# A car dealership offers a $1300 rebate and a 15% discount off the price of a new car. Let p be the sticker price of a new car on the dealer's lot, r the price after the rebate, and d the discounted price. Then r(p) = p − 1300 and d(p) = 0.85p. a) Write a composite function for the dealer taking the rebate first and then the discount. d[r(p)] = b) Write a composite function for the dealer taking the discount first and then the rebate. r[d(p)] = # A car dealership offers a$1300 rebate and a 15% discount off the price of a new car. Let p be the sticker price of a new car on the dealer's lot, r the price after the rebate, and d the discounted price. Then r(p) = p − 1300 and d(p) = 0.85p. a) Write a composite function for the dealer taking the rebate first and then the discount. d[r(p)] = b) Write a composite function for the dealer taking the discount first and then the rebate. r[d(p)] =

Question
Composite functions
A car dealership offers a $1300 rebate and a 15% discount off the price of a new car. Let p be the sticker price of a new car on the dealer's lot, r the price after the rebate, and d the discounted price. Then r(p) = p − 1300 and d(p) = 0.85p. a) Write a composite function for the dealer taking the rebate first and then the discount. d[r(p)] = b) Write a composite function for the dealer taking the discount first and then the rebate. r[d(p)] = ## Answers (1) 2021-01-17 (a). Write the composite function for the dealer taking the rebate first and then discount. d[r(p)]=d[p-1300] =0.85(p-1300) =0.85p-1105 (b). Write the composite function for the dealer taking the discount first and then the rebate r[d(p)]=r[0.85p] =0.85p-1300 ### Relevant Questions asked 2021-05-08 Write an exponential growth or decay function to model each situation. Then find the value of the function after the given amount of time. A new car is worth$25,000, and its value decreases by 15% each year; 6 years.
(1 pt) A new software company wants to start selling DVDs withtheir product. The manager notices that when the price for a DVD is19 dollars, the company sells 140 units per week. When the price is28 dollars, the number of DVDs sold decreases to 90 units per week.Answer the following questions:
A. Assume that the demand curve is linear. Find the demand, q, as afunction of price, p.
B. Write the revenue function, as a function of price. Answer:R(p)=
C. Find the price that maximizes revenue. Hint: you may sketch thegraph of the revenue function. Round your answer to the closestdollar.
D. Find the maximum revenue. Answer:
The regular price of a computer is x dollars. Let f(x) = x - 400 and g(x) = 0.75x. Solve,
a. Describe what the functions f and g model in terms of the price of the computer.
b. Find $$\displaystyle{\left({f}\circ{g}\right)}{\left({x}\right)}$$ and describe what this models in terms of the price of the computer.
c. Repeat part (b) for $$\displaystyle{\left({g}\circ{f}\right)}{\left({x}\right)}$$.
d. Which composite function models the greater discount on the computer, $$\displaystyle{f}\circ{g}$$ or $$\displaystyle{g}\circ{f}$$?
Mr. Maxwell bought new basketball shows with the discount shown. He has a $10-off coupon he can use after the percentage off. If Mr. Maxwell bought the shows for$61.25, what was the original price?
A. If the shoes are discounted 25%, what percent of the original price is the original price?
25% discount is the same as □□% of the original price.
B. Fill in the boxes to set up the equation to find the original price of the shoes.
□□% ⋅⋅ Original Price −=61.25−=61.25
C. What would be the price without a $10-off coupon? 61.25+□=□61.25+□=□$_____
Consider the curves in the first quadrant that have equationsy=Aexp(7x), where A is a positive constant. Different valuesof A give different curves. The curves form a family,F. Let P=(6,6). Let C be the number of the family Fthat goes through P.
A. Let y=f(x) be the equation of C. Find f(x).
B. Find the slope at P of the tangent to C.
C. A curve D is a perpendicular to C at P. What is the slope of thetangent to D at the point P?
D. Give a formula g(y) for the slope at (x,y) of the member of Fthat goes through (x,y). The formula should not involve A orx.
E. A curve which at each of its points is perpendicular to themember of the family F that goes through that point is called anorthogonal trajectory of F. Each orthogonal trajectory to Fsatisfies the differential equation dy/dx = -1/g(y), where g(y) isthe answer to part D.
Find a function of h(y) such that x=h(y) is the equation of theorthogonal trajectory to F that passes through the point P.
A helicopter carrying dr. evil takes off with a constant upward acceleration of $$\displaystyle{5.0}\ \frac{{m}}{{s}^{{2}}}$$. Secret agent austin powers jumps on just as the helicopter lifts off the ground. Afterthe two men struggle for 10.0 s, powers shuts off the engineand steps out of the helicopter. Assume that the helicopter is infree fall after its engine is shut off and ignore effects of airresistance.
a) What is the max height above ground reached by the helicopter?
b) Powers deploys a jet pack strapped on his back 7.0s after leaving the helicopter, and then he has a constant downward acceleration with magnitude 2.0 m/s2. how far is powers above the ground when the helicopter crashes into the ground.
The bulk density of soil is defined as the mass of dry solidsper unit bulk volume. A high bulk density implies a compact soilwith few pores. Bulk density is an important factor in influencing root development, seedling emergence, and aeration. Let X denotethe bulk density of Pima clay loam. Studies show that X is normally distributed with $$\displaystyle\mu={1.5}$$ and $$\displaystyle\sigma={0.2}\frac{{g}}{{c}}{m}^{{3}}$$.
(a) What is thedensity for X? Sketch a graph of the density function. Indicate onthis graph the probability that X lies between 1.1 and 1.9. Findthis probability.
(b) Find the probability that arandomly selected sample of Pima clay loam will have bulk densityless than $$\displaystyle{0.9}\frac{{g}}{{c}}{m}^{{3}}$$.
(c) Would you be surprised if a randomly selected sample of this type of soil has a bulkdensity in excess of $$\displaystyle{2.0}\frac{{g}}{{c}}{m}^{{3}}$$? Explain, based on theprobability of this occurring.
(d) What point has the property that only 10% of the soil samples have bulk density this high orhigher?
(e) What is the moment generating function for X?
Dayton Power and Light, Inc., has a power plant on the Miami Riverwhere the river is 800 ft wide. To lay a new cable from the plantto a location in the city 2 mi downstream on the opposite sidecosts $180 per foot across the river and$100 per foot along theland.
(a) Suppose that the cable goes from the plant to a point Q on theopposite side that is x ft from the point P directly opposite theplant. Write a function C(x) that gives the cost of laying thecable in terms of the distance x.
(b) Generate a table of values to determin if the least expensivelocation for point Q is less than 2000 ft or greater than 2000 ftfrom point P.
A 1300-kg car coasts on a horizontal road, with a speed of18m/s. After crossing an unpaved sandy stretch of road 30.0 mlong, its speed decreases to 15m/s. If the sandy portion ofthe road had been only 15.0 m long, would the car's speed havedecreasedby 1.5 m/s, more than 1.5 m/s, or less than 1.5m/s?Explain. Calculate the change in speed in that case.

A random sample of $$n_1 = 14$$ winter days in Denver gave a sample mean pollution index $$x_1 = 43$$.
Previous studies show that $$\sigma_1 = 19$$.
For Englewood (a suburb of Denver), a random sample of $$n_2 = 12$$ winter days gave a sample mean pollution index of $$x_2 = 37$$.
Previous studies show that $$\sigma_2 = 13$$.
Assume the pollution index is normally distributed in both Englewood and Denver.
(a) State the null and alternate hypotheses.
$$H_0:\mu_1=\mu_2.\mu_1>\mu_2$$
$$H_0:\mu_1<\mu_2.\mu_1=\mu_2$$
$$H_0:\mu_1=\mu_2.\mu_1<\mu_2$$
$$H_0:\mu_1=\mu_2.\mu_1\neq\mu_2$$
(b) What sampling distribution will you use? What assumptions are you making? NKS The Student's t. We assume that both population distributions are approximately normal with known standard deviations.
The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.
The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.
(c) What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate.
(Test the difference $$\mu_1 - \mu_2$$. Round your answer to two decimal places.) NKS (d) Find (or estimate) the P-value. (Round your answer to four decimal places.)
(e) Based on your answers in parts (i)−(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level \alpha?
At the $$\alpha = 0.01$$ level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
At the $$\alpha = 0.01$$ level, we reject the null hypothesis and conclude the data are statistically significant.
At the $$\alpha = 0.01$$ level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the $$\alpha = 0.01$$ level, we reject the null hypothesis and conclude the data are not statistically significant.
(f) Interpret your conclusion in the context of the application.
Reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver. (g) Find a 99% confidence interval for
$$\mu_1 - \mu_2$$.
(Round your answers to two decimal places.)
lower limit
upper limit
(h) Explain the meaning of the confidence interval in the context of the problem.
Because the interval contains only positive numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, we can not say that the mean population pollution index for Englewood is different than that of Denver.
Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains only negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is less than that of Denver.
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