A force platform is a tool used to analyze the performance of athletes by measuring the vertical force the athlete exerts on the ground as a function of time. Starting from rest, a 65.0-kg athlete jumps down onto the platform from a height of 0.600 m. While she is in contact with the platform during the time interval 0 < t < 0.800 s, the force she exerts on it is described by the function $F=9200 t-11500 t^{2}$ where F is in newtons and t is in seconds. (a) What impulse did the athlete receive from the platform? (b) With what speed did she reach the platform? (c) With what speed did she leave it? (d) To what height did she jump upon leaving the platform?

Performance data for a pump are

$$\begin{matrix}\text{H (ft)} & \text{179} & \text{176} & \text{165} & \text{145}\\\text{Q (gpm)} & \text{0} & \text{500} & \text{1000} & \text{1500}\\\text{H (ft)} & \text{119} & \text{84} & \text{43}\\\text{Q (gpm)} & \text{2000} & \text{2500} & \text{3000}\\\end{matrix}$$

Estimate the delivery when the pump is used to move water between two open reservoirs through 1200 ft of 12-in.-diameter commercial steel pipe containing two $90^{\circ}$ elbows and an open gate valve if the elevation increase is 50 ft. Determine the gate valve loss coefficient needed to reduce the volume flow rate by half.

The director of graduate admissions at a local university is analyzing the relationship between scores on the Graduate Record Examination (GRE) and subsequent performance in graduate school, as measured by a student's grade point average (GPA). She uses a sample of seven students who graduated within the past five years. A portion of the data is shown in the accompanying table.

$$\begin{array}{|c|c|} \hline \text { CRE } & \text { CPA } \\ \hline 1500 & 3.4 \\ \hline 1400 & 3.5 \\ \hline \vdots & \vdots \\ \hline 800 & 2.7 \\ \hline \end{array}$$

a. Specify the competing hypotheses to determine whether the Spearman rank correlation coefficient is greater than zero.

b. At the $5 \%$ significance level, are GRE and GPA positively correlated?

The following are 10 technical accounting terms introduced or emphasized in earlier text :

$$\begin{array}{lll}\text { P/e ratio } & \text { Treasury stock } & \text { Discontinued operations } \\ \text { Stock dividend } & \text { Extraordinary item } & \text { Prior period adjustment } \\ \text { Basic earnings per share } & \text { Additional paid-in capital } & \text { Diluted earnings per share }\\ \text{Comprehensive income} \end{array}$$

Each of the following statements may (or may not) describe one of these technical terms. For each statement, indicate the term described, or answer "None" if the statement does not correctly describe any of the terms.
i. A broadly defined measure of financial performance that includes, but is not limited to, net income.

Choose a word to replace the italicized word in the sentence. All of the possible choices have similar definitions, but the correct answer will have a connotation that best suits the context and does not render the sentence awkward in tone or content. When choices seem close, look for a clue in the context that makes one choice better than the other.

$$\begin{array}{llll}\text { typical } & \text { crime } & \text { problem } & \text { hackneyed } \\ \text { imperious } & \text { show } & \text { intentions } & \text { machinations } \\ \text { affectation } & \text { failure } & \text { normal } & \end{array}$$

Not wanting to trouble his grandma with his many worries, Luke put on a[n] performance of cheerfulness when he visited her this week.

Better word: ______

The article “Evaluating Tunnel Kiln Performance” (Amer. Ceramic Soc. Bull., Aug. 1997: 59–63) gave the following summary information for fracture strengths (MPa) of n=169 ceramic bars fired in a particular kiln: $\bar{x}=89.10$, s=3.73. a. Calculate a (two-sided) confidence interval for true average fracture strength using a confidence level of 95%. Does it appear that true average fracture strength has been precisely estimated? b. Suppose the investigators had believed a priori that the population standard deviation was about 4 MPa. Based on this supposition, how large a sample would have been required to estimate $\mu$ to within .5 MPa with 95% confidence?

We could improve the performance of the waterproofing process discussed in the previous exercise by making an adjustment that moves the center of the process to $\mu=2500 \mathrm{~mm}$, the center of the specifications. We should do this even if the original specifications remain in force, because this will require less sealer and therefore cost less. Suppose that we succeed in moving $\mu$ to 2500 with no change in the process variability $\sigma$, estimated by $s=383.8$. (a) What are $\mathrm{C}^{\wedge} \mathrm{p}$ and $\mathrm{C}^{\wedge} \mathrm{pk}$ with the original specifications? Compare the values with those from part (a) of the previous exercise. (b) What are $\mathrm{C}^{\wedge} \mathrm{p}$ and $\mathrm{C}^{\wedge} \mathrm{pk}$ with the tightened specifications? Again compare with the previous results.

Mark Washington, CFA, is an analyst with BIC. One year ago, BIC analysts predicted that the U.S. equity market would most likely experience a slight downturn and suggested delta-hedging the BIC portfolio. As predicted, the U.S. equity markets did indeed experience a downturn of approximately 4% over a 12-month period. However, portfolio performance for BIC was disappointing, lagging its peer group by nearly 10%. Washington has been told to review the options strategy to determine why the hedged portfolio did not perform as expected. Washington considers a put option that has a delta of −.65. If the price of the underlying asset decreases by $6, then what is the best estimate of the change in option price?

The following observations are on stopping distance (ft) of a particular truck at 20 mph under specified experimental conditions (“Experimental Measurement of the Stopping Performance of a Tractor-Semitrailer from Multiple Speeds,” NHTSA, DOT HS 811 488, June 2011):

$$\begin{matrix} \text{32.1} & \text{30.6} & \text{31.4} & \text{30.4} & \text{31.0} & \text{31.9}\\ \end{matrix}$$

The cited report states that under these conditions, the maximum allowable stopping distance is 30. A normal probability plot validates the assumption that stopping distance is normally distributed. Does the data suggest that true average stopping distance exceeds this maximum value? Test the appropriate hypotheses using $\alpha=.01$.

In order to study the relationship between the amount of sleep a student gets and his or her school performance, a researcher collected data from 120 students. The two-way frequency table shows the number of students who passed and failed an exam and the number of students who got more or less than 6 hours of sleep the night before.

To the nearest percent, find the probability that a student who got less than 6 hours of sleep failed the exam.

Select the best answer. To investigate whether standing up while studying affects performance in an algebra class, a teacher assigns half of the 30 students in his class to stand up while studying. To determine who receives which treatment, the teacher identifies the two students who did best on the last exam and randomly assigns one to stand and one to not stand. The teacher does the same for the next two highest-scoring students and continues in this manner until each student is assigned a treatment. Which of the following best describes this plan? (a) This is an observational study. (b) This is an experiment with blocking. (c) This is a completely randomized experiment. (d) This is a stratified random sample. (e) This is a cluster sample.

A power plant is built to provide district heating of buildings that requires 90$^{\circ} \mathrm{C}$ liquid water at 150 kPa. The district heating water is returned at 50$^{\circ} \mathrm{C}$, 100 kPa in a closed loop in an amount such that 20 MW of power is delivered. This hot water is produced from a steam power cycle with a boiler making steam at 5 MPa, 600$^{\circ} \mathrm{C}$, delivered to the steam turbine. The steam cycle could have its condenser operate at 90$^{\circ} \mathrm{C}$, providing the power to the district heating. It could also be done with extraction of steam from the turbine. Suggest a system and evaluate its performance in terms of the cogenerated amount of turbine work.

Performance data for a pump are

$$\begin{matrix} \text{H (ft)} & \text{90} & \text{87} & \text{81} & \text{70} & \text{59} & \text{43} & \text{22}\\ \text{Q (cfm)} & \text{0} & \text{50} & \text{100} & \text{150} & \text{200} & \text{250} & \text{300}\\ \end{matrix}$$

The pump is to be used to move water between two open reservoirs with an elevation increase of 24 ft. The connecting pipe system consists of 1750 ft of commercial steel pipe containing two $90^{\circ}$ elbows and an open gate valve. Find the flow rate if we use (a) 8-in., (b) 10-in., and (c) 12-in. (nominal) pipe.

You have been employed by the local circus to plan their human cannonball performance. For this act, a spring-loaded cannon will shoot a human projectile, the Great Flyinski, across the big top to a net below. The net is located 5.0 m lower than the muzzle of the cannon from which the Great Flyinski is launched. The cannon will shoot the Great Flyinski at an angle of

$$35.0 ^ { \circ }$$

above the horizontal and at a speed of 18.0 m/s. The ringmaster has asked that you decide how far from the cannon to place the net so that the Great Flyinski will land in the net and not be splattered on the floor, which would greatly disturb the audience. What do you tell the ringmaster? {connect interactive: projectile motion)