A study of driving costs based on 2012 medium-sized sedans found that the average cost (car payments, gas, insurance, upkeep, and depreciation) in cents per mile is approximately $C(x)=\frac{1910.5}{x^{1.72}}+42.9 \ (5 \leq x \leq 20)$ where x (in thousands) denotes the number of miles the car is driven each year. Show that C is a decreasing function of x on the interval (5, 20). What does your result tell you about the average cost of driving a 2012 mediumsized sedan in terms of the number of miles driven?

Evaluate each expression if a = 2, b = 4, and c = 3. $36-12 c$

Which of the following is a random variable? a. The population mean b. The population size, N c. The sample size, n d. The sample mean e. The variance of the sample mean f. The largest value in the sample g. The population variance h. The estimated variance of the sample mean

Let us consider the following equations which are given by $f(x)=x e^{-x}$ and $g(x)=x-2 \sqrt{x}$. Plot the graphs of the functions f and g.

For the following exercise, points P(1, 1) and Q(x, y) are on the graph of the function $f(x)=x^{3}$. Complete the following table with the appropriate values: y-coordinate of Q, the point Q(x, y), and the slope of the secant line passing through points P and Q. Round your answer to eight significant digits.

$$\begin{matrix} \text{x} & \text{y} & \text{Q(x, y)} & {m_{sec}}\\ \text{1.1} & \text{a.} & \text{e.} & \text{i.}\\ \text{1.01} & \text{b.} & \text{f.} & \text{j.}\\ \text{1.001} & \text{c.} & \text{g.} & \text{k.}\\ \text{1.0001} & \text{d.} & \text{h.} & \text{l.}\\ \end{matrix}$$

Explain why it is better to allow MATLAB to default to double-precision floating-point number representations for most engineering calculations than to specify single and integer types.

Find the indefinite integral. $\int\left(\sqrt{x}+\frac{3}{\sqrt{x}}\right) d x$

Find the indefinite integral. $\int \frac{x^{2}-1}{x^{3}-3 x+1} d x$

A building contains two elevators, one fast and one slow. The average waiting time for the slow elevator is 3 min. and the average waiting time of the fast elevator is 1 min. If a passenger chooses the fast elevator with probability $\frac{2}{3}$ and the slow elevator with probability $\frac{1}{3}$, what is the expected waiting time?

A study of fishing in a small Jamaican village found that the fishermen used three strategies for locating their fishing pots. Some fished in the inside banks with their safe currents and poorer fishing. Others fished in the outside banks, which yield more and better fish but have dangerous strong currents. Still others put one-third of their pots in the inner banks and the rest in the outer banks. The payoffs per month (in pounds) depended on whether or not there was a strong current, as indicated by the following payoff matrix:

$$\begin{matrix} \text{ } & \text{ } & \text{Environment} & \text{ }\\ \text{ } & \text{ } & \text{Current} & \text{No Current}\\ & \text{Inside} &17.3&11.5\\ \text{Fisherman} & \text{Outside}&-4.4&20.6\\ & \text{Mixture}&5.2&17.0 \\ \end{matrix}$$

(a) Find the optimum strategy for the fishermen and for the environment, as well as the expected payoff to the fishermen. (b) The environment actually had current 25% of the time and no current 75% of the time. What should the fisherman's strategy be in this case, and what is the payoff? (c) Based on your results from parts (a) and (b), discuss the wisdom of considering the environment as a player in the game.

For the following exercise, a. find the inverse function, and b. find the domain and range of the inverse function. $f(x)=x^{2}-4, x \geq 0$

For the following exercise, evaluate the given exponential function as indicated, accurate to two significant digits after the decimal. $f(x)=10^{x}$ a. x = -2 b. x = 4 c. $x=\frac{5}{3}$

(a) identify the claim and state $H_0$ and $H_a$, (b) decide which nonparametric test to use, (c) find the critical value(s), (d) find the test statistic, (e) decide whether to reject or fail to reject the null hypothesis, and (f) interpret the decision in the context of the original claim. An investment company claims that the median age of people with mutual funds is 51 years. The ages (in years) of 20 randomly selected mutual fund owners are listed below. At $\alpha=0.01$, is there enough evidence to reject the company’s claim?

$$\begin{matrix} \text{46 34 33 27 58 64 54 36 38 42}\\ \text{26 51 49 44 46 50 39 34 51 63}\\ \end{matrix}$$

The annual earnings (in dollars) for 30 randomly selected locksmiths are shown below. Assume the population is normally distributed.

$$\begin{matrix} \text{44,044 42,206 38,262 57,022 66,462 50,211}\\ \text{64,804 67,191 55.101 64.962 49,634 47,516}\\ \text{61,710 43,514 60,622 30,600 56,477 60,747}\\ \text{54,275 54,266 54,367 48.420 40,549 65,291}\\ \text{64,842 52,435 49,179 48,042 63,648 49,142}\\ \end{matrix}$$

(a) Construct a 95% confidence interval for the population mean annual earnings ror locksmiths. (b) A researcher claims that the mean annual earnings for locksmiths is $53,000. At$\alpha=0.05$, can you reject the researcher's claim? Interpret the decision in the context of the original claim.