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?

In 2009, the Los Angeles Angels had 1105 singles, 293 doubles, 33 triples, 173 home runs, 547 walks, 148 stolen bases, and made 4070 outs.

a) How many runs does the model predict that they will score?

b) In 2009, the Angels actually scored 883 runs. Calculate and interpret their residual.

c) Interpret the coefficient of singles and the coefficient of walks. Which event is more valuable? Explain why this might make sense.

d) Interpret the value $s=21.6$.

Can we predict the maximum bench press for athletes based on just their height and weight? Using a sample of 64 female Division I athletes from the University of Georgia, the following model was calculated using $y=$ maximum bench press (in pounds), $x_1=$ height (in inches), and $x_2=$ weight (in pounds):

$$\begin{aligned} & \hat{y}=188.12-3.0544 x_1+0.8289 x_2 \\ & s=14.43 \end{aligned}$$

a) If you compared two athletes who were the same height, would a heavier or lighter athlete be predicted to bench press more weight? Explain.

b) If you compared two athletes who were the same weight, would a taller or shorter athlete be predicted to bench press more weight? Explain.

c) Explain why it isn't a good idea to interpret the value $188.12$ in this context.

d) Calculate and interpret the residual for the athlete who was $68.5$ inches tall, weighed 138 pounds, and had a maximum bench press of 100 pounds.

In the 2010 regular season, the New York Jets scored 367 points and allowed 304 points.

a) Predict the number of wins for the 2010 Jets.

b) The Jets actually won 11 games in the 2010 regular season. Calculate and interpret their residual.

c) Interpret the value $s=1.30$.

d) Explain how to determine which model, the multiple regression model or the Pythagorean model, gives better predictions.

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.

a. Does Target have a defined contribution or defined benefit pension plan? Explain.

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).

Use the following information. The table shows regulation distances between hurdles in women's and men's races. In both the women's and men's events, the race consists of a straight track with 10 equally spaced hurdles.

$$\begin{matrix} \text{Event} & \text{Distance of Race} & \text{Distance from Start to First Hurdle} & \text{Distance Between Hurdles} & \text{Distance from Last Hurdle to Finish}\\ \text{Women's} & \text{100 m} & \text{13.00 m} & \text{8.50 m} & \square\\ \text{Men's} & \text{110 m} & \text{13.72 m} & \text{9.14 m} & \square\\ \end{matrix}$$

Find the distance from the last hurdle to the finish line for the men's race.

A $100$-kVA, $8000/277$-V distribution transformer has the following resistances and reactances:

$$\begin{aligned} R_p & = 5\ \Omega & \quad \quad & R_S = 0.005\ \Omega\\ X_p & = 6\ \Omega & \quad \quad & X_S = 0.006\ \Omega\\ R_C & = 50\ \text{k}\Omega & \quad \quad & X_M = 10\ \text{k}\Omega \end{aligned}$$

The excitation branch impedances are given referred to the high-voltage side of the transformer.

(a) Find the equivalent circuit of this transformer referred to the low-voltage side.

(b) Find the per-unit equivalent circuit of this transformer.

(c) Assume that this transformer is supplying rated load at $277$ V and $0.85$ PF lagging. What is this transformer’s input voltage? What is its voltage regulation?

(d) What are the copper losses and core losses in this transformer under the conditions of part (c)?

(e) What is the transformer’s efficiency under the conditions of part (c)?

Write an essay in which you explain how the structure of a story in this unit leads to a specific emotional effect, such as tension or suspense.

• Identify the story's main conflict and summarize the narrative.

• Describe specific structural choices the writer makes. For example, discuss how much exposition the author provides and how he or she introduces the conflict. Also describe any use of plot devices, such as foreshadowing.

• Finally, explain how the story affects you as a reader and how the author's choices regarding structure contribute to that effect.

• Cite textual evidence to support your assertions.

Vitousek and Farrington (1997) investigated nutrient limitations in soils of different ages. In the abstract of their paper, they say, Walker and Syers (1976) proposed a conceptual model that describes the pattern and regulation of soil nutrient pools and availability during long-term soil and ecosystem development. Their model implies that plant production generally should be limited by N [nitrogen] on young soils and by P [phosphorus] on old soils; N and P supply should be more or less equilibrate on intermediate aged soils. Vitousek and Farrington tested this hypothesis by conducting fertilizer experiments along a gradient of soil age, measuring the average increment in diameter (in mm/yr) of Metrosideros polymorpha trees. Denote by D(N, P, t) the diameter increment (in mm/yr) as a function of the amount of nitrogen (N) added, the amount of phosphorus (P) added, and the age (t) of the soil. Vitousek and Farrington’s experiments showed that $\frac{\partial D}{\partial t}(\mathrm{N}, 0, t)<0$ and $\frac{\partial D}{\partial t}(0, \mathrm{P}, t)>0$ for their choices of N > 0 and P > 0. Explain why their results support theWalker and Syers hypothesis.

Use the following information for this exercise .

The table shows regulation distances between hurdles in women's and men's races. In both the women's and men's events, the race consists of a straight track with 10 equally spaced hurdles.

Find the distance from the last hurdle to the finish line for the women's race.

Your company, Sonic Video, Inc., has conducted research that shows the following probability distribution, where X is the number of video arcades in a randomly chosen city with more than 500,000 inhabitants:

$$\begin{matrix} \text{x} & \text{0} & \text{1} & \text{2} & \text{3} & \text{4} & \text{5} & \text{6} & \text{7} & \text{8} & \text{9}\\ \text{P(X=x)} & \text{.07} & \text{.09} & \text{.35} & \text{.25} & \text{.15} & \text{.03} & \text{.02} & \text{.02} & \text{.01} & \text{.01}\\ \end{matrix}$$

a. Compute the mean, variance, and standard deviation (accurate to one decimal place). b. As CEO of Startrooper Video Unlimited, you wish to install a chain of video arcades in Sleepy City, U.S.A. The city council regulations require that the number of arcades be within the range shared by at least 75% of all cities. What is this range? What is the largest number of video arcades you should install so as to comply with this regulation?

Wood bats are required in professional baseball but metal bats are sometimes allowed in youth and college baseball. One result is that the exit speed $v$ of the baseball off a metal bat can be greater. In one set of measurements under the same circumstances, $v=50.98 \mathrm{~m} / \mathrm{s}$ off a wood bat and $v=61.50 \mathrm{~m} / \mathrm{s}$ off a metal bat. Consider a ball hit directly toward the pitcher. The regulation distance between pitcher and batter is $\Delta x=60 \mathrm{ft} 6 \mathrm{in}$. For those measured speeds, how much time $\Delta t$ does the ball take to reach the pitcher for (a) the wood bat and (b) the metal bat? (c) By what percentage would $\Delta t$ be reduced if professional baseball switched to metal bats? Because pitchers do not wear any protective equipment on face or body, the situation is already dangerous and the switch would add to that danger.

A species of bacteria can synthesize the amino acid histidine so it does not require histidine in its growth medium. A key enzyme, which we will call histidine synthetase, is necessary for histidine biosynthesis. When these bacteria are given histidine in their growth media, they stop synthesizing histidine intracellularly. Based on this observation alone, propose three different regulatory mechanisms to explain why histidine biosynthesis ceases when histidine is in the growth medium. To explore this phenomenon further, you measure the amount of intracellular histidine synthetase protein when cells are grown in the presence and absence of histidine. In both conditions, the amount of this protein is identical. Which mechanism of regulation would be consistent with this observation?