A traffic engineer determines that the number of cars passing through a certain intersection each week can be modeled by $C(x)=0.02x^3+0.4x^2+0.2x+35$, where x Is the number of weeks since the survey began. A new road has just opened that affects the traffic at that intersection. Let $N(x)=C(x)+200$.
Emergency roadwork temporarily closes off most of the traffic to this intersection. Write a function R(x) that could model the effect on C(x) Explain how the graph of C(x) might be transformed into R{x).

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.

An emergency cell phone charger requires you to turn a small crank in order to create the energy needed to recharge the phone’s battery. If you turn the crank 120 times per minute, the total number r of revolutions that you turn the crank is given by r = 120t where t is the time (in minutes) spent turning the crank. a. Graph the function and identify its domain and range. b. Identify the domain and range if you stop turning the crank after 4 minutes. Explain how this affects the appearance of the graph.

(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 $\alpha=0.01$ ?

An accident victim who had not been wearing a seat belt received trauma to his forehead when he was thrown against the windshield. The physicians in the emergency room worried that his brain stem may have been driven inferiorly through the foramen magnum. To help assess this, they quickly took a standard X-ray film of his head and searched for the position of the pineal gland. How could anyone expect to find this tiny, boneless gland in a radiograph?

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?

You are working in the emergency department (ED) of a community hospital when the ambulance arrives with A.N., an $18$-year-old woman who was caught in a house fire. She was sleeping when the fire started and managed to make her way out of the house through thick smoke. The emergency medical system crew initiated humidified oxygen at $15 \mathrm{~L} / \mathrm{min}$ per nonrebreather mask and started a $16$-gauge IV with lactated Ringer's solution. On arrival to the ED, her vital signs are $100/66, 125, 34$, $\mathrm{SaO}_2 93 \%$. An additional $16$-gauge IV is inserted. She appears anxious and in pain.

Eighteen hours after the injury, the NAP reports these vital signs for A.N. and states that the urine output for the past hour was $20$ mL.

$$\begin{aligned} &\text { Vital Signs }\\ &\begin{array}{ll} \text { Blood pressure } & 90 / 50 \mathrm{~mm} \mathrm{Hg} \\ \text { Heart rate } & 110 \text { beats } / \mathrm{min} \\ \text { Respiratory rate } & 24 \text { breaths } / \mathrm{min} \end{array} \end{aligned}$$

What treatment do you anticipate?

Ambulance response time. Geographical Analysis (Jan. 2010) presented a study of emergency medical service (EMS) ability to meet the demand for an ambulance. In one example, the researchers presented the following scenario. An ambulance station has one vehicle and two demand locations, $\mathrm{A}$ and $\mathrm{B}$. The probability that the ambulance can travel to a location in under 8 minutes is $.58$ for location $\mathrm{A}$ and $.42$ for location $\mathrm{B}$. The probability that the ambulance is busy at any point in time is $.3$. Find the probability that EMS can meet the demand for an ambulance at location B.

J.R. is a $28$-year-old man who was doing home repairs. He fell from the top of a $6$-foot stepladder, striking his head on a large rock. He experienced a momentary loss of consciousness. By the time his neighbor got to him, he was conscious but bleeding profusely from a laceration over the right temporal area. The neighbor drove him to the emergency department of your hospital. As the nurse, you immediately apply a cervical collar, lay him on a stretcher, and take J.R. to a treatment room.

Differentiate between a primary and secondary head injury.

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

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.

Suppose that you were called upon to give some advice to a lawyer concerning the physics involved in one of her cases. The question is whether a driver was exceeding a $30$-mi/h speed limit before he made an emergency stop, brakes locked and wheels sliding. The length of skid marks on the road was $19.2$ ft. The police officer made the assumption that the maxi- mum deceleration of the car would not exceed the accelera- tion of a freely falling body $(=32$ ft/s$^2)$ and did not give the driver a ticket. Was the driver speeding? Explain.

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.

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%.