A carpet cleaning business has 100 customers when they charge $125 for a cleaning. Research shows that every $5 reduction in price attracts another 20 customers. What price should the business implement to maximize its revenue?
a $75
b $100
c $120
d $90

Answers

Answer 1

Since a $5 decrease in price increases customers by 20 we can say that we have two points:

(125,100) and (120,120), from these we can find the slope or rate of change of customers as a function of price...

m=20/-5

m=-4

m=-4

c(p)=-4p+b, now we can use (125,100) to solve for b

100=-4(125)+b

100=-500+b

600=b, so our number of customers as a function of price is:

c(p)=600-4p

Revenue will simply be the number of customers times the price charged per customer...or p*c(p):

r(p)=600p-4p^2

We can find price that creates maximum revenue by finding when the derivative is equal to zero...

dr/dp=600-8p

dr/dp=0 only when

0=600-8p

8p=600

p=75

So the price that maximizes revenue is $75.

Answer 2

The linear relationship is c(p) = -4p + b. Then the price that maximizes revenue is $75.

What is the linear system?

It is a system of an equation in which the highest power of the variable is always 1.

A carpet cleaning business has 100 customers when they charge $125 for cleaning.

Research shows that every $5 reduction in price attracts another 20 customers.

Since a $5 decrease in price increases customers by 20, we can say that we have two options.

(120, 100) and (120, 120) from these we can find the slope or rate of change of customers as a function of price.

[tex]\rm m = \dfrac{20}{-5}\\\\ m = -4[/tex]

Then we have

[tex]\rm c(p ) = -4 p +b[/tex]

Now, we can use (125, 100) to solve for b

100 = -4(125) + b

b = 600

So our number of customers as a function of price is

[tex]\rm c(p) = 600 - 4p[/tex]

Revenue will simply be the number of customers times the price charged per customer will be

[tex]\rm r(p) = 600 p -4p^2[/tex]

We can find a price that creates maximum revenue by finding when the derivative is equal to zero.

[tex]\rm \dfrac{dr}{dp} = 600 - 8p\\\\[/tex]

WE know that for maximum,

[tex]\rm \dfrac{dr}{dp} = 0\\\\0 = 600 - 8p\\\\p = 75[/tex]

So, the price that maximizes revenue is $75.

More about the linear system link is given below.

Related Questions

GUYS HELP PLEASE URGENT!!!!!!

A newborn baby weighs 3.136x10^3 units. Which unit of measure was used? grams ounces pounds tons

Answers

its grams because it cant be pounds because a baby isnt 3000 pounds, thats is just crazy!

The unit 'gram' will used to measure the weight of newborn baby in this case.

Unit conversion:

Conversion of units is the conversion between different units of measurements for the same quantity.

1 pound = 0.454kilogram1 kg = 1000 g1 ton = 1000 kg1 ounce = 0.0283 kg

According to the given question we have,

Weight of the new born baby = [tex]3.136[/tex] × [tex]10^{3}[/tex] = 3136

From the unit conversion,

3136 pound = 1,423.744kg

3136 gram = 3136/1000 = 3.136gram

3136 ton = 3136000 kg

3136 ounce =88.7488 kg

The range of weight of new born baby in kg is 3 to 4.

Hence, only 3136 gram is possible .So, the unit 'gram' will used to measure the weight of newborn baby in this case.

Learn more about the unit conversion here:

https://brainly.com/question/4736731

#SPJ2

Which polynomial is a perfect square trinomial? (1 point) 49x2 − 28x + 16 4a2 − 20a + 25 25b2 − 20b − 16 16x2 − 24x − 9?

Answers

4a² − 20a + 25 is a perfect square trinomial

4a² − 20a + 25 =
(2a)² - 2*2a*5 + 5² =
(2a - 5)²

What is the process that you need to follow in order to prove a circle?

Answers

The radii has to have the exact same length. The definition of a circle is "a round plane figure whose boundaries consist of points equidistant from the center". So to prove a circle, if you don't have the exact equation for it, would be to prove the radii all the same length.

Line segment
a.a series of points that extend in two directions without end plane
b.two lines that intersect at 90° angles perpendicular lines
c.lines that lie in the same plane and do not intersect line
d.a flat surface that extends infinitely and has no thickness parallel lines
e.part of a line that has two endpoints

Answers

Consider an indefinite Line L as shown in the diagram below
Point A and Point B are two points on Line L
The line between point A and point B that is also a part of Line L is called line segment

The correct definition of a line segment is given by the option e)
Line segment is a part of a line that has two end points

An __________ is used to indicate the repeating part of a repeating decimal.

Answers

line above the repeating number

Why is world population distribution uneven what factors contribute to this uneven distribution?

Answers

World population distribution is uneven because of the different measures of the factors affecting population, such as life expectancy, economic development etc

A mother gives birth to a 9 pound baby. every 4 months, the baby gained 2 pounds. if x is the age of the baby in months, then y is the weight of the baby in pounds. find an equation of a line in the form y = mx + b that describes the baby's weight.

Answers

For the equation of the line of the form y = mx + b, m is the slope of the line and b is the y-intercept which is the value of y when x is equal to zero. The slope is the rate of change of y per change in x. "y" would represent the dependent variable which is the weight of the baby while "x" represents the independent variable which is the number of months or the age of the baby in months. We calculate the slope as follows:

slope = (11 - 9) / ( 4 - 0) = 2/4 = 0.5
at x = 0, it is said that the weight of the baby is 9 lbs so the value of b would be 9.

The equation of the line would be y = 0.5x + 9

Final answer:

The equation of the line that represents the baby's weight as it grows is y = 0.5x + 9, where x is the age of the baby in months, and y is the weight of the baby in pounds.

Explanation:

The student is looking for an equation of a line that represents the weight of a baby as it grows. This situation can be described using a linear equation in the form of y = mx + b, where y represents the weight of the baby in pounds, x represents the age of the baby in months, m is the rate at which the baby gains weight, and b is the initial weight of the baby at birth.

Given that the baby weighs 9 pounds at birth, we have our b value as 9. It is also given that the baby gains 2 pounds every 4 months, which can be converted to a monthly weight gain of ½ pound per month (since 2 pounds ÷ 4 months = ½ pound per month). Consequently, the value of m is ½ or 0.5.

Using these values, the equation of the line that describes the baby's weight over time can be written as:

y = 0.5x + 9

This equation indicates that the baby's weight (y) is 9 pounds at birth (when x = 0) and increases by 0.5 pounds each month.

Double-checking my answer.. Given 3^2x = 9^6, what value of x satisfies this equation? (Use Laws of Exponents).
Thanks:)

Answers

Follow BEDMAS
Solve for X:
3^2x = 9^6
Simplify
9x=9^6
9x=531441
Divide both sides by 9.
(9x)/9=(531441)/9
x=59049

Hope this helps!
-Benjamin

A regular pyramid has a height of 12 cm in a square base if the volume of the pier mid is 236 cm³ how many centimeters are in the length of one side of its base?

Answers

[tex]\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh\qquad \begin{cases} B=\textit{area of the base}\\ h=height\\ ----------\\ h=12\\ V=236 \end{cases}\implies 236=\cfrac{1}{3}B(12) \\\\\\ 3\cdot 236=12B\implies \cfrac{708}{12}=B\implies 59=B[/tex]

now, is a square pyramid, like the picture below, so the base is just a square, so B = length * width, thus

[tex]\bf B=length\cdot width\quad \begin{cases} length=x\\ width=x\\ B=59 \end{cases}\implies B=x\cdot x\implies B=x^2 \\\\\\ 59=x^2\implies \sqrt{59}=x[/tex]

What do the parallel lines shown on segment BD and segment DC represent? _____________________

Answers

the 2 parallel lines mean that the lines are equal

SO since BD = 18, DC is also 18

The parallel lines shown on segments BD and DC represent that they are equal in length.

BD = 18 = DC

Thus, correctly assuming that the point D is the mid point of line segment BC.

Find the difference.

Correct and best explained answer gets brainliest.

Answers

I can't see the Attachment but if you can message me or comment the question i'd be more than happy to help

Hello!

(-3x^4-9x^3-4x^2-4)-(5x^3-7x^2+6)

= -3x^4-9x^3-4x^2-4-(5x^3-7x^2+6)

= -3x^4-9x^3-4x^2-4-5x^3+7x^2-6

=-3x^4-14x^3+3x^2-10

hence, option D is the answer.

HOPE IT HELPED :D ☺☺

What causes water molecules to stick together in liquid water?

A. Water vapor

B. Carbon dioxide

C. Sun's gravity

D. Hydrogen bonds

Answers

D hydrogen bonds since water molecules attract to each other with the positive hydrogen atom with other oxygen atoms

The answer is D.Hydrogen Bonds.

HELP!! QAQ

Create your own piecewise function with at least two functions. Explain, using complete sentences, the steps for graphing the function. Graph the function by hand or using a graphing software of your choice (remember to submit the graph).

An visual of the function would be really appreciated. Thanks!

Answers

You can use y = {-1, x ≤ 0 and y = {x - 1, x > 0 as two functions for your piecewise function. The first function will be a horizontal line. The second function will be a straight line with a slope of 1 and y-intecept of -1. Messaged you the graph.

There are 20 wild pigs on an island and the number of pigs doubled each year for the past 5 years. The independent variable is

Answers

p(t)=20(2^t)

The independent variable is time.

Answer:

The independent variable is time.

Step-by-step explanation:

Given,

The original number of pigs on the island = 20,

Also, the number of pigs doubled each year,

After 1 year the pigs = 20(2),

After 2 years = 20(2)²,

After 3 years = 20(2)³,

......................., so on...

Similarly, the number of pigs after t years would be,

[tex]y=20.2^t[/tex]

⇒ The value of y depends upon t,

⇒ The number of pigs depends upon the time ( in years ),

Since, the variable in which the other variable depends is called independent variable,

Hence, the independent variable must be time.

If f(x)=square root of x+12 and g(x)=2square root of x, what is the value of (f – g)(144)? –84
–60
0
48

Answers

f(x)=(√x)+12
g(x)=2√x

(f-g)(x)=f(x)-g(x)

(f-g)(144)=f(144)-g(144)=
(√144)+12-(2√144)=
12+12-2(12)=
24-24=
0
result is 0

f(x) = √(x)+12
g(x) = 2√x

(f – g)(144) = √(144)+12 - 2√144

(f – g)(144) = 12 +12 - 2(12)

(f – g)(144) = 24 - 24

(f – g)(144) = 0

What is the area of the polygon given below?

Answers

Divide the polygon into three separate rectangles
(4*7)+(13*9)+(6*6)=181

Answer:

181 square units

Step-by-step explanation:

Martin deposits $200 in a savings account that earns 5% annual interest. four years later, cary deposits $200 in an account earning the same interest. let m represent the balance in martin’s account and let c represent the amount of money in cary’s account. choose the pair of expressions that describe the accounts y years after martin opened his account. martin: 200(1.05)y cary: 200(1.05)y+4 martin: 200(1.05)y+4 cary: 200(1.05)y–4 martin: 200(0.05)y cary: 200(0.05)y–4 martin: 200(1.05)y cary: 200(1.05)y–4

Answers

Martin deposits $200 in a savings account that earns 5% annual interest.

year         interest                     balance

1              200 * 5%                    200(1.05)

2              200(1.05) * 5%          200(1.05)^2

3            200(1.05)^2*5%        200(1.05)^3

y                                              200(1.05)^y

=> m = 200 (1.05)^y

four years later, cary deposits $200 in an account earning the same interest.

year         interest                     balance

5              200 * 5%                    200(1.05)

6              200(1.05) * 5%          200(1.05)^2

7           200(1.05)^2*5%        200(1.05)^3

y                                              200(1.05)^(y-4)

=> c = 200(1.05)^ (y-4)

Answer:
Martin: 200(1.05)^y
Cary: 200(1.05)^(y–4)

Answer:

d then d again

Step-by-step explanation:

A circle has a center of (5,-5) and goes through (6,-2). What is the radius?

Answers

Let O(5, -5) be the center of the circle, and P(6, -2) be a point on this circle.

The distance between points O and P, that is |OP|, is the radius of this circle,

We use the distance between 2 points formula:

|OP|=[tex] \sqrt{ (x_2-x_1)^{2} + (y_2-y_1)^{2} }= \sqrt{ (6-5)^{2} + (-2-(-5))^{2} }[/tex]
[tex]= \sqrt{ 1^{2}+ (-2+5)^{2}} = \sqrt{1+9}= \sqrt{10} [/tex] (units)

Answer: [tex]\sqrt{10} [/tex] units

Your goal is to save at least $240.00 over the next 4 week. How much money must you save each week in order to meet that goal? Write and solve an inequality

Answers

4 *x >= 240 ---> x >= 60,

So at least $60/week (notice the = sign, because it at at least, and not 'more than')

The solution is x ≥ $ 60

The value of the inequality equation is x ≥ 60

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Let the minimum money per week to be saved be = x

The number of weeks = 4

The goal is to save at least $240.00 over the next 4 week

So , substituting the values in the equation , we get

x ≥ 240 / number of weeks

x ≥ 240 / 4

On simplifying the equation , we get

x ≥ 60

Therefore , the value of A is x ≥ 60 and should save a minimum of $ 60 per week

Hence , the inequality equation is x ≥ 60

To learn more about inequality equations click :

https://brainly.com/question/11897796

#SPJ2

Luisa knit a rectangular scarf that measures 4 feet by 1 foot. She wants to use the remaining 6 square feet of fabric to create a border around the scarf.

Which equation can she use to find the required width of the border x?

Answers

To solve this problem, let us recall that the formula for Area of a rectangle is:

A = l * w

Where,

l = length of one side = 4 ft

w = width of one side = 1 ft

Therefore the original area is:

Ao = 4 ft * 1 ft

Ao = 4 ft^2

Since each border would be increased by x, therefore the new l and w would be:

l = 4 + 2x

w = 1 + 2x

The new area becomes:

A = (4 + 2x) (1 + 2x)

The difference of the two would be the area of the remaining scarf:

A – Ao = 6 square ft

(4 + 2x) (1 + 2x) – 4 = 6 ---> 1

(4 + 2x) (1 + 2x) = 10 ---> 2

The equation to use can be equation 1 or equation 2.

he time spent dancing (minutes) and the amount of calories burned can be modeled by the equation c = 5.5t. Which table of values matches the equation and includes only viable solutions? Image for option 1 Image for option 2 Image for option 3

Answers

Answer:

0 0

5 27.5

10 55

15 82.5

Step-by-step explanation:

what is the x-intercept of the graph of the function f(x)=x2-16x+64?

Answers

Answer:

x-intercept: (8,0)

Step-by-step explanation:

Given: [tex]f(x)=x^2-16x+64[/tex]

For x-intercept, Put y=0 and solve for x.

x-intercept: It is a point where y-coordinate zero.

[tex]x^2-16x+64=0[/tex]

[tex]x^2-8x-8x+64=0[/tex]

[tex](x-8)(x-8)=0[/tex]

Equate each factor to 0 and solve for x

x-8 = 0 , x-8 = 0

x=8,8

x-intercept: (8,0)

Hence, The x-intercept is 8.

The x-intercept of the function is 8

The equation of the function is given as:

[tex]f(x) = x^2 - 16x + 64[/tex]

Expand the equation

[tex]f(x) = x^2 - 8x - 8x + 64[/tex]

Factorize the above equation

[tex]f(x) = x(x - 8) - 8(x -8)[/tex]

Factor out x - 8

[tex]f(x) = (x - 8) (x -8)[/tex]

Set f(x) to 0, to calculate the x-intercept

[tex](x - 8) (x -8)=0[/tex]

Rewrite as:

[tex](x - 8)^2=0[/tex]

Take the square roots of both sides

[tex]x - 8=0[/tex]

Solve for x

[tex]x = 8[/tex]

Hence, the x-intercept of the function is 8

Answers

[tex]\int{(x^{3} - 3x^{2})}\,dx[/tex]
[tex]= \int{x^{3}}\,dx - \int{3x^{2}}\,dx[/tex]
[tex]= \frac{1}{4}x^{4} - \frac{3}{3}x^{3} + C[/tex]
[tex]= \frac{1}{4}x^{4} - x^{3} + C[/tex]

What 12 multiplied by 3

Answers

the answer to 12•3=? is 36

Andrew makes $6 an hour plus $9 an hour for every hour of overtime. Overtime hours are any hours more than 40 hours for the week. Part A: Create an equation that shows the amount of wages earned, W, for working x hours in a week when there is no overtime. (3 points) Part B: Create an equation that shows the amount of wages earned, S, for working y hours of overtime. Hint: Remember to include in the equation the amount earned from working 40 hours. (3 points) Part C: Andrew earned $330 in 1 week. How many hours (regular plus overtime) did he work? Show your work. (4 points)

Answers

Hey there!

For Part A, all you need to do is write out an equation for how many dollars Andrew would make for x hours during regular hours (not overtime). Since he makes 6 dollars per hour, this will be 6x.

W = 6x

For Part B, create a similar equation for overtime hours. Overtime hours only apply after Andrew has worked 40 hours, so plug that into your first equation and add that to the second equation.

W = 6x
W = 6(40)
W = 240

S = 240 + 9y

For Part C, consider what we now know. If Andrew earns any money over 240 dollars (which is how much he earns after 40 hours), we know he worked overtime. So, we can just plug 330 into the second equation for S and solve for the number of additional hours he worked, y.

330 = 240 + 9y
– 240 – 240

90 = 9y
9 9

10 = y

Now, we can add up the initial 40 hours plus the additional 10 hours, which is 50 hours total.

Hope this helped you out! :-)

What is the midpoint of (4,8) and (3,12)

Answers

I don't remember the midpoint formula exactly, but use the midpoint formula for this problem.

The product of the roots of 8x² - 2x = 1 is:

Answers

AB = c/a = -1 / 8 = -1/8

Answer:

[tex]\text{Product of its zeros = }\frac{-1}{8}[/tex]

Step-by-step explanation:

The quadratic equation is given to be : 8x² - 2x = 1

We need to find the product of its zeros

First finding the number of zeros :

⇒ 8x² - 2x - 1 = 0

⇒ 8x² - 4x + 2x - 1 = 0

⇒ (4x + 1)(2x - 1) = 0

[tex]\implies x = \frac{-1}{4}\:\:and\:\: x = \frac{1}{2}[/tex]

[tex]\text{Product of its zeros = }\frac{-1}{4}\times\frac{1}{2}=\frac{-1}{8}[/tex]

The relationship between feet and inches is described by the equation y = 12x, where x = a given length in feet and y = the equivalent length in inches. If a table is 7.25 feet long, what is its length in inches? A. 84 inches B. 87 inches C. 81 inches D. 90 inches

Answers

Final answer:

The length of the table in inches is 87 inches.

Explanation:

To solve this problem, you can use the equation y = 12x to convert the length from feet to inches. Given that the table is 7.25 feet long, you can substitute x = 7.25 into the equation to find y.

y = 12(7.25) = 87

Therefore, the length of the table in inches is 87 inches.

Given a group of 8 women and 11 men, how many different ways are there of choosing one man and one woman for a committee?

Answers

Final answer:

There are 88 different ways of choosing one man and one woman for a committee.

Explanation:

In order to find the number of different ways of choosing one man and one woman for a committee, we can use the concept of combinations. The number of ways of choosing one item from a group of n items is denoted by n C 1, which is equal to n. So, the number of ways of choosing one man from a group of 11 men is 11, and the number of ways of choosing one woman from a group of 8 women is 8. To find the total number of ways, we multiply these two numbers:

Total number of ways = 11 * 8 = 88

Therefore, there are 88 different ways of choosing one man and one woman for a committee.

For each equation below find y if x=2

Answers

A - would be 7 - 2 = 5
B - would be 2 to the second - 1 = 3

Other Questions

Brett wants to paint the exterior of his two-story home but does not know what length ladder he should buy. The top of his roof is 29 ft above ground level, and (for safety reasons) the ladder should not be at more than an 80 angle from the ground. How long, rounded up to the nearest foot, is the shortest ladder that Brett should buy? A farmer places unhatched chicken eggs under a heat lamp. How does the radiation help the eggs? The laboratory report for a patient taking clozapine (clozaril) shows a white blood cell count of 3000 mm3 and a granulocyte count of 1500 mm3. the nurse should: report the laboratory results to the health care provider. Traditional advertisements for cookware have always focused on appealing to women consumers. such advertisements make use of consumer differences arising out of microcultures based on different _____. What is the part of the gene called where the dna polymerase first binds during transcription? Different budgeting periods and explain each one Which word set completes the analogy?thief : steals ::plants : gardenerchef : cooksmows : grasshopes : faith What Byzantine city was a wealthy center of trade that maintained the commercial links between Europe and Asia? Ravenna Rome Constantinople Carthage What are departments called that resemble separate businesses in that they produce and market their own products? Read the following excerpt from a speech meant for the general public:Welcome to this evening's performance of the The Tale Missy May. I would like to applaud these students for the hard work they put in to make the play one of the best in the annals of this institution.Which revision will make this speech more appropriate for an audience of elementary students? A.Change "evening's performance" to "tonight's dramatic presentation." B.Change "the annals of this institution" to "our school's history." C.Change "The Tale of Missy May" to "The Story of Missy May." D.Change "hard work" to "considerable effort." _____ releases energy that is used to pump hydrogen ions from the stroma into the thylakoid compartment. Bias can occur in sampling. bias refers to HELPPPPPPPPPPP Why is the sum of a rational number and an irrational number rational? A. Because the product is always a non- terminating, non- repeating decimal. B. Because the product is always a fraction C. Because the product is always a negative number D. Because the product is always a repeating or a terminating decimal Since russell's wife died, he has been eating the exact same thingand a very small amount of itfor breakfast and lunch every day. most nights, he skips dinner. sometimes he seems confused when his granddaughter calls to check in on him. based solely on this information, which diagnosis is most likely? A taxi driver makes $24.50 in an hour, but uses $6.75 worth of gas during that time. What will the driver's total earnings for the hour be, after paying for gas? Which element in period 4 has the highest electronegativity? potassium calcium copper bromine At the end of the story what makes montresor feel sick answers On September 30, picture perfect physicians invested$100,000 in new medical equipment. What is the new assets, liabilities and equity What happened every morning in the inca capital? Why a bouncing ball doesn't have simple harmonic motion . Explain with detail Steam Workshop Downloader

A carpet cleaning business has 100 customers when they charge $125 for a cleaning. Research shows that every $5 reduction in price attracts another 20 customers. What price should the business implement to maximize its revenue? a $75 b $100 c $120 d $90

Answers

Related Questions

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

A carpet cleaning business has 100 customers when they charge $125 for a cleaning. Research shows that every $5 reduction in price attracts another 20 customers. What price should the business implement to maximize its revenue?
a $75
b $100
c $120
d $90