A least-squares regression line was used to model the relationship between putting average (on greens hit in regulation) and scoring average for golfers on the 2009 PGA tour. The corresponding residual plot is shown below.

a) Based on the residual plot, is a linear model appropriate for this association? Explain.

b) The point highlighted in red is for the golfer David Duval. Estimate his residual from the graph and interpret its value.

c) If you were to predict the scoring average for a golfer with a putting average of $1.86$, would you expect your prediction to be too low, too high, or just about right? Explain.

Match the structures on the right with their function listed on the left.

$$\begin{matrix} \text{1. Protection from ultraviolet radiation} & \text{a. Reticular layer of the dermis}\\ \text{2. Insulation, energy storage} & \text{b. Dermal blood supply }\\ \text{3. Waterproofing and preventing water loss} & \text{c. Papillary layer of the dermis}\\ \text{4. Temperature regulation} & \text{d. Hypodermis }\\ \text{5. Excretion of water, urea, and salts} & \text{e. Melanocytes }\\ \text{6. Produces the patterns for fingerprints} & \text{f. Stratum corneum}\\ \text{ } & \text{g. Eccrine sweat glands}\\ \end{matrix}$$

Draw a correctly labeled graph showing a natural monopoly. On your graph, label the price and quantity the monopoly will choose if unregulated as

$$P_U$$

and

$$Q_U$$

What happens to the size of consumer surplus when the firm is required to charge

$$P_R$$

rather than

$$P_U?$$

A sporting goods manufacturer produces regulation soccer balls at two plants. The costs of producing $x_1$ units at location 1 and $x_2$ units at location 2 are given by $C_1\left(x_1\right)=0.02 x_1^2+4 x_1+500$ and

$$C_2\left(x_2\right)=0.05 x_2^2+4 x_2+275$$

respectively. If the product sells for $50 per unit, then the profit function for the product is given by

$$P\left(x_1, x_2\right)=50\left(x_1+x_2\right)-C_1\left(x_1\right)-C_2\left(x_2\right) .$$

Find P(300,200).

Underwater pressure. At sea level, the weight of the atmosphere exerts a pressure of $14.7$ pounds per square inch, commonly referred to as $1$ atmosphere of pressure. As an object descends in water, pressure $P$ and depth $d$ are linearly related. In salt water, the pressure at a depth of $33 \mathrm{ft}$ is $2 \mathrm{atms}$, or $29.4$ pounds per square inch. (A) Find a linear model that relates pressure $P$ (in pounds per square inch) to depth $d$ (in feet). (B) Interpret the slope of the model. (C) Find the pressure at a depth of $50 \mathrm{ft}$. (D) Find the depth at which the pressure is $4$ atms.

Refer to the zener diode datasheet. (a) What is the maximum dc power dissipation at $25^{\circ} \mathrm{C}$ for a $1 \mathrm{~N} 4738 \mathrm{~A}$ ? (b) Determine the maximum power dissipation at $70^{\circ} \mathrm{C}$ and at $100^{\circ} \mathrm{C}$ for a $1 \mathrm{~N} 4751 \mathrm{~A}$. (c) What is the minimum current required by the $1 \mathrm{~N} 4738 \mathrm{~A}$ for regulation? (d) What is the maximum current for the $1 \mathrm{~N} 4750 \mathrm{~A}$ at $25^{\circ} \mathrm{C}$ ? (e) The current through a $1 \mathrm{~N} 4740 \mathrm{~A}$ changes from $25 \mathrm{~mA}$ to $0.25 \mathrm{~mA}$. How much does the zener impedance change?

Target Corporation provides the following footnote relating to its retirement plans in its 2017 10-K report: Defined Contribution Plans Team members who meet eligibility requirements can participate in a defined contribution 401(k) plan by investing up to 80 percent of their eligible earnings. as limited by statute or regulation. We match 100 percent of each team member's contribution up to 5 percent of eligible earnings.

Company match contributions are made to funds designated by the participant, none of which are based on Target common stock. Benefits expense related to these matching contributions was $219 million,$197 million, and $224 million in 2017, 2016, and 2015, respectively.

d. Do you see any problems for employees in Target's plan?

For women's collegiate competition, a basketball's circumference, mass, and bounce height must fall within given tolerance levels of regulation measurements. The table shows these tolerance levels äs well as measurements taken on five different basketballs. Which basketball meets all of the specified tolerances? $$ \begin{matrix} \text{ } & \text{Circumference (mm)} & \text{Mass (g)} & \text{Bounce Height (mm)}\\ \text{Tolerance} & {730.56 \pm 6.5} & {53.8.5 \pm 48.5} & {1358.5 \pm 63.5}\\ \text{Basketball #1} & \text{729.8} & \text{509.3} & \text{1343.4}\\ \text{Basketball #2} & \text{723.5} & \text{529.8} & \text{1299.8}\\ \text{Basketball #3} & \text{734.2} & \text{542.6} & \text{1293.5}\\ \text{Basketball #4} & \text{725.5} & \text{528} & \text{1364.5}\\ \text{Basketball #5} & \text{740} & \text{555.9} & \text{1407.4}\\ \end{matrix} $$

In baseball, the more home runs a player hits, the more likely it is that he makes the Hall of Fame. Using the 317 eligible players with the most at-bats, the following logistic model was calculated using the number of home runs as the explanatory variable and Hall of Fame status $(1=$ in the HOF, $0=$ not in the HOF) as the response variable:

$$\hat{p}=\frac{e^{-1.241+0.00256 x}}{1+e^{-1.241+0.00256 x}}$$

a) Calculate and interpret the value of $\hat{p}$ when $x=300$.

b) Calculate the values of $\hat{p}$ when $x=100,200,400,500$ and graph the logistic function.

c) Explain why it would not be appropriate to use a linear model in this context.

To be able to see your complete reflection in a mirror that is hanging on a wall, the mirror must have a minimum length of m inches. The value of m varies directly with your height h (in inches). A person 71 inches tall requires a 35.5 inch mirror. Write a linear model that gives m as a function of h. Then find the minimum mirror length required for a person who is 66 inches tall.

Using data from 176 male golfers on the 2009 PGA tour, a least-squares model was calculated to predict scoring average $(y)$ using $x_1=$ driving average (in yards), $x_2=$ driving accuracy (measured as a percent from 0 to 100), $x_3=$ putts per green-in-regulation (the average number of putts per hole when the green is reached in regulation), $x_4=$ sand save percent (the percentage of times a player hits his ball into a sand trap and successfully makes it into the hole in two or fewer additional strokes, measured as a percent from 0 to 100 ), and $x_5=$ over 40 years old ( 1 if over 40,0 if 40 or younger). Remember that lower scores are better in golf! The model is

$$\begin{aligned} & \hat{y}=69.6-0.041 x_1-0.072 x_2+10.603 x_3-0.0265 x_4-0.026 x_5 \\ & s=0.34 \end{aligned}$$

a) Interpret the value of $s=0.34$.

b) Predict the 2009 scoring average for Tiger Woods, who had a driving average of $298.4$, a driving accuracy of 64.3 %, a putts per green-inregulation average of $1.743$, a sand save percentage of 61.9%, and who is younger than 40 years old in 2009.

c) Tiger Woods actually had a scoring average of $68.84$ in 2009. Calculate and interpret his residual. (d) Interpret the coefficients of driving average and putts per green-inregulation.

e) After factoring in other variables, does the model suggest that it helps to be older? Explain. Why might this be?

Sketch an example of a graph that meets the description below. a. non-linear and decreasing b. linear and increasing

constant of variation direct variation domain function linear equation linear inequality range relation slope slope-intercept form solution system of linear equations system of linear inequalities vertical-line test y-intercept

Choose the vocabulary term that correctly completes the sentence.

A linear function modeled by the equation $y=k x$, where $k \neq 0$, is a ____.

Find the general solutions of the differential equation.

$$y ^ { y ^ { ( 4 ) } } = 16 y$$