A square cross-section duct $(0.5 \mathrm{~m} \times 0.5 \mathrm{~m} \times 30 \mathrm{~m})$ is used to convey air $\left(\rho=1.1 \mathrm{~kg} / \mathrm{m}^{3}\right)$ into a clean room in an electronics manufacturing facility. The air is supplied by a fan and passes through a filter installed in the duct. The duct friction factor is $f=0.03$, the filter has a loss coefficient of $K=12$, and the clean room is kept at a positive gage pressure of $50 \mathrm{~Pa}$. The fan performance is given by $\Delta p=1020-25 Q-30 Q^{2}$, where $\Delta p$ $\mathrm{(Pa)}$ is the pressure generated by the fan at flow rate $Q\left(\mathrm{~m}^{3} / \mathrm{s}\right)$. Find the flow rate delivered to the room.

Most baseball hitters perform differently against right-handed and left-handed pitching. Consider two players, Joe and Moe, both of whom bat right-handed. The table below records their performance against right-handed and left-handed pitchers.

Make a separate two-way table of player versus outcome for each kind of pitcher. From these tables, find the batting averages of Joe and Moe against right-handed pitching. Who does better? Do the same for left-handed pitching. Who does better?

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.

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. Determine the probability of a type II error when $\alpha= .01, \sigma=.65$, and the actual value of m is 31. Repeat this for $\mu=32$.

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.

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 2.65. If the price of the underlying asset decreases by $6, then what is the best estimate of the change in option price?

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, give the probability that a student who failed the exam got less than 6 hours of sleep.

Refer to this chapter's opening feature about Apple. Assume that the owners decide to open a new company with an innovative mobile app devoted to microblogging for accountants and those learning accounting. This new company will be called AccountApp.

Required

1. AccountApp obtains a $500,000 loan and the two owners contribute$250,000 in total from their ownsavings in exchange for ownership of the new company.

a. What is the new company's total amount of liabilities plus equity?

b. What is the new company's total amount of assets?

2. If the new company earns $80,250 in net income in the first year of operation, compute its return on assets (assume average assets equal$750,000). Assess its performance if competitors average a 10% return.

The following list gives a number of measures associated with the Balanced Scorecard:

a. Number of new customers
b. Percentage of customer complaints resolved with one contact
c. Unit product cost
d. Cost per distribution channel
e. Suggestions per employee
f. Warranty repair costs
g. Consumer satisfaction (from surveys)
h. Cycle time for solving a customer problem
i. Strategic job coverage ratio
j. On-time delivery percentage
k. Percentage of revenues from new products

1. Classify each performance measure as belonging to one of the following perspectives: financial, customer, internal business process, or learning and growth.

2. Suggest an additional measure for each of the four perspectives.

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.

A vapor-compression refrigeration cycle with Refrigerant 134 as the working fluid operates with an evaporator temperature of $50^{\circ} \mathrm{F}$ and a condenser pressure of $180\ \mathrm{lbf}/ \mathrm{in}^2$ Refrigerant enters the condenser at $140^{\circ} \mathrm{F}$ and exits as sat urated liquid. The cycle has a refrigeration capacity of $5\ \text{tons}$. Determine (a) the refrigerant mass flow rate, in $\mathrm{lb} / \mathrm{min}$. (b) the compressor isentropic efficiency. (c) the compressor power, in horsepower. (d) the coefficient of performance. Plot each of the quantities calculated in parts (b) through (d) for compressor exit temperatures varying from $130^{\circ} \mathrm{F}$ to for compressor exit temperatures varying from $130^{\circ} \mathrm{F}$ to $140^{\circ} \mathrm{F}$.

The advertisement for a new shoe promises runners less slip. The coefficient of friction $(\mu)$ between concrete and a new material used in the sole of this shoe is 1.5. The force of friction that causes slip is equal to $m g \sin \theta$, where m is a runner's mass and g is the acceleration due to gravity. The force that prevents slip is $\mu m g \cos \theta$.

Mukisa wonders how his old shoes compare to these new shoes. The label on the box of his old shoes states that the coefficient of friction is 1.3.

a. Write an equation to find the angle at which a shoe with a coefficient of friction of 1.3 will slip.

b. At what angle will this shoe start to slip?

c. Suggest how the new shoes might improve Mukisa's performance.

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?