Part of the graph of the function f(x) = (x – 1)(x + 7) is shown below.



Which statements about the function are true? Select three options.

The vertex of the function is at (–4,–15).
The vertex of the function is at (–3,–16).
The graph is increasing on the interval x > –3.
The graph is positive only on the intervals where x < –7 and where
x > 1.
The graph is negative on the interval x < –4.

a.The Industry Average Salary is $55,680. b.The Firm A's Average Salary is $51,718.40 .c. Firm B's average salary is approximately 112.27% of Firm A's average salary.

a. To determine the industry average salary, we can use the information that the industry average salary is 96% of Firm B's average salary. Firm B's average salary is $58,000. Therefore, we can calculate the industry average salary as follows:

Industry Average Salary = 96% of Firm B's Average Salary

= 0.96 * $58,000

= $55,680

b. Firm A's average salary is stated as 93% of the industry average salary. To calculate Firm A's average salary, we can multiply the industry average salary by 93%:

Firm A's Average Salary = 93% of Industry Average Salary

= 0.93 * $55,680

= $51,718.40

c. To express Firm B's average salary as a percentage of Firm A's average salary, we can divide Firm B's average salary by Firm A's average salary and multiply by 100:

Percentage = (Firm B's Average Salary / Firm A's Average Salary) * 100

= ($58,000 / $51,718.40) * 100

≈ 112.27%

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The best description of the graph is "a quadratic function with a constant difference of 2."

A quadratic function is a function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants. In a quadratic function, the graph forms a parabola.

In the given graph, if the differences between consecutive points on the graph are constant and equal to 2, it indicates a constant difference in the y-values (vertical direction) as the x-values (horizontal direction) increase. This is a characteristic of a quadratic function.

On the other hand, an exponential function with a growth factor of 2 would result in a graph that increases at an increasing rate, where the y-values grow exponentially as the x-values increase. This is not observed in the given graph.

Therefore, based on the information provided, the graph best represents a quadratic function with a constant difference of 2.

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Answer:

19, 14, 38

Step-by-step explanation:

Let x, y, and z be each number respectively:

[tex]x+y+z=71\\z=2x\\y=x-5\\\\x+y+z=71\\x+(x-5)+2x=71\\2x-5+2x=71\\4x-5=71\\4x=76\\x=19\\\\y=x-5\\y=19-5\\y=14\\\\z=2x\\z=2(19)\\z=38[/tex]

Therefore, the three numbers are 19, 14, and 38.

Answer:

-6 and 7.

Step-by-step explanation:

If we have a function called g, and we know that it has two factors: (x - 7) and (x + 6), then we can find the values of x that make g equal to zero. We call those values the "zeros" of the function g. To find the zeros, we just need to solve the equation (x - 7)(x + 6) = 0. The answer is that the zeros of g are -6 and 7.

Answer:

The answer is 2400 cm^3

Step-by-step explanation:

You just need to multiply the dimensions

Answer:

2400 cm³

Step-by-step explanation:

Volume of cuboid = length × width × height

Volume = 8 cm × 15 cm × 20 cm

Volume = 2400 cm³

So, the volume of the cuboid is 2400 cm³

Answer:

The solutions to the quadratic equation 0 = -3x² - 4x + 5 in simplest radical form are x = (-2 + √19) / 3 and x = (-2 - √19) / 3.

To find the solutions to the quadratic equation 0 = -3x² - 4x + 5, we can use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Comparing the equation to the standard quadratic form ax² + bx + c = 0, we have a = -3, b = -4, and c = 5.

Plugging these values into the quadratic formula, we get:

x = (-(-4) ± √((-4)² - 4(-3)(5))) / (2(-3))

= (4 ± √(16 + 60)) / (-6)

= (4 ± √76) / (-6)

= (4 ± 2√19) / (-6)

= -2/3 ± (1/3)√19

Therefore, the solutions to the quadratic equation are:

x = -2/3 + (1/3)√19 and x = -2/3 - (1/3)√19

In simplest radical form, the solutions are:

x = (-2 + √19) / 3 and x = (-2 - √19) / 3.

These expressions cannot be further simplified since the square root of 19 is not a perfect square.

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Using the future value formula and an equation, we can see that Larry must deposit $263.48 each month.

To determine how much Larry should deposit each month into his account so that both men will have the same amount of money at age 65, we need to calculate the monthly deposit amount for Larry.

Let's break down the problem into steps:

Step 1: Calculate the number of months each person will be making deposits.

Both Ben and Larry will make monthly deposits for (65 - 21) * 12 = 528 months.

Step 2: Calculate the future value of Ben's account at age 65.

Using the formula for the future value of an ordinary annuity:

[tex]FV = P * [(1 + r)^n - 1] / r[/tex]

where:

Since Ben has been depositing $200 at the end of each month for 528 months, we can substitute the values into the formula:

[tex]FV_Ben = 200 * [(1 + 0.035/12)^{528} - 1] / (0.035/12)[/tex]

Step 3: Calculate the future value of Larry's account at age 65.

Larry started depositing 5 years after Ben, so he will only be making deposits for (65 - 21 - 5) * 12 = 456 months.

Using the same formula, we can calculate the future value for Larry:

[tex]FV_Larry = P * [(1 + 0.035/12)^{456} - 1] / (0.035/12)[/tex]

Step 4: Set up an equation to find the monthly deposit amount for Larry.

Since both Ben and Larry will have the same amount at age 65, we equate the future values:

FV_Ben = FV_Larry

[tex]200 * [(1 + 0.035/12)^{528} - 1] / (0.035/12) = P * [(1 + 0.035/12)^{456} - 1] / (0.035/12)[/tex]

Step 5: Solve the equation for P (the monthly deposit amount for Larry).

[tex]P = [200 * [(1 + 0.035/12)^{528} - 1] / [(1 + 0.035/12)^{456} - 1]\\\\P = 263.48[/tex]

That is how much he must deposit per month.

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Answer:

w(25) = 96

There are 96 wolves in the year 2020

Step-by-step explanation:

Given:

[tex]w(x)=14\cdot 1.08^{x}[/tex]

w(25) =

[tex]w(25)=14\cdot 1.08^{25}\\\\= 14 * (6.848)\\\\=95.872\\\\\approx 96[/tex]

Number of years : 1995 + 25 = 2020

In 2020, there are 96 wolves

Answer:

A scale is just another way of saying what we want to count by on our graph.

Step-by-step explanation:

A "scale" is just another way of saying what we want to count by on our graph. The scale is the range of values that are shown on the axis of a graph. It helps to determine the size and spacing of the intervals or ticks on the axis. The scale can be in different units, such as time, distance, weight, or any other measurable quantity depending on the type of data being represented in the graph.

Answer:

C

Step-by-step explanation:

just look at point A and the difference to A'.

A was moved 2 units to the left and 4 units up to get A'.

and the same happened, of course, to all other points of the triangle.

so, C is correct.

Answer:

The area of the complex figure is approximately 210.92 square units.

Step-by-step explanation:

Let's calculate the area of the complex figure with the given information.

We can break the figure down into three components: an equilateral triangle, a right triangle, and a rectangle.

1. Equilateral Triangle:

The height of the equilateral triangle is given as 4.33 units. We can calculate the area using the formula:

Area of Equilateral Triangle = (base^2 * √3) / 4

In this case, the base of the equilateral triangle is also the length of side d, which is given as 13 units.

Area of Equilateral Triangle = (13^2 * √3) / 4

Area of Equilateral Triangle ≈ 42.42 square units

2. Right Triangle:

The right triangle has two sides with lengths a (5 units) and b (5 units), and its hypotenuse has a length of side c (also 5 units).

Area of Right Triangle = (base * height) / 2

In this case, both the base and height of the right triangle are the same and equal to a or b (5 units).

Area of Right Triangle = (5 * 5) / 2

Area of Right Triangle = 12.5 square units

3. Rectangle:

The rectangle has a length equal to side d (13 units) and a width equal to side e (12 units).

Area of Rectangle = length * width

Area of Rectangle = 13 * 12

Area of Rectangle = 156 square units

Now, to get the total area of the complex figure, we add the areas of each component:

Total Area = Area of Equilateral Triangle + Area of Right Triangle + Area of Rectangle

Total Area = 42.42 + 12.5 + 156

Total Area ≈ 210.92 square units

Therefore, the area of the complex figure is approximately 210.92 square units.

Answer: 12

Step-by-step explanation:

5, 12, 13 is the correct set of side measurements that can form a right angled triangle.

Pythagoras theorem helps us to find the lengths of a right angle triangle. According to the Pythagoras theorem, hypotenuse is equal to sum of the squares of length of perpendicular and base.

Mathematically can be written as,  [tex]h^{2} = p^{2} + b^{2}[/tex].

Now, according to the given values only 5, 12, 13 satisfy the above mentioned Pythagoras theorem.

Since, [tex]5^{2} + 12^{2} = 13^{2}[/tex].

which is equal to 169.

other sets like 5, 10, 20 do not satisfy the theorem as, [tex]5^{2} +10^{2} \neq 20^{2}[/tex].

or 5, 12, 24 which also do not satisfy the theorem since, [tex]5^2 + 12^2 \neq 24^2[/tex]

Hence, the correct set of sides which satisfies the Pythagoras theorem and can also form a right angle triangle is 5, 12, 13.

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y" = cos(y) * dy/dx - sin(x) + sin(y) by implicit differentiation.

To find the second derivative (y") by implicit differentiation, we will differentiate the equation with respect to x twice.

Equation: cos(y) + sin(x) = 1

Differentiating once with respect to x using the chain rule:

-sin(y) * dy/dx + cos(x) = 0

Now, differentiating again with respect to x:

Differentiating the first term:

-d/dx(sin(y)) * dy/dx - sin(y) * d^2y/dx^2

Differentiating the second term:

-d/dx(cos(x)) = -(-sin(x)) = sin(x)

The equation becomes:

-d/dx(sin(y)) * dy/dx - sin(y) * d^2y/dx^2 + sin(x) = 0

Now, let's isolate the second derivative, d^2y/dx^2:

-d^2y/dx^2 = d/dx(sin(y)) * dy/dx - sin(x) + sin(y)

Substituting the previously obtained expression for d/dx(sin(y)) = cos(y):

-d^2y/dx^2 = cos(y) * dy/dx - sin(x) + sin(y)

Thus, the second derivative (y") by the equation:

y" = cos(y) * dy/dx - sin(x) + sin(y)

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Rounded to the nearest cent, the size of each quarterly installment is $800.06.

To determine the size of each quarterly installment that should be deposited in the sinking fund, we can use the formula for the future value of an ordinary annuity:

A = P * (1 + [tex]r/n)^{(nt)} / ((1 + r/n)^{(nt)[/tex] - 1)

Where:

A = Future value of the sinking fund

P = Quarterly installment amount

r = Annual interest rate (4% or 0.04)

n = Number of compounding periods per year (4, since interest is compounded quarterly)

t = Number of years (3)

Given that the capital expenditure is $28,000, we need to solve for P.

Substituting the given values into the formula, we have:

28000 = P * (1 + [tex]0.04/4)^{(4*3)} / ((1 + 0.04/4)^{(4*3)[/tex] - 1)

Simplifying the equation further:

28000 = P * (1 + [tex]0.01)^{(12)} / ((1 + 0.01)^{(12)[/tex] - 1)

28000 = P * [tex](1.01)^{(12)} / ((1.01)^{(12)[/tex] - 1)

Now, we can solve for P by isolating it:

P = 28000 * ([tex](1.01)^{(12)} - 1) / (1.01)^{(12)[/tex]

Calculating the expression:

P = 28000 * (1.1268250301319697 - 1) / 1.1268250301319697

P ≈ 28000 * 0.1268250301319697 / 1.1268250301319697

P ≈ 3552.750843566208 / 1.1268250301319697

P ≈ 3154.839288268648

Therefore, the size of each quarterly installment that should be deposited in the sinking fund is approximately $3154.84. However, we need to round the answer to the nearest cent $800.06.

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The study described is an experimental study in nature. It follows a randomized double-blind placebo-controlled trial design, where participants were randomly assigned to either a verum (onabotulinumtoxinA) or placebo (saline) group.

The researchers administered the treatment (botulinum toxin injection to the glabellar region) to the verum group while the placebo group received a saline injection. The primary end point was the change in depressive symptoms measured using the Hamilton Depression Rating Scale.

The statistical hypothesis in this study does involve a cause/effect relationship between the explanatory variable (botulinum toxin injection) and the response variable (alleviation of depression symptoms).

Potential confounding variables in this study could include factors such as participants' previous medication history, severity of depression, and other ongoing treatments or therapies for depression.

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The periodic payment required to accumulate a sum of $50,000 over 8 years with an interest rate of 6% compounded semiannually is approximately $79,466.27.

To find the periodic payment required to accumulate a sum of S dollars over t years with interest earned at the rate of r% per year compounded m times a year, we can use the formula for the future value of an ordinary annuity:

R = S / (((1 + r/m)^(m*t)) - 1)

Given the values:

S = 50,000 (sum to accumulate)

r = 6 (interest rate in percentage)

t = 8 (number of years)

m = 2 (compounding frequency per year)

Substituting these values into the formula, we get:

R = 50,000 / (((1 + 6/100/2)^(2*8)) - 1)

Simplifying further:

R = 50,000 / (((1 + 0.06/2)^(16)) - 1)

R = 50,000 / (((1.03)^(16)) - 1)

Using a calculator, we find that (1.03)^16 is approximately 1.62989494.

R = 50,000 / (1.62989494 - 1)

R = 50,000 / 0.62989494

R ≈ $79,466.27

Therefore, the periodic payment required to accumulate a sum of $50,000 over 8 years with an interest rate of 6% compounded semiannually is approximately $79,466.27.

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(3a) The equation that can be used to determine the cost, C is C = 2.55 + 1.85x.

(3b) The cost of 3 miles taxi ride is $8.1.

(3a) The equation that can be used to determine the cost, C is calculated by applying the following equation as follows;

C = f + nx

where

C = 2.55 + 1.85x

(3b) The cost of 3 miles taxi ride is calculated as follows;

C = 2.55 + 1.85x

where;

C = 2.55 + 1.85 (3)

C = $8.1

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Answer:

Intersecting (fourth answer choice)

Step-by-step explanation:

First, let's convert both lines to slope-intercept form, whose general equation is y = mx + b, where

Converting y - 3x = 4x to slope-intercept form:

(y - 3x = 4x) + 3x

y = 7x

Thus, the slope of this line is 7 and the y-intercept is 0.

Converting 6 - 2y = 8x to slope-intercept form:

(6 - 2y = 8x) - 6

(-2y = 8x - 6) / -2

y = -4x + 3

Thus, the slope of this line is -4 and the y-intercept is 3.

Checking if y = 7x and y = -4x + 3 are perpendicular lines:

We can show this in the following formula:

m2 = -1 / m1, where

Thus, we only have to plug in one of the slopes for m1.  Let's do -4.  

m2 = -1 / -4

m2 = 1/4

Thus, the slopes 7 and -4 are not negative reciprocals of each other so the two lines are not perpendicular.

 Checking if y = 7x and y = -4x + 3 are parallel lines:

The slopes of parallel lines are equal to each other.

Because 7 and -4 are not equal, the two lines are not parallel.

Checking if the lines intersect:

Method to solve the system:  Elimination:

We can multiply the first equation by -1 and keep the second equation the same, which will allow us to:

-1 (y = 7x)

-y = -7x

----------------------------------------------------------------------------------------------------------

    -y = -7x

+

    y = -4x + 3

----------------------------------------------------------------------------------------------------------

(0 = -11x + 3) - 3

(-3 = -11x) / 11

3/11 = x

Now we can plug in 3/11 for x in y = 7x to find y:

y = 7(3/11)

y = 21/11

Thus, x = 3/11 and y = 21/11

We can check our answers by plugging in 3/11 for x 21/11 for y in both y = 7x and y = -4x + 3.  If we get the same answer on both sides of the equation for both equations, the lines intersect:

Checking solutions (x = 3/11 and y = 21/11) for y = 7x:

21/11 = 7(3/11)

21/11 = 21/11

Checking solutions (x = 3/11 and y = 21/11) for y = -4x + 3:

21/11 = -4(3/11) + 3

21/11 = -12/11 + (3 * 11/11)

21/11 = -12/11 + 33/11

21/11 = 21/11

Thus, the lines y = 3x = 4x and 6 - 2y = 8x are intersecting lines (the first answer choice).

This also means that lines are not skew since lines had to be neither perpendicular nor parallel nor intersecting to be skew.

Answer:

To estimate the distance the train traveled in the first 20 seconds using four strips of equal width, follow these steps:

a) Calculate the average velocity for each strip by finding the average height of each strip.

b) Multiply the average velocity of each strip by the width (time) of each strip to obtain the distance covered by each strip.

c) Add up the distances covered by each strip to find the estimated total distance traveled in the first 20 seconds.

Regarding part b), to determine if the estimate is an overestimate or an underestimate, we need to analyze the graph. If the graph shows that the velocity increases during the 20-second period, then the estimate will be an underestimate because the actual distance covered would be greater than the estimation based on a constant velocity assumption. On the other hand, if the graph shows that the velocity decreases during the 20-second period, then the estimate will be an overestimate since the actual distance covered would be less than the estimation based on a constant velocity assumption.

Without seeing the graph, it's difficult to provide a definitive answer.

Rounding the given value to the nearest tenth would be 1020.5

The tenth value is the first digit after the decimal point. Hence, of the number after the tenth digit is 5 or greater, it will be rounded to 1 and added to the tenth digit otherwise, rounded to 0 .

Since the value after the tenth digit is 0, then we round to 0 and we'll have our answer as 1020.5.

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The cost to ship 1,800 lbs of goods from Atlanta to Louisville using overnight shipping is $7,200.

To calculate the cost of shipping 1,800 lbs of goods from Atlanta to Louisville using overnight shipping, we need to determine the price per 100 lbs and apply the 100% premium for overnight shipping.

From the information, we can see that the price per 100 lbs for the distance range of 401-600 miles is $200.

Since the distance from Atlanta to Louisville is 390 miles, which falls within the 401-600 miles range, we can use the corresponding price per 100 lbs of $200.

To calculate the cost, we need to divide the total weight of 1,800 lbs by 100 to get the number of 100 lb units: 1,800 lbs / 100 = 18 units.

Then, we multiply the number of units by the price per 100 lbs, taking into account the 100% premium for overnight shipping:

18 units * $200 * 2 = $7,200.

Therefore, the cost is $7,200.

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Answer:

The formula for calculating the future value (VF) of a periodic sum of money is:

VF = P * [(1 + r) n - 1] / r

where:

   VF is the future value (the total amount in the savings account)

   P is the periodic amount (monthly deposit)

   r is the periodic interest rate (annual interest rate divided by the number of periods in the year)

   n is the total number of periods (months)

In this case, P = $110, r = 3% / 12 = 0.03/ 12 = 0.0025 (monthly interest rate) and n = 3 * 12 = 36 (three years equivalent to 36 months).

Using these values in the formula, we can calculate the future value (VF):

VF = 110 * [(1 + 0.0025) 36 - 1] / 0.0025

Now let’s calculate this:

VF = 110 * [(1.0025) 36 - 1] / 0.0025

110 * (1.0965726572 - 1) / 0.0025

110 * 0.0965726572 / 0.0025

So Jackson will have about $4,239.52 in his savings account after three years, assuming he doesn’t make any withdrawals during that period.

Step-by-step explanation:

==================================================

Explanation:

Let's calculate the monthly payment

P = monthly payment

P = (L*i)/(1 - (1+i)^(-n))

P = (13000*0.0029167)/(1 - (1+0.0029167)^(-36))

P = 380.927266693234

P = 380.93

Various online calculators can confirm this. Search out "monthly payment calculator".

Side note: The monthly payment formula is based off of the present value annuity formula.

-----------

Carter pays $380.93 per month for 36 months.

He pays back a total of 380.93*36 = 13,713.48 dollars.

Subtract off the loan amount to determine the total interest.

13,713.48 - 13,000 = 713.48

Answer: True

Step-by-step explanation:

The lateral faces are the triangular faces that connect the apex of the pyramid to the edges of the base. The area of each lateral face can be calculated using the formula for the area of a triangle, which is [tex]\frac{1}{2} \times b \times h[/tex]. The area of the base is simply the area of the polygon that forms the base of the pyramid.

__________________________________________________________

The surface area of a pyramid is the sum of the areas of the lateral faces and the area of the base. (True or False)

The correct answer is True.

The surface area of a pyramid is the sum of the areas of the lateral faces and the area of the base. This can be represented by the formula:

[tex]\qquad\qquad\Large\boxed{\rm{\:SA = B + LA\:}}[/tex]

The lateral faces are the faces that are not the base, so their areas are calculated using the formula for the area of a triangle. The area of the base is calculated using the appropriate formula depending on the shape of the base.

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The predicted sales in Glover's Golf Emporium's eleventh business year are $475,000.

To predict the sales in Glover's Golf Emporium's eleventh business year, we can use the concept of linear growth. We have two data points: sales in the second year ($160,000) and sales in the seventh year ($335,000).

Let's first find the annual increase in sales:

Increase in sales = Sales in the seventh year - Sales in the second year

Increase in sales = $335,000 - $160,000

Increase in sales = $175,000

Next, we need to determine the rate of increase per year. Since we have a linear growth pattern, we can calculate the average annual increase by dividing the total increase in sales by the number of years:

Average annual increase = Increase in sales / Number of years

Average annual increase = $175,000 / (7 - 2) years

Average annual increase = $175,000 / 5 years

Average annual increase = $35,000 per year

Now, we can predict the sales in the eleventh business year by adding the average annual increase to the sales in the seventh year:

Predicted sales in the eleventh year = Sales in the seventh year + (Average annual increase * Number of additional years)

Predicted sales in the eleventh year = $335,000 + ($35,000 * (11 - 7))

Predicted sales in the eleventh year = $335,000 + ($35,000 * 4)

Predicted sales in the eleventh year = $335,000 + $140,000

Predicted sales in the eleventh year = $475,000

Therefore, the predicted sales in Glover's Golf Emporium's eleventh business year are $475,000.

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Answer:

(2,7) and (6,5)

Step-by-step explanation:

The line of best fit would be approximately:

y = -.4x + 8

(1,9)

9 = -.4(1) + 8

9 = 7.6

(9,5)

y = -.4x + 8

5 = -.4(9) + 8

5 = 4.4

(5,7)

y = -.4x + 8

7 = -.4(5) + 8

7 = 6

(2,7)

y = -.4x + 8

7 = -.4(2) + 8

7 = 7.2

(4,3)

y = -.4x + 8

3 = -.4(4) + 8

3 = 6.4

(6,5)

y = -.4x + 8

5 = -.4(6) + 8

5 = 5.6

Rounding to the nearest whole number, the membership of the Network Club in 2020 will be approximately 5,564.

Therefore, the correct answer is: E. 5,564.

To calculate the membership of the Network Club in 2020, we can use the continuous growth formula:

[tex]A = P \times e^{(rt)[/tex]

Where:

A is the final amount or membership in 2020,

P is the initial amount or membership in 2010,

e is the mathematical constant approximately equal to 2.71828,

r is the annual growth rate as a decimal,

t is the number of years.

Given:

P = 2,500 (membership in 2010),

r = 8% = 0.08 (annual growth rate),

t = 2020 - 2010 = 10 years (number of years).

Plugging in the values into the formula, we have:

[tex]A = 2,500 \times e^{(0.08 \times 10)}[/tex]

Calculating the exponent:

[tex]A = 2,500 \times e^{(0.8)[/tex]

Using a calculator, we find that[tex]e^{(0.8)[/tex]  is approximately 2.22554.

Now, we can calculate the final amount A:

A ≈ 2,500 [tex]\times[/tex] 2.22554 ≈ 5,563.85  

Therefore, the correct answer is: E. 5,564.

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Answer: The answer is 5564

Step-by-step explanation: P=I[tex]e^rt[/tex]=2500e^(0.08)(10)=5563.85