The function P(x) = –0.015x^2 + 1.2x – 11.5 gives the profit, in thousands of dollars, when a company sells a new product at x dollars per unit. Which of the following statements best interprets the average rate of change of this function from x = 50 to x = 55?
The profit increases by $375 for every $1 increase in the selling price.
The profit decreases by $375 for every $1 increase in the selling price.
The profit increases by $1875 for every $1 increase in the selling price.
The profit decreases by $1875 for every $1 increase in the selling price.

Answers

Answer 1

Answer:

The profit decreases by $ 375 for every $ 1 increase in the selling price.

Step-by-step explanation:

From the definition of the secant line we get that the average rate of change of [tex]P(x) = -0.015\cdot x^{2}+1.2\cdot x -11.5[/tex], where [tex]x[/tex] is the selling price of the product, measured in dollars per unit, is:

[tex]r = \frac{P(55)-P(50)}{55-50}[/tex] (1)

Now we evaluate the function at each bound:

x = 50

[tex]P(50) = -0.015\cdot (50)^{2}+1.2\cdot (50)-11.5[/tex]

[tex]P(50) = 11[/tex]

x = 55

[tex]P(55) = -0.015\cdot (55)^{2}+1.2\cdot (55)-11.5[/tex]

[tex]P(55) = 9.125[/tex]

Then, the average rate of change is:

[tex]r = \frac{9.125-11}{55-50}[/tex]

[tex]r = -0.375[/tex]

Hence, the profit decreases by $ 375 for every $ 1 increase in the selling price.

Answer 2

The statements that best interprets the average rate of change from x = 50 to x = 55 is (b) The profit decreases by $375 for every $1 increase in the selling price.

The profit function is given as:

[tex]P(x) = -0.015x^2 + 1.2x - 11.5[/tex]

Calculate P(x), when x = 50.

So, we have:

[tex]P(50) = -0.015(50)^2 + 1.2(50) - 11.5[/tex]

[tex]P(50) = 11[/tex]

Calculate P(x), when x = 55.

So, we have:

[tex]P(55) = -0.015(55)^2 + 1.2(55) - 11.5[/tex]

[tex]P(55) = 9.125[/tex]

The average rate of change from x = 50, to 55 is then calculated using:

[tex]m = \frac{P(55) - P(50)}{55-50}[/tex]

So, we have:

[tex]m = \frac{9.125 - 11}{55-50}[/tex]

[tex]m = \frac{-1.875}{5}[/tex]

Divide

[tex]m = -0.375[/tex]

The function is in 1000 units.

So, we have:

[tex]m = -0.375\times 1000[/tex]

[tex]m = -375[/tex]

-375 implies a decrease of $375 for every $1 increase in sales

Hence, the correct statement is (b)

Read more about average rates at:

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It is 65 miles because 3 times 20 is 60, a fourth of 20 is 5, so you add them together and get 65 miles

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Answer:

C(12)=$570.18

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Step-by-step explanation:

Exponential Decay Function

The exponential function is often used to model natural growing or decaying processes, where the change is proportional to the actual quantity.

An exponential decaying function is expressed as:

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Answers

No. All triangles must have a total of 180 degrees. If a triangle had two small angles (smaller than 90) the last angle must be larger than 90 and adds up to be 180 in total.

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Answers

Answer:

y=5

Step-by-step explanation:

y= 5 is always parallel to x axis

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Answers

Answer:

8/4 and 2/1(or just 2)

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Answer: True

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Answer:

48°

Step-by-step explanation:

The m in front of the angle notation refers to the measure of the angle labeled A, B and C (with vertex at B)

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HENCE,

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Answer:

48

Step-by-step explanation:

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Step-by-step explanation:

2

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Answers

Answer:

30° and 150°

Step-by-step explanation:

Given

Parallel lines a and b

Transversal c

Angle = 150°

Required

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A transversal divides a parallel line into two measure which add up to 180°

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30 and 150

Step-by-step explanation:

Given

Parallel lines a and b

Transversal c

Angle = 150°

Required

Determine the list of possible angles

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231

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What is Unitary Method?

The unitary technique involves first determining the value of a single unit,  followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

given:

Visitor in first month= 6000

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Learn more about unitary method here:

https://brainly.com/question/22056199

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Answers

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Answer:

Step-by-step explanation:

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Answer:

t = [tex]\sqrt{\frac{-2(h-1)}{a} }[/tex]

Step-by-step explanation:

solve for t

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Answers

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Step-by-step explanation:

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Answers

Answer:

Total distance traveled = 200 miles

Step-by-step explanation:

Total time taken for the trip = 4 hours

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distance = speed × time

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time = 2 hours

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Answer:

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Answers

Answer:

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Step-by-step explanation:

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Answers

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

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