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 debtor days ratio for Total Oil in $2013$.

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.

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.

SAT Performance. The Scholastic Aptitude Test (SAT) contains three parts: critical reading, mathematics, and writing. Each part is scored on an 800 -point scale. Information on test scores for the 2009 version of the SAT is available at the College Board website. A sample of SAT scores for six students follows.

$$\begin{array}{cccc} \text { Student } & \begin{array}{c} \text { Critical } \\ \text { Reading } \end{array} & \text { Mathematics } & \text { Writing } \\ 1 & 526 & 534 & 530 \\ 2 & 594 & 590 & 586 \\ 3 & 465 & 464 & 445 \\ 4 & 561 & 566 & 553 \\ 5 & 436 & 478 & 430 \\ 6 & 430 & 458 & 420 \end{array}$$

Using a .05 level of significance, do students perform differently on the three portions of the SAT?

Consider the following key performance indicators, and classify each according to the balanced scorecard perspective it addresses. Choose from financial perspective, customer perspective, internal business perspective, or learning and growth perspective.

a. Number of employee suggestions implemented b. Revenue growth c. Number of on-time deliveries d. Percentage of sales force with access toreal-time inventory levels e. Customer satisfaction ratings f. Number of defects found during manufacturing g. Number of warranty claims h. Return on investment i. Variable cost per unit j. Percentage of market share k. Number of hours of employee training L Number of new products developed m. Yield rate (number of units produced per hour) n. Average repair time o . Employee satisfaction p. Number of repeat customers

A123 shares were originally offered for sale at a price of $\$ 13.50$. Three months later, the stock traded for about $\$ 18$. What return did investors earn over this period? On November 10, 2009, A123 reported its 3rd quarter financial results. From November 9 to November 11 , the firm's stock price fell from $\$ 17.85$ to $\$ 16.88$. Given that $\mathrm{A} 123$ has 102 million shares outstanding, what were the dollar and percentage losses that shareholders endured in the days surrounding the earnings release? Over the same three days (November 9-11), the Nasdaq stock index moved up $0.6 \%$. How does this influence your thinking about A123's stock performance around this time?

The job performance of a new employee when learning a repetitive task (as on an assembly line) improves very quickly at first, then grows more slowly over time. This can be modeled by the function $P(t)=a+b \ln t$, where a and b are constants that depend on the type of task and the training of the employee. The number of circuit boards an associate can assemble from its component parts depends on the length of time the association has been working. This output is modeled by $B(t)=1+2.3 \ln t$, where $B(t)$ is the number of boards assembled daily after working $t$ days. (a) How many boards are an employee completing after 9 days on the job? (b) How long will it take until the employee is able to complete 10 boards per day?

Two basketball players on a school team are working hard on consistency of their performance. In particular, they are hoping to bring down the variance of their scores. The coach believes that the players are not equally consistent in their games. Over a 10-game period, the scores of these two players are shown in the accompanying table. Assume that the two samples are drawn independently from normally distributed populations.

$$\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|} \hline \text { Player 1 } & 13 & 15 & 12 & 18 & 14 & 15 & 11 & 13 & 11 & 16 \\ \hline \text { Player 2 } & 11 & 21 & 18 & 9 & 20 & 11 & 13 & 11 & 19 & 8 \\ \hline \end{array}$$

Refrigeration units can be rated in "tons." A 1-ton air conditioning system can remove sufficient energy to freeze 1 British ton $\left(2000\right.$ pounds $=909 \mathrm{~kg}$ ) of $0^{\circ} \mathrm{C}$ water into $0^{\circ} \mathrm{C}$ ice in one 24-h day. If, on a $35^{\circ} \mathrm{C}$ day, the interior of a house is maintained at $22^{\circ} \mathrm{C}$ by the continuous operation of a 5 -ton air conditioning system, how much does this cooling cost the homeowner per hour? Assume the work done by the refrigeration unit is powered by electricity that costs $\$ 0.10$ per $\mathrm{kWh}$ and that the unit's coefficient of performance is $15 \%$ that of an ideal refrigerator. $1 \mathrm{kWh}=3.60 \times 10^6 \mathrm{~J}$.

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 a strategy Total Oil might use to improve its efficiency and gearing.

Consider the storage tank with sightglass in Fig.mentioned. The parameter values are $R_1=0.5 \mathrm{~min} / \mathrm{ft}^2, R_2=2 \mathrm{~min} / \mathrm{ft}^2$, $A_1=10 \mathrm{ft}^2, K_v=2.5 \mathrm{cfm} / \mathrm{mA}, A_2=0.8 \mathrm{ft}^2, K_m=1.5 \mathrm{~mA} / \mathrm{ft}$, and $\tau_m=0.5 \mathrm{~min}$. (a) Suppose that $R_2$ is decreased to $0.5 \mathrm{~min} / \mathrm{ft}^2$. Compare the old and new values of the ultimate gain and the critical frequency. Would you expect the control system performance to become better or worse? Justify your answer. (b) If PI controller settings are calculated using the ZieglerNichols rules, what are the gain and phase margins? Assume $R_2=2 \mathrm{~min} / \mathrm{ft}$.

Prof. Hardtack gave four Friday quizzes last semester in his senior tax accounting class. A random sample of 10 student scores is shown for each quiz.

(a) Find the sample mean, standard deviation, and coefficient of variation for each quiz.

(b) How do these data sets differ in terms of center and variability?

(c) Briefly describe and compare student performance on each quiz.

Quiz 1: 60, 60, 60, 60, 71, 73, 74, 75, 88, 99

Quiz 2: 65, 65, 65, 65, 70, 74, 79, 79, 79, 79

Quiz 3: 66, 67, 70, 71, 72, 72, 74, 74, 95, 99

Quiz 4: 10, 49, 70, 80, 85, 88, 90, 93, 97, 98

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.