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?

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).

The table shows regulation distances between hurdles in woman'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.

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

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

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?

If you have trouble sleeping, you are in good company: About 50 million American adults suffer from sleep deprivation. Some causes, such as drinking caffeine in the evening, are avoidable. Certain medical conditions, such as asthma and depression, can interfere with sleep-and so can some medications. Sleep deprivation is something you should take seriously. It can leave you without the energy or physical strength to meet the day's demands. You may find it harder to think clearly, to solve problems, or to remember things, too. Irritability, moodiness, and anxiety often can be traced to a lack of sleep

The passage explains that sleep deprivation may result in-

A. moodiness and an inability to solve problems.

B. asthma and emotional irritability.

C. weight loss and anxiety.

D. anxiety and an increased need for medication.

We often describe our emotional reaction to social rejection as "pain." Does social rejection cause activity in areas of the brain that are known to be activated by physical pain? If it does, we really do experience social and physical pain in similar ways. Psychologists first included and then deliberately excluded individuals from a social activity while they measured changes in brain activity. After each activity, the subjects filled out questionnaires that assessed how excluded they felt. Here are data for 13 subjects:

$$\begin{array}{ccc} \hline \text { SUBJECT } & \begin{array}{c} \text { SOCIAL } \\ \text { DISTRESS } \end{array} & \begin{array}{c} \text { BRAIN } \\ \text { ACTIVITY } \end{array} \\ \hline 1 & 1.26 & 0.055 \\ \hline 2 & 1.85 & -0.040\hspace{8pt} \\ \hline 3 & 1.10 & -0.026\hspace{8pt} \\ \hline 4 & 2.50 & -0.017\hspace{8pt} \\ \hline 5 & 2.17 & -0.017 \hspace{8pt}\\ \hline 6 & 2.67 & 0.017 \\ \hline 7 & 2.01 & 0.021 \\ \hline 8 & 2.18 & 0.025 \\ \hline 9 & 2.58 & 0.027 \\ \hline 10 & 2.75 & 0.033 \\ \hline 11 & 2.75 & 0.064 \\ \hline 12 & 3.33 & 0.077 \\ \hline 13 & 3.65 & 0.124 \\ \hline \end{array}$$

The explanatory variable is "social distress" measured by each subject's questionnaire score after exclusion relative to the score after inclusion. (So values greater than 1 show the degree of distress caused by exclusion.) The response variable is change in activity in a region of the brain that is activated by physical pain. Negative values show a decrease in activity, suggesting less distress. Discuss what the data show about the relationship between social distress and brain activity.

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)?

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. 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 women's race.

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.

Optimal goal target in soccer. When attempting to score a goal in soccer, where should you aim your shot? Should you aim for a goalpost (as some soccer coaches teach), the middle of the goal, or some other target? To answer these questions, Chance (Fall 2009) utilized the normal probability distribution. Suppose the accuracy $x$ of a professional soccer player's shots follows a normal distribution with a mean of 0 feet and a standard deviation of 3 feet. (For example, if the player hits his target, $x=0$; if he misses his target 2 feet to the right, $x=2$; and if he misses 1 foot to the left, $x=-1$.) Now, a regulation soccer goal is 24 feet wide. Assume that a goalkeeper will stop (save) all shots within 9 feet of where goalkeeper who stands in the middle of the goal. If the player aims for halfway between the right goalpost and the outer limit of the goalkeeper's reach, what is the probability that he will score?

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.

The City of Imperial Falls contracts with Evergreen Waste Collection to provide solid waste collection to households and businesses. Until recently, Evergreen had an exclusive franchise to provide this service in Imperial Falls, which meant that other waste collection fi rms could not operate legally in the city. The price per pound of waste collected was regulated at 20 percent above the average total cost of collection.

Cost data for the most recent year of operations for Evergreen are shown below:

Data on customers for the most recent year are:

The City Council of Imperial Falls is considering allowing other private waste haulers to collect waste from businesses, but not from households. Service to businesses from other waste collection firms would not be subject to price regulation. Based on information from neighboring cities, the price that other private waste collection firms will charge is estimated to be$0.04 per pound (= $80 per ton).

Evergreen’s CEO has approached the city council with a proposal to change the way costs are allocated to households and businesses, which will result in different rates for households and businesses. She proposes that administrative costs and truck operating costs be allocated based on the number of customers and the other collection costs be allocated based on pounds collected. The total costs allocated to households would then be divided by the estimated number of pounds collected from households to determine the cost of collection. The rate would then be 20 percent above the cost. The rate for businesses would be determined using the same calculation.

Required
As a staff member to one of the council members, would you support the proposal to change the way costs are allocated? Explain.

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?