for every mile traveled (4 quarters), the additional cost will be 80 cents per mile traveled. The equation that will relate the fare, y, to the number of miles traveled, m, is y = 0.50 + 0.80m.

B) The equation E = 50 + 0.10V shows that the weekly earning of a salesman starts at $50 and increases by 10 percent of the retail value of the goods he sells. The slope of this line is 0.10, which represents the rate of change in earnings with respect to sales volume. This slope is called the marginal revenue, as it represents the additional revenue earned for each additional unit of sales volume.

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Therefore, the sequence of transformations that maps △RST to △R′S′T′ is a reflection across the y=x line followed by a rotation of 90 degrees clockwise about the origin.

an arrangement of elements that faithfully represent an angle. The first number on a graph indicates the distance along, while the second number indicates the distance up or down. The point (12,5), for instance, is situated 12 below and 5 above.

A sequence of transformations that maps △RST to △R′S′T′ is a reflection across the y=x line followed by a rotation of 90 degrees clockwise about the origin.

Explanation:

First, we need to reflect the original triangle RST across the y=x line. This will result in a new triangle that is congruent to the original one but with its vertices in different positions. The new vertices will be R(-1, -3), S(-1, -1), and T(-5, -4).

Next, we need to rotate this new triangle 90 degrees clockwise about the origin. This will result in another new triangle that is congruent to the previous one but with its vertices in different positions. The new vertices will be R'(3, -3), S'(3, -1), and T'(-1, -4), which are the vertices of △R′S′T′.

Therefore, the sequence of transformations that maps △RST to △R′S′T′ is a reflection across the y=x line followed by a rotation of 90 degrees clockwise about the origin.

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NO, the ordered pair (9,2) is not the solution to the system 8x-4y=64 3y=6x-47.

The given ordered pair is (9,2) and the system of equations is:

8x-4y=64
3y=6x-47

To determine whether the given ordered pair is a solution to the system, we can substitute the values of x and y into the equations and see if they are true.

For the first equation:

8(9)-4(2)=64
72-8=64
64=64

For the second equation:

3(2)=6(9)-47
6=54-47
6=7

The first equation is true, but the second equation is not true. Therefore, the given ordered pair is not a solution to the system.

The final answer is: No, the given ordered pair is not a solution to the system.

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Answer:

C. Exchange the $100 bill for ten $10 bills.

Since the money is to be divided among 4 people, it is easier to divide it if the money is in equal denominations. Therefore, the first step should be to exchange the $100 bill for ten $10 bills, so that each person can receive an equal share of $25. This way, we can avoid having to deal with different denominations while dividing the money among the four people.

Lina hops linearly and Kavier hops exponentially

The equations of the functions are Lina: y = 2x + 3 and Kavier: y = 3(2)^x

Linear pattern

The table of values represent the given parameter

For Lina's distance from the tree, we can see that

As the hop increases by 1, the distance covered increases constantly by 2 feet

This represents a linear function

Exponential pattern

For Kavier's distance from the tree, we can see that

As the hop increases by 1, the distance covered doubles

This represents an exponential function

Lina Linear Function

From the question, we have the following parameters that can be used in our computation:

(0, 3) and (1, 5)

A linear function is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 3

Using the points, we have

m + 3 = 5

m = 2

So, we have

y = 2x + 3

Kavier Exponential Function

Here, we have

(0, 3) and (1, 6)

An exponential function is represented as

y = ab^x

Where

a = y when x = 0

So, we have

y = 3b^x

Using the points, we have

3b = 6

b = 2

So, we have

y = 3(2)^x

Hence, Kavier's equation is y = 3(2)^x

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In interval notation, the domain and range of the function are:
Domain: (-∞, ∞)
Range: [1, ∞)

The domain of a function is the set of all possible values of x that can be plugged into the function. The range of a function is the set of all possible values of f(x) that can be obtained by plugging in values of x into the function.

For the given function f(x) = 9x² + 1, the domain is all real numbers, because any value of x can be plugged into the function. Therefore, the domain is (-∞, ∞).

The range of the function is the set of all possible values of f(x) that can be obtained by plugging in values of x into the function. Since the function is a quadratic with a positive leading coefficient (9), the graph of the function will be a parabola that opens upward. The minimum value of the function will occur at the vertex of the parabola, which is (0, 1). Therefore, the range of the function is [1, ∞).

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The expected value of consumption for each activity is $60 for Activity 1, $40 for Activity 2, and $50 for Activity 3.

The expected value of consumption for each activity can be calculated using the formula: E(x) = P(x) * X, where P(x) is the probability of an event occurring and X is the value of that event.

For Activity 1: Full time farming, the expected value of consumption is:
E(x) = (0.5 * $100) + (0.5 * $20) = $50 + $10 = $60

For Activity 2: Full time construction work, the expected value of consumption is:
E(x) = (1 * $40) = $40

For Activity 3: Part-time farming, the expected value of consumption is:
E(x) = (0.25 * $100) + (0.75 * $20) + (1 * $10) = $25 + $15 + $10 = $50

Therefore, the expected value of consumption for each activity is $60 for Activity 1, $40 for Activity 2, and $50 for Activity 3.

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The equation for the line of best fit is y = 5.43x + 76.41.

The correlation coefficient is 0.79

In order to determine a linear equation for the line of best fit (trend line) that models the data points contained in the table, we would have to use a graphing calculator (scatter plot).

In this scenario, the number of hours would be plotted on the x-axis of the scatter plot while the test scores would be plotted on the y-axis of the scatter plot.

On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the number of hours and test scores, a linear equation for the line of best fit is given by:

y = 5.43x + 76.41

In conclusion, the type of correlation between the variables is a strong positive correlation.

Read more on scatter plot here: brainly.com/question/28605735

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