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

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

Find the covariance of the random variables X and Y.

$$\text{ The joint density function of the random variables } X \text{ and } Y \text{ is }$$

$$f(x,y)=6x, \text{ for } 0<x<1, \text{ } 0<y<1-x,$$

$$f(x,y)=0, \text{ elsewhere.}$$

[

$$(a) \text{ Show that } X \text{ and } Y \text{ are not independent. }$$

$$(b) \text{ Find } P(X >0.3 | Y = 0.5).$$

You are on duty in the emergency department (ED) when a "code blue" is called. As the code nurse, you grab the crash cart and run to the code, which is in the employee lounge of the operating room. On the couch, you find a nurse, Z.H., unconscious, dusky, and barely breathing
Z.H.'s respiratory rate is 8 and shallow. The respiratory therapist intubates her and continues to ventilate her manually. You attach ECG leads to her chest and find the results shown in the figure. What is your interpretation of Z.H.'s rhythm?

Find a fraction whose decimal equivalent is

$$0 . \overline { 61 }$$

.

The Fugitive Slave Act made it a federal crime to A. assist runaway slaves. B. give jobs to freedmen . C. sell slaves in the North. D. allow African Americans to vote.

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.

Identify at least five signs and symptoms of increased ICP.

Define Type I and Type II error for each scenario, and identify the cost(s) of each type of error.

Approaching O'Hare for landing, a British Air flight from London has been in a holding pattern for $45$ minutes due to bad weather. Landing is expected within $15$ minutes. The flight crew could declare an emergency and land immediately, but an FAA investigation would be launched and other flights might be endangered. The null hypothesis is that there is enough fuel to stay aloft for $15$ more minutes.

Oxygen masks for producing $\mathrm{O}_2$ in emergency situations contain potassium superoxide $\left(\mathrm{KO}_2\right)$. It reacts according to this equation:

$$4\mathrm{~KO}_2+2\mathrm{~H}_2 \mathrm{O}+4\mathrm{~CO}_2\longrightarrow 4\mathrm{~KHCO}_3+3\mathrm{~O}_2$$

(a) If a person wearing such a mask exhales $0.85 \mathrm{~g}$ of $\mathrm{CO}_2$ every minute, how many moles of $\mathrm{KO}_2$ are consumed in $10.0$ minutes?
(b) How many grams of oxygen are produced in $1.0$ hour?

O A door in a hospital has a pneumatic closer that pulls the door shut such that the doorknob moves with constant speed over most of its pach. In this part of its motion, (a) does the doorknob experience a centripetal acceleration? (b) Does it experience a tangential acceleration? Hurrying to an emergency, a nurse gives a sharp push to the closed door. The door swings open against the pneumatic device, slowing down and then reversing its motion. At the moment the door is open the widest, (c) does the doorknob have a centripetal acceleration? (d) Does it have a tangential acceleration?

Assume that people and businesses have reasonable expectations. Explain how the events listed below will affect aggregate output and the price level. a. The Fed reduces the required reserve ratio unexpectedly. b. Congress passes a tax-cut bill that takes effect in a year and lasts ten years. c. The Fed announces a reduction in the money supply. d. OPEC abruptly reduces oil production by half. e. The government passes an unannounced emergency defence spending bill, authorising a $500 billion increase in funding immediately.

For many years Colonel John P. Stapp, USAF, held the world’s land speed record. He participated in studying whether a jet pilot could survive emergency ejection. On March $19$, $1954$, he rode a rocket-propelled sled that moved down a track at $632$ mi/h. He and the sled were safely brought to rest in $1.40$ s. Determine (a) the negative acceleration he experienced and (b) the distance he traveled during this negative acceleration, assumed to be constant.

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.

Mrs. E. is given a new prescription for azithromycin (Zithromax) PO $160$ mg qd $\times$ $5$ days.

5. Azithromycin is dispensed $200$ mg/$5$ mL. Calculate the dosage for Mrs. E. to administer to C.E

In a study of patients arriving at a hospital emergency room, the gender of the patients is considered, together with whether the patients are younger or older than 30 years of age, and whether or not the patients are admitted to the hospital. It is found that $45\%$ of the patients are male, $30\%$ of the patients are younger than 30 years of age, $15\%$ of the patients are females older than 30 years of age who are admitted to the hospital, and $21\%$ of the patients are females younger than 30 years of age. What proportion of the patients are females older than 30 years of age who are not admitted to the hospital?

The flywheel of an old steam engine is a solid homogeneous metal disk of mass $M=120 \mathrm{~kg}$ and radius $R=80.0 \mathrm{~cm}$. The engine rotates the wheel at 500 . rpm. In an emergency, to bring the engine to a stop, the flywheel is disengaged from the engine and a brake pad is applied at the edge to provide a radially inward force $F=100$. N. If the coefficient of kinetic friction between the pad and the flywheel is $\mu_{\mathrm{k}}=0.200$, how many revolutions does the flywheel make before coming to rest? How long does it take for the flywheel to come to rest? Calculate the work done by the torque during this time.