SilverEdge Systems Software hired Catherine Conrad to perform a singing telegram. SilverEdge arranged for James Bendewald to record Conrad’s performance of her copyrighted song to post on its Web site. Conrad agreed to wear a microphone to assist in the recording, told Bendewald what to lm, and asked for an additional fee only if SilverEdge used the video for a commercial purpose. Later, the company chose to post a video of a different performer’s singing telegram instead. Conrad filed a suit in a federal district court against SilverEdge and Bendewald for copyright infringement. Are the defendants liable? Explain. [Conrad v. Bendewald, 500 Fed.Appx. 526 (7th Cir. 2013)] (See Copyrights.)

Air at $5^\circ C,$ with a convection heat transfer coefficient of $30 W/m^2 \cdot K,$ is used for cooling metal plates coming out of a heat treatment oven at an initial temperature of $300^\circ C.$ The plates $(k = 180 W/m \cdot K, = 2800 kg/m^3,$ and $c_p = 880 J/kg \cdot K)$ have a thickness of 10 mm. Using EES (or other) software, determine the effect of cooling time on the temperature gradient in the metal plates at the surface. By varying the cooling time from 0 to 3000 s, plot the temperature gradient in the plates at the surface as a function of cooling time.

Use graph paper, the Line( command from the DRAW menu of your graphing calculator, or interactive geometry software to draw a model of a kite with vertices A(5, -6), B(7, -2), C(5, 2), and D(-9, -2). a. Does your drawing appear to be that of a kite? Use careful reasoning with the coordinates to justify that ABCD is a kite, that is, a quadrilateral with exactly two pairs of congruent adjacent sides. b. Draw the cross braces of the kite and find their lengths using coordinates. c. Use coordinates to find the midpoints of $\overline { A C }$ and $\overline { B D }.$ d. Justify that the midpoint of $\overline { A C }$ is on $\overline { B D }.$ How is this fact seen in your drawing?

This problem concerns the parametrized surface $\mathbf{X}(s, t)=\left(s^{3}, t^{3}, s t\right)$. (a) Find an equation of the plane tangent to this surface at the point (1,−1,−1). (b) Is this surface smooth? Why or why not? (c) Use a computer to graph this surface for $-1 \leq s \leq 1,-1 \leq t \leq 1$. (d) Verify that this surface may also be described by the xyz-coordinate equation $z=\sqrt[3]{x y}$. Try using a computer to graph the surface when described in this form. Many software systems will have trouble, or will provide an incomplete graph, which is one reasonwhy parametric descriptions of surfaces are desirable.

Setting aside money (saving) for the future is known as deferred spending. You are setting aside money today so that you will have it when you need it. Most financial planners recommend you save 10 percent or more of your earnings. This is a good first step toward your retirement. Use spreadsheet software to complete the following problem if available, or complete them manually. Round to the nearest cent.

Assume you will earn $\$25,000$ in gross pay the first year you work. Each year after that, you will get a 3 percent increase in pay. How much money will you have earned in 10 years?

A heat engine operates between a source at 477$^\circ{}$C and a sink at 25$^\circ{}$C. If heat is supplied to the heat engine at a steady rate of 65,000 kJ/min, using appropriate software, study the effects of the temperatures of the heat source and the heat sink on the power produced and the cycle thermal efficiency. Let the source temperature vary from 300 to 1000$^\circ{}$C, and the sink temperature to vary from 0 to 50$^\circ{}$C. Plot the power produced and the cycle efficiency against the source temperature for sink temperatures of 0$^\circ{}$C, 25$^\circ{}$C, and 50$^\circ{}$C, and discuss the results.

Suppose that a fair coin is flipped n = 100 times. (a). Calculate the mean and standard deviation of X = number of heads. (b). Use the normal approximation to the binomial distribution to estimate the probability that the number of heads is greater than or equal to 60. (c). Repeat part (b) using the continuity correction. To do this, find the probability that the number of heads is greater than or equal to 59.5. (d). Use statistical software, Excel, or a graphing calculator to find the exact binomial probability that the number of heads will be greater than or equal to 60. (e). Which of the results in parts (b), (c), and (d) is the most accurate value and which is the least accurate value for the probability that the number of heads is greater than or equal to 60?

Hydrogen gas at 1 atm is flowing in parallel over the upper and lower surfaces of a 3-m-long flat plate at a velocity of 2.5 m/s. The gas temperature is $120^\circ C$ and the surface temperature of the plate is maintained at $30^\circ C.$ Using the EES (or other) software, investigate the local convection heat transfer coefficient and the local total convection heat flux along the plate. By varying the location along the plate for $0.2 \leq x \leq 3 \mathrm{m},$ plot the local convection heat transfer coefficient and the local total convection heat flux as functions of x. Assume flow is laminar but make sure to verify this assumption.

Air at 1 atm is flowing in parallel over a 3-m- long flat plate with a velocity of 7 m/s. The air has a free stream temperature of $120^{\circ} \mathrm{C}$ and the surface temperature of the plate is maintained at $20^{\circ} \mathrm{C}.$ Determine the distance x from the leading edge of the plate where the critical Reynolds number $\left(\mathrm{Re}_{\mathrm{cr}}=5 \times 10^{5}\right)$ is reached. Then, using an appropriate software, evaluate the local convection heat transfer coefficient along the plate. By varying the location along the plate for $0.2 \leq x \leq 3 \mathrm{m},$ plot the local convection heat transfer coefficient as a function of x and discuss the results.

Previous exercises describes a study that compared the proportions of athletes who use illegal drugs in two similar high schools, one that tests for drugs and one that does not. Drug testing is intended to reduce the use of drugs. Do the data give good reason to think that drug use among athletes is lower in schools that test for drugs? State hypotheses, find the test statistic, and use either software or the bottom row of Table C for the P-value. Be sure to state your conclusion. (Because the study is not an experiment, the conclusion depends on the condition that athletes in these two schools can be considered SRSs from all similar schools.)

Imagineering, Inc., is considering an investment in CAD-CAM compatible design software with the cash flow profile shown in the table below. Imagineering’s MARR is 18 percent/year.

$$\begin{array}{|l|c|c|c|c|c|c|c|c|} \hline \text { EOY } & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \text { Cash Flow (M\$) } & -\$ 12 & -\$ 1 & \$ 5 & \$ 2 & \$ 5 & \$ 5 & \$ 2 & \$ 5 \\ \hline \end{array}$$

a. What is this investment’s internal rate of return?

b. What is the decision rule for judging the attractiveness of investments based on internal rate of return?

c. Should Imagineering invest?

Psychologists have developed mathematical models to predict performance P (the percent of correct responses in decimal form) as a function of the number of times a task is performed. One such model is $P=\frac{0.5+0.9(n-1)}{1+0.9(n-1)}, \quad n>0$. (a) Use a spreadsheet software program to complete the table for the model.

$$\begin{matrix} \text{n} & \text{1} & \text{2} & \text{3} & \text{4} & \text{5} & \text{6} & \text{7} & \text{8} & \text{9} & \text{10}\\ \text{P}\\ \end{matrix}$$

(b) Find the limit as approaches infinity. (c) Use a graphing utility to graph this learning curve, and interpret the graph in the context of the problem.

Bird songs have been hypothesized to be a secondary sexual character signaling an individual's health status. Researchers designed an experiment in which they randomly assigned male collared flycatchers (Ficedula albicollis) to two groups. One group received an immune challenge in the form of an injection of sheep red blood cells, and the other group received a placebo injection. The researchers then recorded the changes in song rate (in strophes per minute) after the injection for the 15 males in the immune challenge group and the 12 males in the placebo group.

(a) Outline the design of this experiment.

(b) Number the birds from 1 through 27. Use software or Table A at line 131 to carry out the randomization your design requires.

Refer to the Biology of Sport (Vol. 31, 2014) study of the physiological performance of top-level water polo players. Recall that the in-game heart rate (y, expressed as a percentage of maximum heart rate) of a player was modeled as a straight-line function of the player's maximal oxygen uptake (x, $VO_2$max). A researcher desires an estimate of the average in-game heart rate of all top-level water polo players who have a maximal oxygen uptake of 150 $VO_2$max. a. Which interval is desired by the researcher, a 95 % prediction interval for y or a 95% confidence interval for E(y)? Explain. b. Use statistical software to compute the desired interval. c. Give a practical interpretation of the interval.