A hiker caught in a thunderstorm loses heat when her clothing becomes wet. She is packing emergency rations that if completely metabolized will release $35 \mathrm{~kJ}$ of heat per gram of rations consumed. How much rations must the hiker consume to avoid a reduction in body temperature of $2.5 \mathrm{~K}$ as a result of heat loss? Assume the heat capacity of the body equals that of water and that the hiker weighs $51 \mathrm{~kg}$. State any additional assumptions.

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

Doctors treated a patient at an emergency room from 2:00 P.M. to 7:00 P.M. The patient’s blood oxygen level L (in percent) during this time period can be modeled by $L=-0.270 t^{2}+3.59 t+83.1, \quad 2 \leq t \leq 7$ where t represents the time of day, with t=2 corresponding to 2:00 P.M. Use the model to estimate the time (rounded to the nearest hour) when the patient’s blood oxygen level was 93%.

Let X denote the number of times a certain numerical control machine will malfunction: 1, 2, or 3 times on any given day. Let Y denote the number of times a technician is called on an emergency call. Their joint probability distribution is given as

$$\begin{matrix} & & & x & \\ \hline & & 1 & 2 & 3 \\ & 1 & 0.05 & 0.05 & 0.10 \\ y & 3 & 0.05 & 0.10 & 0.35 \\ & 5 & 0.00 & 0.20 & 0.10 \end{matrix}$$

(a) Evaluate the marginal distribution of X. (b) Evaluate the marginal distribution of Y. (c) Find P(Y=3|X=2).

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.

After a heavy meal rich with fried foods, Debby Collins, an overweight 45-year-old woman, was rushed to the emergency room with severe spasmodic pains in her epigastric region that radiated to the right side of her rib cage. She indicated that the attack came on suddenly, and her abdomen was found to be tender to the touch and somewhat rigid. What do you think is this patient's problem and why is her pain discontinuous (colicky)? What are the treatment options and what might happen if the problem is not resolved?

The temperature T (in degrees Fahrenheit) of a patient t hours after arriving at the emergency room of a hospital at 10:00 P.M. is given by $T(t)=98.6+4 \cos \frac{\pi t}{36}, \quad 0 \leq t \leq 18$. Find the patient’s temperature at (a) 10:00 P.M., (b) 4:00 A.M., and (c) 10:00 A.M. (d) At what time do you expect the patient’s temperature to return to normal? Explain your reasoning.

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?

Hos pitals typically req uire backup generators to provide electricity in the event of a power outage. Assume that emergency backup generato rs fai l 22% of the times when they are needed (based on data from Arshad Mansoor, senior vice president with the Electric Power Research In stitute). A hospital has two backup generators so that power is avail able if one of them fails during a power outage. Find the probability that both generators fail during a power outage.

$$\left. \begin{array} { l } { \text { . The interval between patient arrivals in an emergency room } } \\ { \text { is a random variable with exponential density function } p ( t ) = } \\ { 0.125 e ^ { - 0.125 t } ( t \text { in minutes). What is the average time between pa- } } \\ { \text { tient arrivals? What is the probability of two patients arriving within } 3 } \\ { \text { min of each other? } } \end{array} \right.$$

Just an instant before reaching the very bottom of a semicircular section of a roller coaster ride, the automatic emergency brake inadvertently goes on. Assume the car has a total mass of 750 kg, the radius of that section of the track is 55.0 m, and the car entered the bottom after descending vertically (from rest) 25.0 m on a frictionless straight incline. If the braking force is a steady 1700 N, determine (a) the car's centripetal acceleration (including direction), (b) the normal force of the track on the car, (c) the tangential acceleration of the car (including direction), and (d) the total acceleration of the car.

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 $(\mathrm{Hz})$

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

(a) A light-rail commuter train accelerates at a rate of 1.35 m/s². How long does it take to reach its top speed of 80.0 km/h, starting from rest? (b) The same train ordinarily decelerates at a rate of 1.65 m/s². How long does it take to come to a stop from its top speed? (c) In emergencies, the train can decelerate more rapidly, coming to rest from 80.0 km/h in 8.30 s. What is its emergency acceleration in meters per second squared?

A plane traveling horizontally at 80 m/s} over flat ground at an elevation of 3000 m releases an emergency packet. The trajectory of the packet is given by

$$x=80 t, \quad y=-4.9 t^2+3000, \quad \text { for } t \geq 0,$$

where the origin is the point on the ground directly beneath the plane at the moment of the release. Graph the trajectory of the packet and find the coordinates of the point where the packet lands.