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)

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Related Questions

A map has a scale of 1 inch = 20 miles. The distance on a map between two cities is 3 1/4 inches. How far apart are the two cities?​

Answers

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

A brand new car costs $18,000, this price depreciates at 25% every year, how much would the car be after 12 years? 20 years?

Answers

Answer:

C(12)=$570.18

C(20)=$57.08

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:

[tex]C(t)=C_o\cdot(1-r)^t[/tex]

Where:

C(t) is the actual value of the function at time t

Co is the initial value of C at t=0

r is the decaying rate, expressed in decimal

The depreciation of goods is often modeled as an exponential function. The new car costs $18,000 and its price depreciates at r=25%= 0.25 every year.

The depreciation model is:

[tex]C(t)=18,000\cdot(1-0.25)^t[/tex]

Operating:

[tex]C(t)=18,000\cdot 0.75^t[/tex]

At t=12 years, the price will be:

[tex]C(12)=18,000\cdot 0.75^{12}[/tex]

C(12)=$570.18

At t=20 years, the price will be:

[tex]C(20)=18,000\cdot 0.75^{20}[/tex]

C(20)=$57.08

1.5m^6(-2m^2)^4
find the product​

Answers

the answer is:
24m^14

Lines a and b are parallel. Line c is a transversal. FInd the measures of all angles formed by a, b, and c, given each scenario. One of the angles measures 150 degrees.

Answers

Answer:

30° and 150°

Step-by-step explanation:

Given

Parallel lines a and b

Transversal c

Angle = 150°

Required

Determine the list of possible angles

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

Given that one of the angles is 150°, the other angle would be 180° - 150°

Other angle = 180° - 150°

Other angle = 30°

Aside 30° and 150°, there's no other possible angle that can be formed by the given information

Answer:

30 and 150

Step-by-step explanation:

Given

Parallel lines a and b

Transversal c

Angle = 150°

Required

Determine the list of possible angles

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

Given that one of the angles is 150°, the other angle would be 180° - 150°

Other angle = 180° - 150°

Other angle = 30°

Aside 30° and 150°, there's no other possible angle that can be formed by the given information

A museum has 6,000 visitors in its first month of operation. The museum staff predicts that the number of visitors will increase by 5% each month. Assuming that this prediction is true, how many visitors does the museum expect on the 7th month of operation?​

Answers

Multiply 5 by 6000 aka 30,000 then multiply 7 then to 210,000 please give brainliest

8100 visitors in 7th month.

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

If the visitors will increase at the rate of 5% then

Visitors in second month

=6000+  6000 x 5/100

=6000 + 300

=6000

So, the visitors in 7 month

=6000+ 7(300)

=6000 +2100

=8100

Hence, there 8100 visitors in 7th month.

Learn more about unitary method here:

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Martin traveled at an average rate of 40 miles per hour for the first half of his trip. For the second half of his trip, he traveled at a rate of 60 miles per hour. How far did he travel in the 4-hour trip?

Answers

Answer:

Total distance traveled = 200 miles

Step-by-step explanation:

Total time taken for the trip = 4 hours

∴ The trip can be divided into two halves of 2 hours each.

1st half:

speed = 40 miles per hour

distance = speed × time

when time = 2 hours

distance = 40 × 2 = 80 miles

2nd half:

distance = speed × time

speed = 60 miles per hour

time = 2 hours

∴ distance = 60 × 2 = 120 miles

Combined distance traveled = 80 + 120 = 200 miles

Please help me I will really appreciate it!!!

Answers

Answer:

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

Step-by-step explanation:

solve for t

h = -[tex]\frac{1}{2}[/tex]a[tex]t^{2}[/tex] + 1; multiply both sides by -2

-2h = a[tex]t^{2}[/tex] - 2; add 2 to both sides

-2h + 2 = a[tex]t^{2}[/tex]; divide by a

(-2h + 2) / a = [tex]t^{2}[/tex] ; take the square root

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

True or False: A system of two equations in two variables whose graphs are a parabola and a circle can have four real ordered-pair solutions.

Answers

Answer: True

The parabola can intersect the circle four times as the graph shows below. Each intersection point is a solution in the form (x,y).

WORTH 15 POINTS
⚠️MAKE SURE TO USE SURDS ⚠️
ANSWER ASAP WILL GIVE BRAINLIEST

Answers

Answer:

i got 1.23 don't think its right though so someone check me

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

First thing is you have to do the square root of 3. Which will give you a crazy long decimal but then after you square it, it becomes 3 perfectly.

ax = bc - c solve for x

Answers

Answer:

X = c - b/a

Step-by-step explanation:

Answer:

x=bc/a - c/a

You simplify it like you would any equation, only difference is it does not have numbers.

The midpoint of a segment with endpoint (8,a) and (b,4) is (-1,-1)
What’s the value of a and b
Answer choices is
A. 10 b. 6
A.6 b.10
A. -6 b. -10
A. -10 b.-6

Answers

Answer:

(-10,-6)

Step-by-step explanation:

(8 + b) / 2 = - 1

(8 + b) = - 1 * 2

8 + b = - 2

b+8-8 = -2 - 8

b = - 10

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

(a + 4)/2 = -1

(a + 4) = - 2

a + 4 = -2

a + 4-4 = - 2 - 4

a = - 6

Which of the following mathematical properties is described by the statement, “whatever is done on one side of the equation must also be done on the other side of the equation”?
Identity Property of Addition
Associative Property
Communitive Property
Property of Equality
today guys please

Answers

Answer:

Property of Equality

Step-by-step explanation:

Answer:Property of Equality

STEP BY STEP EXPLANATION HAS BEEN CANCELED ITS EASY:

PLEB

What's the answer help pls

Answers

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)

Two Angles are Supplementary when they add up to 180 degrees.

HENCE,

∠A + ∠B =180 (given)

⇒4x - 16 +8x + 4 = 180°

⇒12x - 12 = 180°

⇒12x = 192

⇒x = 16 ----1

substituting eq1 in ∠A,

=> 4(16) -16

=> 64 - 16

=> ∠A = 48°

Answer:

48

Step-by-step explanation:

The definition of supplementary means that the two angles add up to 180. so you set both expressions up to where they add to 180. like this

4x-16+8x+4=180

combine like terms

12x-12=180

12x=192

divide to get x

x=16.

You need the measure of angle A so you plug it back in

4(16)-16

64-16

48 is the measure of angle A, and since these angles are supplementary, that means angle B is 132

Can someone plzz answer this!!?

Answers

Answer: B Angle Side Angle

Step-by-step explanation:

Since line AB and CD are parallel angles D and A are congruent by the alternate interior theorem and both angles AOB and DOC are congruent by the vertical angle theorem and it already shows line OC and line OB are congruent.

Nov 06, 7:43:52 PM
Which equation represents a line which is parallel to the line y =
= -x - 8?
O 8x + 3y = -6
O 8x – 3y = 3
Submit Answer
8y - 3x = -48
3x + 8y = 48
O

Answers

Answer:

8x-3y=3

Step-by-step explanation:

Its the only one that would give you a negative x

Write the expression in simplest form.
(11 + 3) – 2(- 4 1 - 1) =
NIO

Answers

Answer:

11+3=14

-41-1=-42

14-2(-42)

-2(-42)

14+84

98

I hope this is good enough:

Which pair of radicals is a pair of like radicals

Answers

The last choice, since they have the same number in their square roots.

Please I’m really confused which one it is please help

Answers

Answer:

The top one on the left

Step-by-step explanation:

The graph shows that the distance a dog runs is proportional to the time the dog is running. You want to use only one plotted point to find the unit rate. Which of the three plotted points could you choose? Select all that apply.

(0,0)

(1,9.7)

(4,38.8)
Question 2
The unit rate is
feet per second.

Answers

Answer:

2

Step-by-step explanation:

2

slope of (-3, 1), (1, 9) and slope of (-2, -9), (-1, -7)

Answers

Answer:

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

Step-by-step explanation:

slope formula- (y2-y1)/(x2-x1)

plug in the numbers-

(9-1)/(1+3) and (-7+9)/(-1+2)

You make a necklace using blue,purple and green beads in ratio of 1:3:5. You use a total of 126 beads. How many green beads are in the necklace?

Answers

14 blue, 42 purple, 70 green. i believe

Answer:

Step-by-step explanation:

x + 3x + 5x = 126

9x = 126

x = 14 (blue beads)

3(14) = 42 (purple beads)

5(14) = 70 (green beads)

Translate the following statement: "Your grade, g, must be at least
75 to pass this class."

Answers

Answer:

"Your grade, g, must be at least  75 to pass this class'' is translated as:

g ≥︎ 75

Step-by-step explanation:

Given the grade is denoted by 'g'.

In algebra '≥︎' denotes that something must be 'greater than or equal to'. In other words, it means 'at least'.

As the gade must be at least 75, it means it can be greater than 75, but it can not be less than 75.

Therefore, "Your grade, g, must be at least  75 to pass this class'' is translated as:

g ≥︎ 75

(1,-19),(-2 -7) finnd the slope to this equation

Answers

Answer:

slope is 4

Step-by-step explanation:

Is 46 a number in the sequence generated by 5n + 1

Answers

Answer:

231

Step-by-step explanation:

5.46+1

230+1

231

answer this?

Answer:

yes

Step-by-step explanation:

Equate 5n + 1 and 46 to find n, that is

5n + 1 = 46 ( subtract 1 from both sides )

5n = 45 ( divide both sides by 5 )

n = 9

Thus 46 is the ninth term in the sequence

Estimate the area of the figure. Each square represents 2 units^2.

Answers

Answer:

60 units²

Step-by-step explanation:

Approximate area is about 50 units²

The closest option is the last one

Can a right triangle have sides of 12, 16, and 20?

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.

help meeeeeeeeee plzzzzzzzzzzzzz

Answers

Answer:

91 x

Step-by-step explanation:

Extremely easy question marking Brainliest answer

Answers

Answer:

It is hard to tell from this image, but I believe the word you are looking for is Integer. Integers are any positive or negative whole number.

Will mark brainliest!! Please answer ASAP

Will give extra points!!!

Please let me know if the picture above answer is correct or not and tell me the right answer!

Second question-

Which linear equation can be used to represent a line parallel to the x axis that passes through the point (8,5)

1) y=5

2) y=x+8

3) y=x+5

Answers

Answer:

y=5

Step-by-step explanation:

y= 5 is always parallel to x axis

For a soccer game, Mr Morant prepared 32 hot dogs. He sold 1/2 of the hot dogs to the fans. He sold 1/4 of the hot dogs to the coaches. How many hot dogs were left?

Answers

Answer:

it is nothing

Step-by-step explanation:

1-1=2

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