Professor Grant Alexander wanted to find a linear model that relates the number of hours a student plays video games each week, h, to the cumulative grade-point average, G, of the student. He obtained a random sample of 10 full-time students at his college and asked each student to disclose the number of hours spent playing video games and the student’s cumulative grade-point average.

$$\begin{matrix} \text{Hours of} & \text{Grade-Point}\\ \text{Video Games} & \text{Average, G}\\ \text{per Week, h} & \text{ }\\ \text{0} & \text{3.49}\\ \text{0} & \text{3.05}\\ \text{2} & \text{3.24}\\ \text{3} & \text{2.82}\\ \text{3} & \text{3.19}\\ \text{5} & \text{2.78}\\ \text{8} & \text{2.31}\\ \text{8} & \text{2.54}\\ \text{10} & \text{2.03}\\ \text{12} & \text{2.51}\\ \end{matrix}$$

Use a graphing utility to draw a scatter diagram.

Professor Grant Alexander wanted to find a linear model that relates the number of hours a student plays video games each week, h, to the cumulative grade-point average, G, of the student. He obtained a random sample of 10 full-time students at his college and asked each student to disclose the number of hours spent playing video games and the student’s cumulative grade-point average.

$$\begin{matrix} \text{Hours of} & \text{Grade-Point}\\ \text{Video Games} & \text{Average, G}\\ \text{per Week, h} & \text{ }\\ \text{0} & \text{3.49}\\ \text{0} & \text{3.05}\\ \text{2} & \text{3.24}\\ \text{3} & \text{2.82}\\ \text{3} & \text{3.19}\\ \text{5} & \text{2.78}\\ \text{8} & \text{2.31}\\ \text{8} & \text{2.54}\\ \text{10} & \text{2.03}\\ \text{12} & \text{2.51}\\ \end{matrix}$$

Predict the grade-point average of a student who plays video games for 8 hours each week.

Professor Grant Alexander wanted to find a linear model that relates the number of hours a student plays video games each week, h, to the cumulative grade-point average, G, of the student. He obtained a random sample of 10 full-time students at his college and asked each student to disclose the number of hours spent playing video games and the student’s cumulative grade-point average.

$$\begin{matrix} \text{Hours of} & \text{Grade-point}\\ \text{Video Games} & \text{Average, $G$}\\ \text{per Week, $h$} & \text{ }\\ \hline \text{0} & \text{3.49}\\ \text{0} & \text{3.05}\\ \text{2} & \text{3.24}\\ \text{3} & \text{2.82}\\ \text{3} & \text{3.19}\\ \text{5} & \text{2.78}\\ \text{8} & \text{2.31}\\ \text{8} & \text{2.54}\\ \text{10} & \text{2.03}\\ \text{12} & \text{2.51}\\ \end{matrix}$$

How many hours of video game playing do you think a student plays whose grade-point average is 2.40?

Professor Grant Alexander wanted to find a linear model that relates the number of hours a student plays video games each week, h, to the cumulative grade-point average, G, of the student. He obtained a random sample of 10 full-time students at his college and asked each student to disclose the number of hours spent playing video games and the student’s cumulative grade-point average.

$$\begin{matrix} \text{Hours of} & \text{Grade-Point}\\ \text{Video Games} & \text{Average, G}\\ \text{per Week, h} & \text{ }\\ \text{0} & \text{3.49}\\ \text{0} & \text{3.05}\\ \text{2} & \text{3.24}\\ \text{3} & \text{2.82}\\ \text{3} & \text{3.19}\\ \text{5} & \text{2.78}\\ \text{8} & \text{2.31}\\ \text{8} & \text{2.54}\\ \text{10} & \text{2.03}\\ \text{12} & \text{2.51}\\ \end{matrix}$$

Use a graphing utility to find the line of best fit that models the relation between number of hours of video game playing each week and grade-point average. Express the model using function notation.

Racing cars driven by Chris and Kelly are side by side at the start of a race. The table shows the velocities of each car (in kilometres per hour) during the first 10 seconds of the race. Use the Midpoint Rule to estimate how much farther Kelly travels than Chris does during the first 10 seconds.

$$\begin{array}{|c|r|r||c|c|c|} \hline t & v_{C} & v_{K} & t & v_{C} & v_{K} \\ \hline 0 & 0 & 0 & 6 & 110 & 128 \\ 1 & 32 & 35 & 7 & 120 & 138 \\ 2 & 51 & 59 & 8 & 130 & 150 \\ 3 & 74 & 83 & 9 & 138 & 157 \\ 4 & 86 & 98 & 10 & 144 & 163 \\ 5 & 99 & 114 & & & \\ \hline \end{array}$$

The maintenance manager at a trucking company wants to build a regression model to forecast the time until the first engine overhaul (Time in years) based on four explanatory variables: (1) annual miles driven (Miles in 1,000s), (2) average load weight (Load in tons), (3) average driving speed (Speed in mph), and (4) oil change interval (Oil in 1,000 s miles). Based on driver logs and onboard computers, data have been obtained for a sample of 25 trucks.

a. Estimate the time until the first engine overhaul as a function of all four explanatory variables.

b. At the $10 \%$ significance level, are the explanatory variables jointly significant? Show the relevant steps of the test.

c. Are the explanatory variables individually significant at the $10 \%$ significance level? Show the relevant steps of the test.

Professor Grant Alexander wanted to find a linear model that relates the number of hours a student plays video games each week, h, to the cumulative grade-point average, G, of the student. He obtained a random sample of 10 full-time students at his college and asked each student to disclose the number of hours spent playing video games and the student’s cumulative grade-point average.

$$\begin{matrix} \text{Hours of} & \text{Grade-Point}\\ \text{Video Games} & \text{Average, G}\\ \text{per Week, h} & \text{ }\\ \text{0} & \text{3.49}\\ \text{0} & \text{3.05}\\ \text{2} & \text{3.24}\\ \text{3} & \text{2.82}\\ \text{3} & \text{3.19}\\ \text{5} & \text{2.78}\\ \text{8} & \text{2.31}\\ \text{8} & \text{2.54}\\ \text{10} & \text{2.03}\\ \text{12} & \text{2.51}\\ \end{matrix}$$

Interpret the slope.

Consider a driven undamped spring/mass system described by the initial-value problem

$$\frac { d ^ { 2 } x } { d t ^ { 2 } } + \omega ^ { 2 } x = F _ { 0 } \sin ^ { n } \gamma t , \quad x ( 0 ) = 0 , x ^ { \prime } ( 0 ) = 0.$$

(a) For $n = 2$, discuss why there is a single frequency $\gamma_1/2\pi$ at which the system is in pure resonance. (b) For $n = 3$, discuss why there are two frequencies $\gamma_1/2\pi$ and $\gamma_2/2\pi$ at which the system is in pure resonance. (c) Suppose $\omega = 1$ and $F_0 = 1$. Use a numerical solver to obtain the graph of the solution of the initial-value problem for $n = 2$ and $\gamma=\gamma_1$ in part (a). Obtain the graph of the solution of the initial-value problem for $n = 3$ corresponding, in turn, to $\gamma=\gamma_1$ and $\gamma=\gamma_2$ in part (b).

Gina Gomez, a devout Roman Catholic, worked for Sam’s Department Stores, Inc., in Phoenix, Arizona. Sam’s considered Gomez a productive employee because her sales exceeded $200,000 per year. At the time, the store gave its managers the discretion to grant unpaid leave to employees but prohibited vacations or leave during the holiday season—October through December. Gomez felt that she had a “calling” to go on a “pilgrimage” in October to a location in Bosnia where some persons claimed to have had visions of the Virgin Mary. The Catholic Church had not designated the site an official pilgrimage site, the visions were not expected to be stronger in October, and tours were available at other times. The store managers denied Gomez’s request for leave, but she had a nonrefundable ticket and left anyway. Sam’s terminated her employment, and she could not find another job. Can Gomez establish a prima facie case of religious discrimination? Explain.

Biologists Peter and Rosemary Grant spent many years collecting data on finches in a remote part of the Galapagos Islands. In fact, their research team caught and measured all of the birds in more than 20 generations of finches! The back-to-back stemplot shows the beak depths (in millimeters) of 89 finches captured the year before a drought occurred and 89 finches captured the year after the drought occurred. Compare the distributions of beak depth in these two years. (Note: These data provide evidence that the finches evolved in response to the drought.)

$$\begin{array}{r|l|l|} \text{ Before drought } & &\text{ After drought } \\ 2 & 6 & \\ 8 & 6 & \\ 411 & 7 & 1 \\ 98 & 7 & 9 \\ 44420 & 8 & 044 \\ 9999977765555 & 8 & 778 \\ 444321111100000 & 9 & 0011123344 \\ 99999888887777655 & 9 & 5666666777789999 \\ 444433322111111000 & 10 & 000222223333334444 \\ 8766655555 & 10 & 55555566666777778999 \\ 440 & 11 & 0000111134444 \quad \boxed{\text{KEY: 10 | 0=10.0 mm}} \\ 7 & 11 & 5667 \end{array}$$

When the Richmonds filed for Chapter 7 liquidation under the Bankruptcy Code, their unsecured debts totaled a little more than $19,000. All but$225 of the unsecured debts was owed on credit cards. The trustee in bankruptcy noted that the Richmond’s monthly expenses included voluntary payments in support of their grandchildren. The trustee also pointed out to the court that, if these payments were stopped, the Richmonds would have an additional $300 per month with which to pay off the credit cards. In fact, under a three year Chapter 13 plan, the Richmonds could pay off more than 90 percent of the credit card debt in 36 months. As a consequence, the trustee filed a motion to dismiss the Richmond’s case, contending that to grant relief to them would be an abuse of Chapter 7. The court noted that in making such a decision, it must decide whether the debtors are seeking an advantage or are truly needy in the sense that their financial situation warrants dismissal of the debts. How should the judge decide this case, and why? (In Re Richmond, 144 Bankruptcy Reporter 539)

Professor Grant Alexander wanted to find a linear model that relates the number of hours a student plays video games each week, h, to the cumulative grade-point average, G, of the student. He obtained a random sample of 10 full-time students at his college and asked each student to disclose the number of hours spent playing video games and the student’s cumulative grade-point average.

$$\begin{matrix} \text{Hours of} & \text{Grade-Point}\\ \text{Video Games} & \text{Average, G}\\ \text{per Week, h} & \text{ }\\ \text{0} & \text{3.49}\\ \text{0} & \text{3.05}\\ \text{2} & \text{3.24}\\ \text{3} & \text{2.82}\\ \text{3} & \text{3.19}\\ \text{5} & \text{2.78}\\ \text{8} & \text{2.31}\\ \text{8} & \text{2.54}\\ \text{10} & \text{2.03}\\ \text{12} & \text{2.51}\\ \end{matrix}$$

How many hours of video game playing do you think a student plays whose grade-point average is 2.40?

Safety Trucking Company uses the units-of-production (UOP) depreciation method because UOP best measures wear and tear on the trucks. Consider these facts about one Mack truck in the company’s fleet. When acquired in 2010, the rig cost $450,000 and was expected to remain in service for 10 years or 1,000,000 miles. Estimated residual value was$150,000. The truck was driven 82,000 miles in 2010, 122,000 miles in 2011, and 162,000 miles in 2012. After 45,000 miles in 2013, the company traded in the Mack truck for a less-expensive Freightliner. Safety also paid cash of $22,000. Fair value of the Mack truck was equal to its net book value on the date of the trade. Requirement

1. Determine Safety’s cost of the new truck. Journal entries are not required.

Racing cars driven by Chris and Kelly are side by side at the start of a race. The table shows the velocities of each car (in miles per hour) during the first ten seconds of the race. Use the Midpoint Rule to estimate how much farther Kelly travels than Chris does during the first ten seconds.

$$\begin{array}{|c|r|r||r|r|r|} \hline t & v_C & v_K & t & v_C & v_K \\ \hline 0 & 0 & 0 & 6 & 69 & 80 \\ 1 & 20 & 22 & 7 & 75 & 86 \\ 2 & 32 & 37 & 8 & 81 & 93 \\ 3 & 46 & 52 & 9 & 86 & 98 \\ 4 & 54 & 61 & 10 & 90 & 102 \\ 5 & 62 & 71 & & & \\ \hline \end{array}$$