Is the number of years of competitive running experience related to a runner's distance running performance? The data on nine runners, obtained from the study by Scott Powers and colleagues, are shown in the table:

Runner: 1, 2, 3, 4, 5, 6, 7, 8, 9 Years of Competitive Running: 9, 13, 5, 7, 12, 6, 4, 5, 3 10-Kilometer Finish Time (minutes): 33.15, 33.33, 33.50, 33.55, 33.73, 33.86, 33.90, 34.15, 34.90

a. Calculate the rank correlation coefficient between years of competitive running x and a runner's finish time in the 10-kilometer race. b. Do the data provide evidence to indicate a significant rank correlation between y and x? Test using $\alpha$=.05.

For the centrifugal water pump of the earlier problem, plot the pump's performance data: $H$ (ft), bhp (hp), and $\eta_{\text {purp }}$ (percent) as functions of $\dot{V}$ (gpm), using symbols only (no lines). Perform linear least-squares polynomial curve fits for all three parameters, and plot the fitted curves as lines (no symbols) on the same plot. For consistency, use a first-order curve fit for $H$ as a function of $\dot{V}^2$, use a second-order curve fit for bhp as a function of both $\dot{V}$ and $\dot{V}^2$, and use a third-order curve fit for $\eta_{\text {pamp }}$ as a function of $\dot{V}, \dot{V}^2$, and $\dot{V}^3$. List all curve-fitted equations and coefficients (with units) for full credit. Find the BEP of the pump based on the curve-fitted expressions.

Oil executives frequently compare the performance and efficiency of their company with those of other major oil companies. The following data is taken from Total Oil's $2013$ accounts.

$$\begin{array}{|l|l|l|l|l|l|l|l|} \hline\text{ Credit } & \text{ Creditors } & \text{ Debtors } & \text{ Long-term } & \text{ Inventories } & \text{ Cost of } & \text{ Capital } & \text{ Credit }\\ \text{ sales (\$m)} & \text{ (accounts } & \text{ (accounts } & \text{ loans(\$m)} & \text{ (\$m) } & \text{ sales (\$m) } & \text{ employed } & \text{ purchases } \\ & \text{ payable) } & \text{ receivable) } &&&& \text{ (\$m) } & \text{ (author’s } \\ & \text{ (\$m) } & \text{ (\$m) } &&&&& \text{ estimate)(\$m)} \\ \hline227969 & 30282 & 23422 & 34574 & 22097 & 160849 & 177555 & 160000 \\ \hline \end{array}$$

Calculate the creditor days ratio for Total Oil in $2013$.

A spring-mass-damper system, as shown in Figure , is used as a shock absorber for a large high-performance motorcycle. The original parameters selected are $m=1 \mathrm{~kg}, b=9 \mathrm{~N} \mathrm{~s} / \mathrm{m}$, and $k=20 \mathrm{~N} / \mathrm{m}$. (a) Determine the system matrix, the characteristic roots, and the transition matrix $\boldsymbol{\Phi}(t)$. The harsh initial conditions are assumed to be $y(0)=1$ and $d y /\left.d t\right|_{t=0}=2$. (b) Plot the response of $y(t)$ and $y(t)$ for the first two seconds. (c) Redesign the shock absorber by changing the spring constant and the damping constant in order to reduce the effect of a high rate of acceleration force $\dot{y}(t)$ on the rider. The mass must remain constant at $1 \mathrm{~kg}$.

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?

A simple solar collector is built by placing a 5-cm-diameter clear plastic tube around a garden hose whose outer diameter is 1.6 cm. The hose is painted black to maximize solar absorption, and some plastic rings are used to keep the spacing between the hose and the clear plastic cover constant. During a clear day, the temperature of the hose is measured to be $65^\circ C,$ while the ambient air temperature is $26^\circ C.$ Determine the rate of heat loss from the water in the hose per meter of its length by natural convection. Also, discuss how the performance of this solar collector can be improved. Evaluate air properties at an average temperature of $50^\circ C$ and 1 atm pressure. Is this a good assumption?

To formulate the performance of a multiple-access network, we need a mathematical model. When the number of stations in a network is very large, the Poisson distribution, $p[x] = (e^{−\lambda} \times \lambda^x)/(x!)$, is used. In this formula, p[x] is the probability of generating x number of frames in a period of time and $\lambda$ is the average number of generated frames during the same period of time. Using the Poisson distribution: a. Find the probability that a pure Aloha network generates x number of frames during the vulnerable time. Note that the vulnerable time for this network is two times the frame transmission time (Tfr). b. Find the probability that a slotted Aloha network generates x number of frames during the vulnerable time. Note that the vulnerable time for this network is equal to the frame transmission time (Tfr).

A two-stage compression refrigeration system operates with refrigerant-134a between the pressure limits of 1.4 and 0.10 MPa. The refrigerant leaves the condenser as a saturated liquid and is throttled to a flash chamber operating at 0.4 MPa. The refrigerant leaving the low-pressure compressor at 0.4 MPa is also routed to the flash chamber. The vapor in the flash chamber is then compressed to the condenser pressure by the high-pressure compressor, and the liquid is throttled to the evaporator pressure. Assuming the refrigerant leaves the evaporator as saturated vapor and both compressors are isentropic, determine (a) the fraction of the refrigerant that evaporates as it is throttled to the flash chamber, (b) the rate of heat removed from the refrigerated space for a mass flow rate of 0.25 kg/s through the condenser, and (c) the coefficient of performance.

Oil executives frequently compare the performance and efficiency of their company with those of other major oil companies. The following data is taken from Total Oil's $2013$ accounts.

$$\begin{array}{|l|l|l|l|l|l|l|l|} \hline\text{ Credit } & \text{ Creditors } & \text{ Debtors } & \text{ Long-term } & \text{ Inventories } & \text{ Cost of } & \text{ Capital } & \text{ Credit }\\ \text{ sales (\$m)} & \text{ (accounts } & \text{ (accounts } & \text{ loans(\$m)} & \text{ (\$m) } & \text{ sales (\$m) } & \text{ employed } & \text{ purchases } \\ & \text{ payable) } & \text{ receivable) } &&&& \text{ (\$m) } & \text{ (author’s } \\ & \text{ (\$m) } & \text{ (\$m) } &&&&& \text{ estimate)(\$m)} \\ \hline227969 & 30282 & 23422 & 34574 & 22097 & 160849 & 177555 & 160000 \\ \hline \end{array}$$

Evaluate Total Oil's efficiency and gearing.

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?

You are concerned about the effects of texting on driving performance. Design a study to test the response time of drivers while texting and while driving only. How many seconds does it take for a driver to respond when a leading car hits the brakes? a. Describe the explanatory and response variables in the study. b. What are the treatments? c. What should you consider when selecting participants? d. Your research partner wants to divide participants randomly into two groups: one to drive without distraction and one to text and drive simultaneously. Is this a good idea? Why or why not? e. Identify any lurking variables that could interfere with this study. f. How can blinding be used in this study?

Performance of stock screeners. Recall, from Exercise $6.36$ (p. 326), that stock screeners are automated tools used by investment companies to help clients select a portfolio of stocks to invest in. The data on the annualized percentage return on investment (as compared to the Standard & Poor's 500 Index) for 13 randomly selected stock screeners provided by the American Association of Individual Investors (AAII) are repeated in the accompanying table. You want to determine whether $\mu$, the average annualized return for all AAII stock screeners, is positive (which implies that the stock screeners perform better, on average, than the S&P 500). An XLSTAT printout of the analysis is shown on the top of page 394. Locate the observed significance level ( $p$-value) on the printout.

Find the perimeter of each rectangle with the given base and height. 3.5 cm, 7 cm

Performance of stock screeners. Investment companies provide their clients with automated tools-called stock screeners to help them select a portfolio of stocks to invest in. The American Association of Individual Investors (AAII) provides statistics on stock screeners at its Web site, www.aaii.com. The next table lists the annualized percentage return on investment (as compared to the Standard & Poor's 500 Index) for 13 randomly selected stock screeners. (Note: A negative annualized return reflects a stock portfolio that performed worse than the S&P 500.) Compute the median for the data set. Interpret its value.

$$\begin{array}{lllllllllllll}9.0 & -.1 & -1.6 & 14.6 & 16.0 & 7.7 & 19.9 & 9.8 & 3.2 & 24.8 & 17.6 & 10.7 & 9.1\end{array}$$