An equipment rental business currently charges $32. 00 per power tool rental and averages 24 rentals a day. The company recently performed a study and found that for every $2. 00 increase in rental price, the average number of customers decreased by one rental.
The company determined that the function f(x) = (32 + 2x)(24 – x) can be used to represent the total revenue earned from the rentals, where x represents the number of rental price increases and f(x) represents the revenue earned.
Part A: Explain what the expressions (32 + 2x) and (24 – x) represent in the given scenario.
Part B: What is the revenue after 3 rental price increases? Show your work or explain how you found your answer.
Part C: What rental price would give the maximum revenue for the company?
Answers
Part A: In the given scenario, the expression (32 + 2x) represents the rental price charged by the equipment rental business after x price increases of $2 each. The initial rental price is $32, and for every $2 increase in rental price, the rental price is raised by 2 units. The expression (24 – x) represents the number of rentals the equipment rental business can expect to make after x price increases. As the rental price increases, the number of customers is expected to decrease by one rental for every $2 increase in rental price.
Part B: To find the revenue after 3 rental price increases, we need to calculate f(3), where f(x) = (32 + 2x)(24 – x).
Substituting x = 3, we get:
f(3) = (32 + 2(3))(24 – 3) = (32 + 6)(21) = 38 × 21 = $798
Therefore, the revenue after 3 rental price increases is $798.
Part C: To find the rental price that would give the maximum revenue for the company, we need to find the value of x that maximizes the function f(x) = (32 + 2x)(24 – x). We can do this by finding the critical points of the function, which occur when the derivative of the function is equal to zero:
f'(x) = (32 + 2x)(-1) + (24 - x)(2) = -32 + 16x + 48 - 2x = 14x + 16
Setting f'(x) = 0 and solving for x, we get:
14x + 16 = 0
\(x = \frac{-16}{14} = \frac{-8}{7}\)
However, \(x = \frac{-8}{7}\) is not a valid solution since it represents a negative number of rental price increases, which is not possible in this scenario. Therefore, we need to test the endpoints of the interval [0, 6], since x represents the number of rental price increases and cannot exceed 6 (which would result in a rental price of $44, the maximum price in this scenario).
f(0) = (32 + 2(0))(24 - 0) = 32 × 24 = $768
f(6) = (32 + 2(6))(24 - 6) = 44 × 18 = $792
Comparing the values of f(0), f(3), and f(6), we see that f(6) gives the maximum revenue of $792. Therefore, the rental price that would give the maximum revenue for the company is $44, which is the rental price after 6 price increases of $2 each.
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Related Questions
Jamie has a half-sheet cake. If she has six friends, how much will each one get?
Answers
Answer:
1/7th of the cake
Step-by-step explanation:
because you can cut it up into 7 pieces and each friend gets one and you get one too.
In 2015 the population of 895 quail increases at an annual rate of 3.5%. In writing an
exponential function to model the quail population, using f(t) = a(b)+ what is the value
of a
?
and b =
Please help!!
Answers
Answer:
y=895•1.07^x Y is the population of quails and X is the amount of years that have passed.
Step-by-step explanation:
hope this helps
A store pays $328 for a playground slide. The store marks up the price by 45 1/8% what is the new price?
Answers
The new price of the playground slide after a 45 1/8% markup is $476.25.
To find the new price after a 45 1/8% markup, we need to first calculate the markup amount and then add it to the original price.
Markup amount = original price x markup rate
Markup rate = 45 1/8% = 45.125%
We need to convert the percentage to a decimal by dividing by 100
Markup rate = 45.125% ÷ 100 = 0.45125
Now we can calculate the markup amount
Markup amount = $328 x 0.45125 = $148.25
To find the new price, we add the markup amount to the original price
New price = original price + markup amount
New price = $328 + $148.25 = $476.25
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i need to know what x equals
Answers
Answer:
x = 13
Step-by-step explanation:
The tiny marks on all three sides means this shape is an equilateral triangle (all three sides are the same) This means that all three angles are also the same. 180° degrees in a triangle, so all three angles are 60°.
Use this info to set up an equation.
4x + 8 = 60°
Subtract 8.
4x = 5 2
Divide by 4.
x = 13
What is the width of a rectangle with a length of
5/6 feet and an area of 2 square feet?
Answers
Answer:
2.4 feet
Step-by-step explanation:
\( \frac{5}{6} w = 2\)
\(w = 2 \times \frac{6}{5} = \frac{12}{5} = 2.4\)
which sample size will produce the widest 95onfidence interval, given a sample proportion of 0.5?  a. 60  b. 80
Answers
For a given sample proportion of 0.5, the sample size that will produce the widest confidence interval is the largest option given, which in this case is 80.
The sample size that will produce the widest 95% confidence interval, given a sample proportion of 0.5, is option b, 80. This is because the width of the confidence interval is directly proportional to the sample size, meaning that as the sample size increases, the confidence interval becomes narrower.
Additionally, the width of the confidence interval is inversely proportional to the square root of the sample size. Therefore, for a given sample proportion of 0.5, the sample size that will produce the widest confidence interval is the largest option given, which in this case is 80.
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If this rectangle is dilated using a scale factor of 5 through point B, what is the result?
Answers
Answer:
of course you are going to get a bigger rectangle
Step-by-step explanation:
remember that when you scale something by less than a whole that object with decrease in size
increasing the sample size of an opinion poll will reduce the responses bias of the estimates made from the data collected in the poll. bias of the estimates made from the data collected in the poll. variability of the estimates made from the data collected in the poll. variability of the estimates made from the data collected in the poll. effect of nonresponse on the poll. effect of nonresponse on the poll. variability of opinions in the sample. variability of opinions in the sample. variability of opinions in the population.
Answers
increasing the sample size of an opinion poll will lead to (b) variability of the estimates made from the data collected in the poll.
An opinion poll is a human research survey of the public's opinion from a specific sample. It is frequently referred to as just a survey or a poll, even though strictly speaking an election is a poll. To assess the sentiments and beliefs of the entire population, interviews or surveys with representative samples of citizens are utilised. Students can participate actively in discussions using almost any device with well-designed polls. Each poll must be adjusted separately, and many features that teachers might find helpful demand a subscription package. A greater sample size yields more data on the population and, thus, more accurate population estimates. Better population estimates will also let us know that there is less fluctuation.
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Layla rents a table at the farmers market for $8.50 per hour. She wants to sell enough $6 flower bouquets to earn at least $400.
Part A
Write an inequality to represent the number ofbouquets, x, Layla needs to sell and the number of
hours, y, she needs to rent the table.
Part B
How many bouquets does she have to sell in a given
number of hours in order to meet her goal?
(A) 70 bouquets in 3 hours
(B) 72 bouquets in 4 hours
(C) 74 bouquets in 5 hours
(D) 75 bouquets in 6 hours
Answers
Answer:
Step-by-step explanation:
Let's assume Layla needs to sell at least a certain number of bouquets, x, and rent the table for a maximum number of hours, y. We can represent this with the following inequality:
x ≥ y
This inequality states that the number of bouquets, x, should be greater than or equal to the number of hours, y.
Part B:
To determine how many bouquets Layla needs to sell in a given number of hours to meet her goal, we can use the inequality from Part A.
(A) For 70 bouquets in 3 hours:
In this case, the inequality is:
70 ≥ 3
Since 70 is indeed greater than 3, Layla can meet her goal.
(B) For 72 bouquets in 4 hours:
Inequality:
72 ≥ 4
Again, 72 is greater than 4, so she can meet her goal.
(C) For 74 bouquets in 5 hours:
Inequality:
74 ≥ 5
Once more, 74 is greater than 5, so she can meet her goal.
(D) For 75 bouquets in 6 hours:
Inequality:
75 ≥ 6
Again, 75 is greater than 6, so she can meet her goal.
In all four cases, Layla can meet her goal by selling the given number of bouquets within the specified number of hours.
Math question too tough for me, for every math question, i have to ask
Answers
Answer:
I'm pretty sure that the answer is 55.
Sorry if I'm wrong.
what mathematical shape is this?
Answers
Answer:
A quadrilateral.
Step-by-step explanation:
The shape has 4 sides, so it is a quadrilateral.
Answer:
dart
Step-by-step explanation:
10x^3/5x^2 2/x. 2x 2 x/2
Answers
please help me this assignment is due todayyy it is 12 points
Answers
Answer:
B
Step-by-step explanation:
the range is the y-values
What is -0.37 written as a rational number
Please help I would really appreciate it.
Answers
Answer:
1,000,000.0000001 - rational
Step-by-step explanation:
A solid has faces that consist of 4 triangles, 3 rectangles, and 1 hexagon. The solid has 9 vertices. How many edges does the solid have?
A 12 edges
B. 15 edges
C 18 edges
D 21 edges
Answers
Answer:
Step-by-step explanation:
c)18
Answer:
B. 15 edgesStep-by-step explanation:
According to Euler's formula:
F + V = E + 2, where F- faces, V- vertices, E- edgesSubstitute known values and solve for E:
(4 + 3 + 1) + 9 = E + 217 = E + 2E = 17 - 2E = 15Correct choice is B
what happens to a distribution if each data is transformed linearly by adding or subtracting some value to each data value?
Answers
Data value in a distribution is transformed linearly by adding or subtracting some value, the distribution is shifted either to the right or left on the number line.
This process is known as centering.
The effect of centering can be seen in the measures of central tendency, such as the mean and median.
Data is centered by subtracting a constant value, the mean of the distribution is shifted by the same amount in the opposite direction.
If we center data by subtracting 10 from each data point, the mean of the new distribution will be 10 less than the mean of the original distribution.
The median, on the other hand, is not affected by centering, as it is simply the middle value of the dataset.
Centering can change the position of the median in relation to the mean, depending on the shape of the distribution.
Centering can also affect measures of dispersion, such as the range and standard deviation.
Data is centered by subtracting a constant value, the range of the distribution remains the same, but the standard deviation is reduced by the same amount.
This is because centering moves the data closer to the mean, which reduces the spread of the data.
Overall, centering data by adding or subtracting a constant value is a useful tool in data analysis, as it can help to reveal patterns and relationships that may not be apparent in the original dataset.
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Use Green's Theorem to evaluate the line integral along the given positively oriented curve. integral_c ye^x dx + 2e^x dy, C is the rectangle with vertices (0, 0), (3, 0), (3, 4), and (0, 4)
Answers
Applying Green's Theorem, the line integral can be evaluated as the double integral over the region enclosed by the curve. By calculating the double integral, we find the value of the line integral to be 6e^3 - 6.
The line integral along the given curve can be expressed as:
∮C ye^x dx + 2e^x dy
We apply Green's Theorem, which states that for a vector field F = (M, N):
∮C M dx + N dy = ∬R (dN/dx - dM/dy) dA
First, let's calculate the partial derivatives of the given functions:
∂/∂x (2e^x) = 2e^x
∂/∂y (ye^x) = e^x
Now, we substitute these derivatives into Green's Theorem:
∮C ye^x dx + 2e^x dy = ∬R (e^x - 2e^x) dA
The region R is defined by the vertices of the rectangle (0, 0), (3, 0), (3, 4), and (0, 4).
To evaluate the double integral, we integrate with respect to x and y over the region R:
∬R (e^x - 2e^x) dA = ∫[0,3] ∫[0,4] (e^x - 2e^x) dy dx
Integrating with respect to y first, we get:
∫[0,3] [(e^x - 2e^x)y] [0,4] dx
Simplifying, we have:
∫[0,3] (4e^x - 8e^x) dx
Combining like terms, we obtain:
∫[0,3] (-4e^x) dx
Integrating, we have:
[-4e^x] [0,3] = -4e^3 + 4
Thus, the value of the line integral along the given curve is 6e^3 - 6.
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The distance from Salvador's job to
his house is 3 times greater than the distance
from his house to school. If his house is between
his job and school and the distance from his job
to school is 6 miles, how far is it from Salvador's
house to school?
Answers
Answer:
54
Step-by-step explanation:
(a)A sports statistician determined that the probability of a certain rugby team winning its next match is
11/19
Find the odds against the team winning its next match.
(b)Linda entered a raffle at a festival and hopes to win a new TV. The odds in favor of winning a new TV are 3/13
Find the probability of winning a new TV.
Answers
a) the odds against the team winning its next match are 8/19.
b) the probability of winning a new TV is 3/16.
(a) To find the odds against the rugby team winning its next match, we can use the probability of the team winning. The odds against an event are calculated by subtracting the probability of the event from 1 and expressing it as a ratio.
Probability of the team winning = 11/19
Odds against the team winning = 1 - (11/19) = 8/19
Therefore, the odds against the team winning its next match are 8/19.
(b) To find the probability of winning a new TV, we can use the given odds in favor of winning. The odds in favor of an event can be expressed as a ratio of favorable outcomes to total outcomes.
Odds in favor of winning a new TV = 3/13
Probability of winning a new TV = favorable outcomes / total outcomes
Probability of winning a new TV = 3 / (3 + 13) = 3/16
Therefore, the probability of winning a new TV is 3/16.
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the perimeter of this isosceles triangle is 47 cm. what is the length of each of its legs? a. 15 cm b. 17.5 cm c. 19.5 cm d. 35 cm
Answers
17.5 cm is the length of each of its legs
Kyle wants to go to a big concert coming up. The original price of the ticket is $60.00, but with taxes and fees, the price goes up to $75.00. By what percent did the taxes and fees increase the ticket price?
Answers
NEED THE ANSWER NOWWW!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
i think the answer would be y=4
Step-by-step explanation:
Answer:
ponte las pilas niño
Step-by-step explanation:
The box-and-whisker plot below represents some data set. What is the range of the data?
Answers
Answer: 50 to 140
Step-by-step explanation:
Answer:
range = 90
Step-by-step explanation:
the range is the difference between the maximum and minimum values of the data set.
the maximum value = 140 and minimum value = 50 , then
range = 140 - 50 = 90
About 42% of people who get their eyes examined are found to be nearsighted (unable to see objects at a distance). What is the probability of an ophthalmologist examining five people until he finds the first patient who is nearsighted?.
Answers
The probability that first patient is who is nearsighted is 0.027552
What is probability?
Probability is a synonym for potential. It is a field of mathematics that examines how random events happen. From zero to one, the value is stated. To forecast the likelihood of events, probability has been introduced in mathematics.
42% people are examined nearsighted
∴ 100- 42
= 58%
So 58% people are examined with no nearsighted
The likelihood that an ophthalmologist will first evaluate 5 people who are not nearsighted, then 1 person who is, is:
\(P = 0.58^{5}* 0.42^{1}\)
P = 0.0656 * 0.42
= 0.027552
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Twice a number decrease by four is less than 8
Answers
Twice a number decreased by four is less than 8 is x< 6.
2x - 4 < 8
2x < 8 + 4
2x < 12
x < 12 / 2
x < 6
Inequality refers to the unequal distribution of resources, opportunities, and outcomes among individuals or groups in a society. It can manifest in various forms, including economic inequality, social inequality, gender inequality, and racial inequality. Economic inequality refers to the unequal distribution of wealth and income, where some individuals or groups have access to more resources and opportunities than others.
Social inequality refers to the unequal distribution of social status and power, which can lead to marginalized groups being excluded from certain societal benefits. Gender and racial inequality refer to the unequal treatment and opportunities that certain genders or races face in society. Inequality can have negative consequences on individuals and society, including lower levels of social trust, reduced economic growth, and increased social tensions.
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Complete Question: -
Twice a number decreased by four is less than 8 is equation or inequality
Please HELP I Will Give 85 Brainy Points!
Answers
Answer: a) -1, 0, 1, 2 b) 14, 15, 16
a)
We want to find the value of "b" that makes the inequality 28 < 18 - 5b true.
We'll start by adding 5b to both sides to isolate "b".
Then, we'll simplify the equation to get 5b < -10.
Dividing both sides by 5 (and flipping the inequality because we're dividing by a negative number) gives b > -2.
So, b > -2, which means any value of "b" that is greater than -2 will make the inequality true.
b)
we want to isolate the variable "y" on one side of the inequality.
First, we'll simplify the left-hand side by dividing both sides by -3:
y/17 < 1
Next, we'll multiply both sides by 17 to isolate "y":
y < 17
So, y < 17. This means that any value of "y" less than 17 will make the inequality true.
What is 40009,547+24719,783? I need to know now
Answers
Answer:
64729,330
You add the numbers together using place value.
If a gallon of gas costs $1.85, how many gallons would you purchase for $15.54?
Answers
Answer:
8.4 Gallons
Step-by-step explanation:
The answer is 8.4 because 15.54 divided by 1.85 is 8.4
Answer:
About 8.4 gallons
Step-by-step explanation:
15.54/1.85=8.4
Which conversion requires multiplication?
A. Kiloliters to milliliter B. Centimeters to kilometer
C. millimeters to dekagram
D. Decimeter to hectometer
Answers
Answer:
i beleive its centimeters
Step-by-step explanation:
how do u do this question...
please explain
Answers
Answer: by the looks of it you’re dealing with exponents. so the exponent of 3 ^2 would be 3 • 3 =9. So now the equation is 10-9 = 1.
Step-by-step explanation: The next one is the same. 9•9=81 // 3 + 81= 84
Hope that helps!:) -Andi