A sporting goods store finds that if it sells x exercise machines per day, its costs will be $C(x)=100 x+3200$ and its revenue will be $R(x)=-2 x^{2}+300 x$ (both in dollars). a. Find the store’s break-even points. b. Find the number of sales that will maximize profit, and the maximum profit.

Explain the structure and function of the parasympathetic nervous system.

Find $f^{\prime}(x)$ by using the definition of the derivative. $f(x)=x^{3}+x^{2}$

For the quadratic function $f(x)=a x^{2}+b x+c$, what condition on one of the coefficients will guarantee that the function has a highest value? A lowest value?

If the revenue function for a particular commodity is $R(p)=-50 p^{2}+60 p$, what is the (linear) demand function? Give a reason for your answer.

The table shows the retail market share of passenger cars from Ford Motor Company as a percentage of the U.S. market.

$$\begin{matrix} \text{Year } & \text{Market Share}\\ \text{1980} & \text{}{17.2 \%}\\ \text{1985} & \text{}{18.8 \%}\\ \text{1990} & \text{}{20.0 \%}\\ \text{1995} & \text{}{20.7 \%}\\ \text{2000} & \text{}{20.2 \%}\\ \text{2005} & \text{}{17.4 \%}\\ \text{2010} & \text{}{16.4 \%}\\ \end{matrix}$$

A mathematical model for this data is given by $f(x)=-0.0169 x^{2}+0.47 x+17.1$ where x=0 corresponds to 1980 (A) Complete the following table. Round values of f(x) to one decimal place.

$$\begin{matrix} \text{x} & \text{Market Share} & \text{f(x)}\\ \text{0} & \text{17.2}\\ \text{5} & \text{18.8}\\ \text{10} & \text{20.0}\\ \text{15} & \text{20.7}\\ \text{20} & \text{20.2}\\ \text{25} & \text{17.4}\\ \text{30} & \text{16.4}\\ \end{matrix}$$

(B) Sketch the graph of f and the market share data in the same coordinate system. (C) Use values of the modeling function f to estimate Ford's market share in 2020 and in 2025. (D) Write a brief description of Ford's market share from 1980 to 2010.

The Better Baby Buggy Co. has just come out with a new model, the Turbo. The market research department predicts that the demand equation for Turbos is given by q=-2p+320, where q is the number of buggies it can sell in a month if the price is $p per buggy. At what price should it sell the buggies to get the largest revenue? What is the largest monthly revenue?

Use technology to find the quadratic regression curve through the given points. (Round all coefficients to four decimal places.) {(−1, 2), (−3, 5), (−4, 3)}

The energy, $E$, in foot-pounds, delivered by an ocean wave is proportional to the length, $L$, of the wave times the square of its height, $h$.

(a) Write a formula for $E$ in terms of $L$ and $h$.

(b) A 30-foot high wave of length 600 feet delivers 4 million foot-pounds of energy. Find the constant of proportionality and give its units.

(c) If the height of a wave is one-fourth the length, find the energy $E$ in terms of the length $L$.

(d) If the length is 5 times the height, find the energy $E$ in terms of the height $h$.

Table 2.8 shows world gold production, G=f(t), as a function of year, t.

$$\begin{matrix} \text{t (year)} & \text{2005} & \text{2006} & \text{2007} & \text{2008} & \text{2009}\\ \text{G (metric tons)} & \text{2470} & \text{2370} & \text{2360} & \text{2290} & \text{2450}\\ \end{matrix}$$

Use the estimated value of f'(2009) to estimate f(2010) and f(2015), and interpret your answers.

As sales manager for Montevideo Productions, Inc., you are planning to review the prices you charge clients for television advertisement development. You currently charge each client an hourly development fee of $2,500. With this pricing structure, the demand, measured by the number of contracts Montevideo signs per month, is 15 contracts. This is down 5 contracts from the figure last year, when your company charged only$2,000. a. Construct a linear demand equation giving the number of contracts q as a function of the hourly fee p Montevideo charges for development. b. On average, Montevideo bills for 50 hours of production time on each contract. Give a formula for the total revenue obtained by charging $p per hour. c. The costs to Montevideo Productions are estimated as follows:$

$$\begin{matrix} \text{Fixed costs:} & \text{\$120,000 per month}\\ \text{Variable costs:} & \text{\$80,000 per contract}\\ \end{matrix}$$

$Express Montevideo Productions’ monthly cost (i) as a function of the number q of contracts and (ii) as a function of the hourly production charge p. d. Express Montevideo Productions’ monthly profit as a function of the hourly development fee p and hence the price it should charge to maximize the profit.

Suppose that a company has fixed costs of $11 per unit and variable costs$6 per unit when 11,000 units are produced. What are the fixed costs per unit when 20,000 units are produced?

Besides bone, what other types of tissue are included in the skeletal system?

Dysplasia is a malformation of the hip socket that is very common in certain dog breeds and causes arthritis as a dog gets older. According to the Orthopedic Foundation for Animals, 11.6% of all Labrador retrievers have hip dysplasia. A veterinarian tests a random sample of 50 Labrador retrievers and records Y= the number of Labs with dysplasia in the sample. Calculate the mean and standard deviation of the sampling distribution of Y.