Suppose an emergency van has a single-tone siren with the pitch of the musical note $\mathrm{G}$. If the van is traveling at $80 \mathrm{mph}$ approaching a standing observer, name the pitch the observer hears (rounded to the nearest tenth) and the musical note closest to that pitch.

Pitch of an Octave of Musical Notes in Hertz $(\mathrm{Hz})$

$$\begin{aligned} &\begin{array}{c|c} \hline Note & Pitch \\ \hline Middle\ C & 261.63 \\ \hline D & 293.66 \\ \hline E & 329.63 \\ \hline F & 349.23 \\ \hline G & 392.00 \\ \hline A & 440.00 \\ \hline B & 493.88 \\ \hline \end{array} \end{aligned}$$

Two small liquid-propellant rocket motors are mounted at the tips of a helicopter rotor to augment power under emergency conditions. The diameter of the helicopter rotor is $7 \mathrm{~m}$, and it rotates at $1 \mathrm{rev} / \mathrm{s}$. The air enters at the tip speed of the rotor, and exhaust gases exit at $500 \mathrm{~m} / \mathrm{s}$ with respect to the rocket motor. The intake area of each motor is $20 \mathrm{~cm}^2$, and the air density is $1.2 \mathrm{~kg} / \mathrm{m}^3$. Estimate the power provided by the rocket motors. Ignore the mass rate of flow of fuel in this calculation.

A defibrillator is used by emergency medical staff to shock the heart of an accident victim by applying a 10,000- $\mathrm{V}$ potential difference across the victim's chest.

(a) If the defibrillator has an internal resistance of $10 \Omega$ and the victim's heart has a resistance of $300 \Omega$, what is the current that passes through the victim's heart the moment the defibrillator is discharged?

(b) If the defibrillator delivers this current over a $10-\mathrm{ms}$ time interval, how many electrons pass through the heart during this process?

Desert Samaritan Hospital, in Mesa, Arizona, keeps records of emergency room traffic. Those records reveal that the times between arriving patients have a special type of reverse-J-shaped distribution called an exponential distribution. The records also show that the mean time between arriving patients is 8.7 minutes. a. Simulate four random samples of 75 interarrival times each. b. Perform a correlation test for normality on each sample in part (a). Use $\alpha=0.05$. c. Are the conclusions in part (b) what you expected? Explain your answer.

A group of hikers is lost in a national park. Two ranger stations have received an emergency SOS signal from the hikers. Station B is 75 miles due east of station A. The bearing from station A to the signal is S 60° E and the bearing from station B to the signal is S 75° W. A rescue party is in the park 20 miles from station A at a bearing of S 80° E. Find the distance and the bearing the rescue party must travel to reach the lost hikers.

(Use Excel) Color coding is often used in manufacturing operations to display production status or to identify/prioritize materials. For example, suppose "green" status indicates that an assembly line is operating normally, "yellow" indicates it is down waiting on personnel for set up or repair, "blue" indicates it is down waiting on materials to be delivered, and "red" indicates an emergency condition. Management has set realistic goals whereby the assembly line should be operating normally 80% of the time, waiting on personnel 9% of the time, waiting on materials $9 \%$ of the time, and in an emergency condition 2% of the time. Based on $250$ recent status records, the status was green $185$ times, yellow $24$ times, blue $32$ times, and red $9$ times.

a. State the appropriate null and alternative hypotheses to test if the proportions of assembly line statuses differ from the goals set by management.

b. Calculate the value of the test statistic.

c. Use Excel's CHISQ.DIST.RT function to calculate the $p$-value.

d. Are management's goals being met at $\alpha=0.05$ ? Will your conclusion change at $\alpha=0.01$ ?

A nuclear reactor is equipped with two independent automatic shutdown systems to shut down the reactor when the core temperature reaches the danger level. Neither system is perfect. System A shuts down the reactor 90% of the time when the danger level is reached. System B does so 80% of the time. The reactor is shut down if either system works.

Now simulate 100 trials of the reactor's response to an emergency of this kind. Estimate the probability that it will shut down. This probability is higher than the probability that either system working alone will shut down the reactor.

The waiting time until service at a hospital emergency department is modeled with the pdf $f (x) = \frac{1}{9} x \quad 0<x<3$ hours and $f (x) = \frac{2}{3}-\frac{1}{9} x \quad 3<x<6.$ Determine the following: (a) Probability the wait is less than 4 hours (b) Probability the wait is more than 5 hours (c) Probability the wait is less than or equal to 30 minutes (d) Waiting time that is exceeded by only 10% of patients (e) Mean waiting time

An emergency drain pump, shown in figure, should be able to pump $0.1 \mathrm{~m}^3 / \mathrm{s}$ of liquid water at $15^{\circ} \mathrm{C}, 10 \mathrm{~m}$ vertically up, delivering it with a velocity of $20 \mathrm{~m} / \mathrm{s}$. It is estimated that the pump, pipe, and nozzle have a combined isentropic efficiency expressed for the pump as $60 \%$. How much power is needed to drive the pump?

The following table, reproduced from earlier exercise, gives the probability distribution of the number of patients who enter Millard Fellmore Memorial Hospital's emergency room in a given hour.

$$\begin{array}{l|ccccccc} \hline \text { Patients per hour } & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text { Probability } & .2725 & .3543 & .2303 & .0998 & .0324 & .0084 & .0023 \\ \hline \end{array}$$

Calculate this probability distribution's mean and standard deviation.

A plane leaves Seattle, flies $85 \mathrm{mi}$ at $22^{\circ}$ north of east, and then changes direction to $48^{\circ}$ south of east. After flying at $115 \mathrm{mi}$ in this new direction, the pilot must make an emergency landing on a field. The Seattle airport facility dispatches a rescue crew.
($a$) In what direction and how far should the crew fly to go directly to the field? Use components to solve this problem.
($b$) Check the reasonableness of your answer with a careful graphical sum.

Five-year-old Amy wakes her parents up at 3 AM crying and complaining of a sore neck, a severe headache, and feeling sick to her stomach. She has a temperature of $40^{\circ} \mathrm{C}$ $\left(104^{\circ} \mathrm{F}\right)$ and hides her eyes, saying that the lights are too bright. The emergency physician suspects meningitis and performs a lumbar tap. Using your knowledge of neuroanatomy, explain into which space and at what level of the vertebral column the needle will be inserted to perform this test. Which fluid is being obtained and why?

Three-year-old C.E. is admitted to the Emergency Department (ED) fast track clinic. Her mother tells the nurse that C.E. has had a low-grade fever for $2$ days and is complaining of ear pain and a sore throat. Mrs. E. states that C.E.'s appetite has been “off,” but she has been drinking and using the bathroom as usual.

As you get C.E. settled in the exam room, what routine information regarding risk factors for otitis media (OM) would you want to obtain from Mrs. E.?

The following exercises describe apportionment problems for situations besides the House of Representatives. Do the following: a. Find the apportionment by Hamilton's method. b. Find the apportionment by Jefferson's method. c. Find the apportionment by Webster's method. d. Find the apportionment by the Hill-Huntington method. e. Compare the results of the various methods. A city plans to purchase 16 new emergency vehicles. They are to be apportioned among 485 members of the police department, 213 members of the fire department, and 306 members of the paramedic squad.