A demographic study of a certain city indicates that P(r) hundred people live r miles from the civic center, where $P(r)=\frac{5(3 r+1)}{r^{2}+r+2}.$ a. What is the population at the city center? b. For what values of r is P(r) increasing? For what values is it decreasing? c. At what distance from the civic center is the population largest? What is this largest population?

A demographic study of a certain city indicates that $P(r)$ hundred people live $r$ miles from the civic center, where

$$P(r)=\frac{5(3 r+1)}{r^2+r+2}$$

a. What is the population at the city center?

b. For what values of $r$ is $P(r)$ increasing? For what values is it decreasing?

c. At what distance from the civic center is the population largest? What is this largest population?

To produce x units of a particular commodity, a monopolist has a total cost of $C(x)=2 x^{2}+3 x+5$ and total revenue of R(x) = xp(x), where p(x) = 5 - 2x is the price at which the x units will be sold. Find the profit function P(x) = R(x) - C(x), and sketch its graph. For what level of production is profit maximized?

A company determines that if x thousand dollars are spent on advertising a certain product, then S(x) units of the product will be sold, where $S(x)=-2 x^{3}+27 x^{2}+132 x+207$ for $0 \leq x \leq 17.$ a. Sketch the graph of S(x). b. How many units will be sold if nothing is spent on advertising? c. How much should be spent on advertising to maximize sales? What is the maximum sales level?

Commissioners of a certain city determine that when x million dollars are spent on controlling pollution, the percentage of pollution removed is given by $P(x)=\frac{100 \sqrt{x}}{0.04 x^{2}+12}.$ a. Sketch the graph of P(x). b. What expenditure results in the largest percentage of pollution removal?

Determine which of the following is correct regarding the yeast Saccharomyces cerevisiae. a. It reproduces asexually by a process called budding. b. It produces an ascocarp during reproduction. c. It belongs in the group Zygomycota. d. All of the above are correct.

A company determines that if $x$ thousand dollars are spent on advertising a certain product, then $S(x)$ units of the product will be sold, where

$$S(x)=-2 x^3+27 x^2+132 x+207 \quad 0 \leq x \leq 17$$

a. Sketch the graph of $S(x)$.

b. How many units will be sold if nothing is spent on advertising?

c. How much should be spent on advertising to maximize sales? What is the maximum sales level?

The concentration of a drug t hours after being injected into the arm of a patient is given by $C(t)=\frac{0.15 t}{t^{2}+0.81}.$ Sketch the graph of the concentration function. When does the maximum concentration occur?

The marketing manager at Levi-Strauss wishes to find a function that relates the demand D for men’s jeans and p, the price of the jeans. The following data were obtained based on a price history of the jeans.

$$\begin{matrix} \text{Price (\$/Pair), $\boldsymbol{p}$} & \text{Demand (Pairs of Jeans}\\ \text{ } & \text{Sold per Day), D}\\ \text{20} & \text{60}\\ \text{22} & \text{57}\\ \text{23} & \text{56}\\ \text{23} & \text{53}\\ \text{27} & \text{52}\\ \text{29} & \text{49}\\ \text{30} & \text{44}\\ \end{matrix}$$

Draw a scatter diagram of the data.

Choose the best answer. What is the missing term in the proportion $\frac{18}{114}=\frac{3}{x} ?$ A. x = 19 B. x = 38 C. x = 342 D. x = 684

rewrite each angle in radian measure as a multiple of π. (Do not use a calculator.) -60°

Prove that the zero transformation $T_0:R^n\to R^n$ equals $T_O$ and hence is linear.

Sketch a graph of a function that has all the following properties: a. f'(x) > 0 when x < -5 and when x > 1 b. f'(x) < 0 when -5 < x < 1 c. f(-5) = 4 and f(1) = -1

A bus comes to a station once every 10 minutes and waits at the station for 1.5 minutes. Find the probability that the bus will be at the station when you arrive.