Determine the range of the following graph

Your balance in 30 weeks will be $680.

To calculate Jossie's balance we can use the following formula:

Balance = Initial deposit + (Weekly deposit * Number of weeks)

Given:

Initial deposit = $230

Weekly deposit = $15

Number of weeks = 30

Putting these values into the formula, we get:

Balance = $230 + ($15 * 30)

Balance = $230 + $450

Balance = $680

Therefore, Jossie's balance after 30 weeks will be $680.

[tex]x+3\geq0 \wedge 2x-6\not=0\\x\geq- 3 \wedge 2x\not=6\\x\geq-3 \wedge x\not =3\\x\in\langle-3,3)\cup(3,\infty)[/tex]

The rate of Asters expense for transportation is 16.67% of her income.

1. Given information:

  - Asters monthly income is 3000 birr.

  - Asters uses 500 birr for transportation.

2. Calculate the remaining expenses after deducting the transportation cost:

  Remaining expenses = Total expenses - Transportation cost

  Asters' total expenses = Asters' income

  Remaining expenses = 3000 birr - 500 birr

  Remaining expenses = 2500 birr

3. Calculate the rate of Asters' expense for transportation:

  Rate of transportation expense = (Transportation cost / Asters' income) * 100

  Rate of transportation expense = (500 birr / 3000 birr) * 100

  Rate of transportation expense ≈ 16.67%

Therefore, the rate of Asters' expense for transportation is approximately 16.67% of her income.

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Triangle PYX is congruent to triangle YQZ because PY = QY and PX = YZ

Congruent triangles are triangles having corresponding sides and angles to be equal.

This means that for two triangles to be congruent, the corresponding sides and angles must be equal.

Since Point X is the mid point of line PR , then PX = XR

and since point Y is the mid point of QP, then QY = YP

Therefore since QP = YP and PR = PX, then YZ = PX

Therefore we can say that Triangle PYX is congruent to triangle YQZ.

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The number line for the fractions given are as shown in the attached files

In order for us to represent rational numbers on a number line, we will draw a line and mark a point on it representing rational zero. Positive rational numbers are usually represented to the right of 0 and negative rational numbers are usually represented to the left of 0.

Now, just as any integer can be represented on a number line, rational numbers can also be represented on a number line.

Thus, we have:

For -2/3 and 3/4, we have the number line as attached

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Answer:

a) Let's say the number of owls is "x" and the number of foxes is "y".

Each owl has 2 eyes and 2 legs, so "x" owls would have 2x eyes and 2x legs.

Each fox has 2 eyes and 4 legs, so "y" foxes would have 2y eyes and 4y legs.

According to the problem, there are 22 eyes and 32 legs in total:

2x + 2y = 22 (equation 1)

2x + 4y = 32 (equation 2)

We can use these two equations to solve for "x" and "y".

Subtracting equation 1 from equation 2:

2x + 4y - (2x + 2y) = 32 - 22

2y = 10

y = 5

Substituting "y" = 5 into equation 1:

2x + 2(5) = 22

2x = 12

x = 6

Therefore, there are 6 owls and 5 foxes.

b) Let's use the same approach to solve for "x" and "y":

2x + 2y = 24 (equation 1')

2x + 4y = 38 (equation 2')

Subtracting equation 1' from equation 2':

2x + 4y - (2x + 2y) = 38 - 24

2y = 14

y = 7

Substituting "y" = 7 into equation 1':

2x + 2(7) = 24

2x = 10

x = 5

Therefore, there are 5 owls and 7 foxes.

Answer:

∠ BCD = 22.5°

Step-by-step explanation:

since BD and CD are congruent then Δ BDC is isosceles with the 2 base angles congruent , that is

∠ BCD = ∠ DBC = 22.5°

Answer:

Step-by-step explanation:

are two isosceles triangles, the left one is right and has 1 angle of 90° and two congruent angles, the sum of the internal angles (triangles only) is 180°, therefore 180 - 90° = 90° (sum of the angle ABD and BDC) we divide by two and we find the value of the single angles, 90:2=45°.

Then pass to AC which is a straight line, value 180°, subtract 45° and you have 135° of the angle BDC, subtract 135 from 180 and you have the sum of the two congruent angles (DBC and BCD) , finally divide by two and you have 22.5° which is the your answer. I hope I was clear.

The proof is completed as follows

   Statement                               Reason

6. Δ ABC ~ Δ CDB            AA similarity postulate

7. a/x = c/a                        Ratios of corresponding sides of similar triangles

8. a² = cx                          Cross multiplying

9. ∠ CDA ≅ ∠ BDA          All right angles are congruent

10. ∠ A ≅ ∠ A                   Reflexive property

11. Δ ABC ~ Δ ADC          AA similarity postulate

12. b/y = c/b                     Ratios of corresponding sides of similar triangles

13. b² = cy                        Cross multiplying

14. a² + b² = cx + cy         Addition property

15. a² + b² = c(x + y)         Distributive property

16. x + y = c                      Addition property

17. a² + b² = c²                 Substitution property

Pythagoras' theorem, named after the ancient Greek mathematician Pythagoras, states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Mathematically, it can be expressed as:

c² = a² + b²

The step by step proof allowed to prove Pythagoras theorem using similar triangles

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Answer:

$17.95

Step-by-step explanation:

To calculate the stock price of Z-prime, we can use the dividend discount model (DDM), which values a stock based on the present value of its future dividends.

Given that Z-prime's earnings and dividends per share are expected to grow by 4% per year until year 4, and it will pay out all earnings as dividends from year 5 onwards, we can calculate the dividends for years 1 to 4 and the terminal dividend in year 5.

First, we need to calculate the dividends for years 1 to 4:

Year 1 dividend = $4

Year 2 dividend = Year 1 dividend * (1 + 4%) = $4 * 1.04 = $4.16

Year 3 dividend = Year 2 dividend * (1 + 4%) = $4.16 * 1.04 = $4.3264

Year 4 dividend = Year 3 dividend * (1 + 4%) = $4.3264 * 1.04 = $4.502656

From year 5 onwards, Z-prime will pay out all earnings as dividends. So, the dividend in year 5 and beyond will be equal to the EPS (earnings per share) value.

Year 5 and onwards dividend = $9

Now, we can calculate the present value of these dividends using the market capitalization rate of 14%:

PV (present value) = Dividend / (1 + Market Capitalization Rate)^(Year - Current Year)

Let's calculate the present value for each dividend:

PV1 = $4 / (1 + 14%)^(1-0) = $4 / 1.14 = $3.5088

PV2 = $4.16 / (1 + 14%)^(2-0) = $4.16 / 1.2996 = $3.1994

PV3 = $4.3264 / (1 + 14%)^(3-0) = $4.3264 / 1.4895 = $2.9073

PV4 = $4.502656 / (1 + 14%)^(4-0) = $4.502656 / 1.6906 = $2.6639

PV5 = $9 / (1 + 14%)^(5-0) = $9 / 1.925 = $4.6753

Finally, we can calculate the stock price by summing up the present values of the dividends:

Stock Price = PV1 + PV2 + PV3 + PV4 + PV5

Stock Price = $3.5088 + $3.1994 + $2.9073 + $2.6639 + $4.6753

Stock Price = $17.9547

Therefore, Z-prime's stock price is $17.95.

Answer:

[tex]\frac{(x-7)^2}{8^2} + \frac{(y-2)^2}{17^2} = 1[/tex]

Step-by-step explanation:

Major axis length 2a

⇒ 2a = 34

⇒ a = 34/2

⇒ a = 17

General eq of ellipse:

[tex]\frac{(x-h)^2}{b^2} + \frac{(y-k)^2}{a^2} = 1[/tex]

centre : (h,k)

foci: (h, k+c) and (h,k-c)

Gn. foci : (7, 17) and (7, -13)

Comparing the above 2 lines,

h = 7,

k + c = 17   -eq(1)

k - c = -13   -eq(2)

eq(1) + eq(2):

(k + c) + (k - c) = 17 + (-13)

2k = 4

k = 2

sun k = 2 in eq(1):

2 + c = 17

c = 15

Also, c² = a² - b²

b² = a² - c²

= 17² - 15²

= 64

b² = 8²

b = 8

substituting in ellipse eq,

[tex]\frac{(x-7)^2}{8^2} + \frac{(y-2)^2}{17^2} = 1[/tex]

Answer:

[tex]\dfrac{(x-7)^2}{64}+\dfrac{(y-2)^2}{289}=1[/tex]

Step-by-step explanation:

As the foci of the ellipse have the same x-value, the ellipse is vertical.

The formula for a vertical ellipse is:

[tex]\boxed{\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1}[/tex]

where:

Given the major axis is 34:

The center of an ellipse is located at the midpoint between its two foci.

Given the foci are (7, 17) and (7, -13), the center of the ellipse is:

[tex](h, k) = (7, 2)[/tex]

As the formula for the foci is (h, k±c), then (k, h±c) = (7, 2±c). Therefore:

[tex]\begin{aligned}2\pm c &= 17, -13\\\pm c &= 15, -15\\c &= 15\end{aligned}[/tex]

The vertices are:

[tex]\begin{aligned}(h, k\pm b) &= (7, 2 \pm 17)\\& = (7, 19) \; \textsf{and}\; (7, -15)\end{aligned}[/tex]

To find the value of a, substitute the values of b and c into c² = b² - a²:

[tex]\begin{aligned}c^2&=b^2-a^2\\15^2&=17^2-a^2\\a^2&=\sqrt{17^2-15^2}\\a^2&=64\\a&=8\end{aligned}[/tex]

The co-vertices are:

[tex]\begin{aligned}(h \pm a, k) &= (7 \pm 8, 2)\\& = (-1,2) \; \textsf{and}\; (15,2)\end{aligned}[/tex]

Therefore:

To find the equation of the ellipse, substitute these values into the formula:

[tex]\boxed{\dfrac{(x-7)^2}{64}+\dfrac{(y-2)^2}{289}=1}[/tex]

The magnitude of the acceleration is a constant value of 18

Each part of the location vector's second derivative must be calculated.

Given:

x = 402 + 8t

y = 2 cos(3t)

z = 2 sin(3t)

The position vector r(t) = (x, y, z)

First, let's find the velocity vector v(t) by taking the first derivative of each component:

v(t) = (dx/dt, dy/dt, dz/dt)

v(t) = (8, -6 sin(3t), 6 cos(3t))

Next, let's find the acceleration vector a(t) by taking the first derivative of each component of the velocity vector:

a(t) = (d²x/dt², d²y/dt², d²z/dt²)

a(t) = (0, -18 cos(3t), -18 sin(3t))

Finally, we can find the magnitude of the acceleration vector:

|a(t)| = √[(d²x/dt²)² + (d²y/dt²)² + (d²z/dt²)²]

|a(t)| = √[0² + (-18 cos(3t))² + (-18 sin(3t))²]

|a(t)| = √(324 cos²(3t) + 324 sin²(3t))

|a(t)| = √324 (cos²(3t) + sin²(3t))

|a(t)| = 18

Therefore, the magnitude of the acceleration is a constant value of 18.

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From the given parameters the magnitude of the acceleration is  18

Recall that the magnitude of acceleration is a physical term defined as the ratio of velocity variation to time, represented by the equation a = v/t. It is a vector quantity that includes both magnitude and direction

x = 402 + 8t

y = 2 cos(3t)

z = 2 sin(3t)

The position vector r(t) = (x, y, z)

But, the velocity vector v(t) by taking the first derivative of each component:

v(t) = (dx/dt, dy/dt, dz/dt)

v(t) = (8, -6 sin(3t), 6 cos(3t))

And  the acceleration vector a(t) by taking the first derivative of each component of the velocity vector:

a(t) = (d²x/dt², d²y/dt², d²z/dt²)

a(t) = (0, -18 cos(3t), -18 sin(3t))

Now, the magnitude of the acceleration vector:

|a(t)| = √[(d²x/dt²)² + (d²y/dt²)² + (d²z/dt²)²]

|a(t)| = √[0² + (-18 cos(3t))² + (-18 sin(3t))²]

|a(t)| = √(324 cos²(3t) + 324 sin²(3t))

|a(t)| = √324 (cos²(3t) + sin²(3t))

|a(t)| = 18

In conclusion,  magnitude of the acceleration is 18.

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In triangle APQR, we have:

AP = AQ = 400 inches

PQ = 420 inches

PR = 440 inches

In triangle APQ, we have:

AP = AQ = p = 400 inches (sides of an isosceles triangle are equal)

In triangle PQR, we have:

PQ = q = 420 inches

Let's calculate the length of side PR:

PR = 2PQ - AP

PR = 2(420) - 400

PR = 840 - 400

PR = 440 inches

Therefore, in triangle APQR, we have:

AP = AQ = 400 inches

PQ = 420 inches

PR = 440 inches

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The probability of selecting a white marble from the box is approximately 0.381 or 8/21.

To find the probability of selecting a white marble, we need to determine the total number of marbles in the box and the number of white marbles specifically.The total number of marbles in the box is the sum of the red, white, and blue marbles:

Total marbles = 4 (red marbles) + 8 (white marbles) + 9 (blue marbles) = 21 marbles.

Now, we can calculate the probability of selecting a white marble by dividing the number of white marbles by the total number of marbles:

Probability of selecting a white marble = Number of white marbles / Total number of marbles = 8 / 21.

To express this probability as a decimal, we divide 8 by 21:

8 / 21 = 0.381.Rounded to three decimal places, the probability of selecting a white marble from the box is approximately 0.381.In fraction form, the probability can be written as 8/21.

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The three shapes that have rectangular cross-sections when cut perpendicular to the base are the rectangular prism, while the cylinder, cone, and sphere do not.

To determine which shapes have rectangular cross-sections when cut perpendicular to the base, we need to consider the properties of each shape.

Rectangular Prism: A rectangular prism has a rectangular base, and when cut perpendicular to the base, the cross-sections will also be rectangles. This is because the cuts will be parallel to the base, resulting in rectangular slices.

Cylinder: A cylinder has a circular base, and when cut perpendicular to the base, the cross-sections will be circles. This is because the cuts will be parallel to the circular base, resulting in circular slices. Therefore, a cylinder does not have a rectangular cross-section.

Cone: A cone has a circular base, and when cut perpendicular to the base, the cross-sections will be triangles. This is because the cuts will intersect the circular base at an angle, resulting in triangular slices. Therefore, a cone does not have a rectangular cross-section.

Sphere: A sphere is a perfectly round shape, and when cut perpendicular to any direction, the cross-sections will always be circles. Therefore, a sphere does not have a rectangular cross-section.

Based on the above analysis, the three shapes that have rectangular cross-sections when cut perpendicular to the base are the rectangular prism, while the cylinder, cone, and sphere do not.

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Answer:

? ≈ 33.40°

Step-by-step explanation:

using the Sine rule in the triangle

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex]

with a = 12.34, b = 7 , ∠ A = 76° , ∠ B = ? , then

[tex]\frac{12.34}{sin76}[/tex] = [tex]\frac{7}{sin?}[/tex] ( cross- multiply )

12.34 × sin? = 7 × sin76° ( divide both sides by 12.34 )

sin ? = [tex]\frac{7sin76}{12.34}[/tex] . then

? = [tex]sin^{-1}[/tex] ( [tex]\frac{7sin76}{12.34}[/tex] ) ≈ 33.40° ( to the nearest hundredth )

The p-value is given as follows:

0.2297.

The correct statement is given as follows:

A. Since p-value > α, do not reject the null hypothesis.

The equation for the test statistic is given as follows:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]n = 150, \pi = \frac{78}{150} = 0.52[/tex]

The test statistic is given as follows:

[tex]z = \frac{0.52 - 0.55}{\sqrt{\frac{0.52(0.48)}{150}}}[/tex]

z = -0.74.

The p-value of z = -0.74 on the z-table is given as follows:

0.2297.

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Answer:

The probability that your favorite song is played first is 1/60

Step-by-step explanation:

We assume that all 5 CDs have different songs so that only one of CDs will have our favorite song.

Then The probability that the CD that contains the song comes first will be,

(since there are 5 CDs)

1/5

And that CD has 12 songs, the probability that our favorite song will play first is then,

1/12

The total probability of our favorite song playing will be the product of these two, so,

P = (1/5)(1/12) = 1/60

P = 1/60

The probability that your favorite song is played first is 1/60

The width of the rectangular playing field is 51 yards, and the length is 4(51) + 3 = 207 yards.

Let's assume the width of the rectangular playing field is 'x' yards.

According to the given information, the length is 3 yards longer than quadruple the width, which means the length is 4x + 3 yards.

The formula for the perimeter of a rectangle is P = 2(l + w), where P represents the perimeter, l represents the length, and w represents the width.

Substituting the given values into the formula, we have 516 = 2((4x + 3) + x).

Simplifying the equation, we get 516 = 10x + 6.

By rearranging the equation, we have 10x = 516 - 6, which gives 10x = 510.

Dividing both sides by 10, we find x = 51.

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The partial fraction decomposition of 4x + 40 in terms of x is: 4x + 40 = 8(x + 6) - 4(x + 2)

To find the partial fraction decomposition of the expression 4x + 40, we start by setting it equal to the sum of two fractions with unknown numerators and common denominators. In this case, the common denominator is (x + 6)(x + 2).

The equation is:

4x + 40 = A(x + 6) + B(x + 2)

Next, we distribute the factors on the right side of the equation:

4x + 40 = Ax + 6A + Bx + 2B

To simplify the equation, we combine like terms on the right side:

4x + 40 = (A + B)x + (6A + 2B)

Now, we can equate the coefficients of the like terms on both sides. Since the equation holds true for all values of x, the coefficients must be equal.

The coefficients of x on both sides of the equation are:

4 = A + B

The constant terms on both sides of the equation are:

40 = 6A + 2B

We have obtained a system of equations:

A + B = 4

6A + 2B = 40

We can solve this system of equations to find the values of A and B.

From the first equation, we have A = 4 - B.

Substituting this value of A into the second equation, we get:

6(4 - B) + 2B = 40

24 - 6B + 2B = 40

-4B + 24 = 40

-4B = 16

B = -4

Substituting the value of B back into the first equation, we find:

A + (-4) = 4

A - 4 = 4

A = 8

Therefore, the partial fraction decomposition of 4x + 40 in terms of x is:

4x + 40 = 8(x + 6) - 4(x + 2)

or, simplifying:

4x + 40 = 8x + 48 - 4x - 8

4x + 40 = 4x + 40

The original expression 4x + 40 is already decomposed into partial fractions, and it simplifies back to itself.

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(f+g)(4) = 37, and it does exist. The value of (f+g)(4) is equal to the sum of f(x) and g(x) evaluated at x=4, which is 37.

To find (f+g)(4), we need to first determine what the sum of f(x) and g(x) is, and then substitute x = 4 into the resulting expression.

Summing f(x) = x^2-2 and g(x) = 5x+3, we get:

(f+g)(x) = x^2-2 + 5x+3

(f+g)(x) = x^2 + 5x + 1

Substituting x = 4 into f+g, we get:

(f+g)(4) = 4^2 + 5(4) + 1

(f+g)(4) = 16 + 20 + 1

(f+g)(4) = 37

This means that if we add the functions f(x) and g(x) together and then compute the resulting function at x=4, we get 37 as the final answer.

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Answer:  The discrepancy between the stated distance and the actual distance is 499.2 kilometers.

Step-by-step explanation:

, the distance between Bloemfontein and Upington is approximately 663 kilometers.

Therefore, the statement made by Siphenathi that the distance from Bloemfontein to Upington is 163.8 km is incorrect. The actual distance is significantly longer,

Calculations:

Distance from Bloemfontein to Upington according to Siphenathi: 163.8 km

Actual distance from Bloemfontein to Upington: 663 km

Discrepancy: 663 km - 163.8 km = 499.2 km

Answer:

12x^2 + 9x - 8 = 0

Step-by-step explanation:

To find the quadratic equation with roots 2/3 and -3/4, we can use the fact that if a quadratic equation has roots r and s, then it can be written in the form:

(x - r)(x - s) = 0

Expanding this equation gives:

x^2 - (r + s)x + rs = 0

So, for the roots 2/3 and -3/4, we have:

(x - 2/3)(x + 3/4) = 0

Expanding this equation gives:

x^2 + (3/4 - 2/3)x - (2/3)(3/4) = 0

Multiplying through by 12 to eliminate the fractions, we get:

12x^2 + 9x - 8 = 0

So, the quadratic equation with roots 2/3 and -3/4 is:

12x^2 + 9x - 8 = 0

The member earns a total of 325 points. This is how we write a function rule for total points in a popular coffee store.

To write a function rule for total points that members earn in a popular coffee store, some factors need to be considered. These factors are the value of each point, the amount of points members earn for signing up, and the total amount of money members spend to earn points.

To begin, each $1 spent is worth 2.5 points.

Therefore, if members spend x dollars, they earn 2.5x points. For instance, if a member spends $10, they will earn 2.5 × 10 = 25 points.

Additionally, members can earn 200 points when they sign up. This implies that the total points members can earn is 200 + 2.5x.

This total point earned can be expressed as a function of the amount spent in the store. Hence, we can use the following formula:

y = 200 + 2.5xWhere y represents the total points earned and x represents the total amount spent in the store.

To illustrate, if a member spends $50 on coffee, their total point earned will be:

y = 200 + 2.5(50)y = 200 + 125y = 325

Therefore, the member earns a total of 325 points. This is how we write a function rule for total points in a popular coffee store.

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Answer:

Step-by-step explanation:

Because ABCD is a parallelogram, then ∠A = ∠C and ∠B = ∠D. In a parallelogram, all angles will sum up to 360°.

So,

∠A + ∠B + ∠C + ∠D = 360°

2x + (9x+15°) + 2x + (9x+15°) = 360°

22x + 30° = 360°

22x = 330°

x = 15°

Now, we know the value of x. Let's find the value of ∠A

∠A = 2x

∠A = 2 . 15°

∠A = 30°

The final answer is, ∠A = 30°

The value of [tex]\displaystyle\sf (-1+\sqrt{-3})^{33}+(-1-\sqrt{-3})^{33}[/tex] is approximately -2.

15

We can use the properties of equality to find unknown variables.

Properties of Equality

The properties of equality (PoE) show us how we can manipulate an equation while maintaining equality. One of the most common properties of equality is the subtraction property of equality. The addition PoE says that if you add the same number to each side then the equation is still true. The other PoEs like subtraction, multiplication, and division PoEs work the same.

Solving for x

Using the PoEs above, we can solve for x. First, we need to rewrite the equation.

Then, add 17 to both sides using the addition PoE.

Finally, divide both sides by 2 using the division PoE.

In this equation, x = 15. Additionally, this shows how we can manipulate equations to solve for x.

Answer:

OL = 14 or 10

Step-by-step explanation:

Let OL = x

               ON = LN - OL

                      = 24 - x

Chord intersecting theorem:

    If two chords intersect inside a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

        OL * ON = OM * OP

      x * (24 - x) = 20 * 7

       x*24 - x*x = 140

        24x - x²   = 140

 x² - 24x + 140 = 0

Factors are (-14) and (-10). When we add (-14) and (-10), we get -24 & when we multiply (-14) and (-10), we get 140.

Rewrite the middle term using the factors.

x² - 14x - 10x + 140 = 0

x(x - 14) - 10(x - 14)   = 0

         (x - 14)(x - 10)  = 0

x - 14 = 0   or x - 10 = 0

      x = 14  or x = 10

OL = 14 or 10

Answer:

(149625π) / 1512

Step-by-step explanation:

Area of Sector = (θ/360) * π * r^2

Where θ is the central angle of the sector, π is the value of pi, and r is the radius of the sector

Given:

θ = 299 degrees

π = 3 1/7

r = 15 m

1. Convert the angle θ to radians by multiplying it by (π/180)

θ = 299 degrees * (π/180) = (299π/180) radians

2. Substitute the values into the formula

Area of Sector = ((299π/180)/360) * (3 1/7) * (15^2)

3. Simplify the expression

Area of Sector = (299π/64800) * (22/7) * 225

4. Multiply the fractions and simplify

Area of Sector = (299 * 22 * 225 * π) / (64800 * 7)

Final Answer:

Area of Sector = (149625π) / 1512

In simplest form, the average rate of change of the function over the interval 4 ≤ x ≤ 8 is 751.75.

To find the average rate of change of the function over the interval 4 ≤ x ≤ 8, we need to calculate the difference in function values and divide it by the difference in x-values.

The function values corresponding to the given x-values are as follows:

x f(x)

4 225

5 446

6 887

7 1616

8 3232

To calculate the average rate of change, we use the formula:

Average Rate of Change = (Change in f(x))/(Change in x)

The change in f(x) over the interval is f(8) - f(4) = 3232 - 225 = 3007.

The change in x over the interval is 8 - 4 = 4.

Therefore, the average rate of change is:

Average Rate of Change = 3007/4 = 751.75.

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