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.

Evaluate the expression to complete the table. "

$$\begin{matrix} & \text{Mammals with the Longest Tails}\\ \text{Mammal} & \text{Expression} & \text{Tail Length}\\ \text{African buffalo} & \mathrm{51 + 6 ^ { 2 } \div 9 - 12} & \text{\_\_\_\_\_}\\ \end{matrix}$$

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Sean and Mason run out of gas while fishing from their boat in the bay. They set off an emergency flare with an initial vertical velocity of 30 meters per second. The height of the flare in meters can be modeled by $h(t)=-5 t^2+30 t$, where t represents the number of seconds after launch.

Sean wants to know how high the flare will reach above the surface of the water.

a. Write the function in vertex form, factoring so the coefficient of $t^2$ is 1 .

b. Complete the square using the vertex form of the function.

c. How high will the flare reach?

A patient is admitted to the emergency department with suspected carbon monoxide poisoning. Even though the patient's color is ruddy and not cyanotic, the nurse understands the patient is at a risk for decreased oxygen-carrying capacity of blood because carbon monoxide does which of the following:

1. Stimulates hyperventilation, causing respiratory alkalosis
2. Forms a strong bond with hemoglobin, thus preventing oxygen binding in the lungs
3. Stimulates hypoventilation, causing respiratory acidosis
4. Causes alveoli to overinflate, leading to atelectasis

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 of having a working generator in the event of a power outage. Is that probability high enough for the hospital?

A vehicle is stuck on the railroad tracks as a 430,000 lb locomotive is approaching with a speed of 75 mph. As soon as the problem is detected, the locomotive’s emergency brakes are activated, locking the wheels and causing the locomotive to slide. If the coefficient of kinetic friction between the locomotive and the track is 0.45, what is the minimum distance d at which the brakes must be applied to avoid a collision? What would that distance be if instead of a locomotive, there was a $30 \times 106 lb$ train? Treat the locomotive and the train as particles, assume that the railroad tracks are rectilinear and horizontal, and note that only the locomotive’s brakes are applied.

While playing on her swing set, 10-year-old Rebecca falls and breaks her right leg. At the emergency room, the doctor tells her parents that the proximal end of the tibia where the epiphysis meets the diaphysis is fractured. The fracture is properly set and eventually heals. During a routine physical when she is 18, Rebecca learns that her right leg is 2.54 cm (1 in.) shorter than her left. What might account for this difference?

Walking to her car after her 65th birthday party, Mrs. Schultz tripped on ice and fell forward on her outstretched palms. When she arrived at the emergency room, her right wrist and hand were bent like a fork. Dr. Jefferson felt that the styloid process of her radius was outside of the anatomical snuff box and slightly proximal to the styloid process of the ulna. When he checked her elbow, he found that the olecranon lay 2 cm proximal to the two epicondyles of the right humerus. Explain all these observations, and describe what had happened to Mrs.Schultz’s limb.

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.

Potassium superoxide, $KO_2$, is employed in a self-contained breathing apparatus used by emergency personnel as a source of oxygen. The reaction is\

$4KO_2(s) + 2H_2O(l) \longrightarrow 4KOH(s) + 3O_2(g)$\

Say a self-contained breathing apparatus is charged with 750 g $KO_2$ and then is used to produce 195 g of oxygen. Was all of the $KO_2$ consumed in this reaction? If the $KO_2$ wasn’t all consumed, how much is left over and what mass of additional $O_2$ could be produced?

Malcolm injured himself after trying to break his fall with outstretched arms. The emergency room physician took one look at his shoulder and saw that Malcolm had a broken clavicle (and no other injury). Describe the position of Malcolm’s shoulder. What part of the clavicle was most likely broken? Malcolm was worried about injury to the main blood vessels to his arm (the subclavian vessels), but he was told such injury was unlikely. Why could the doctor predict this?

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. C.E.'s mother 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, you suspect C.E may have otitis media (OM).
Place an arrow where you suspect fluid would be found.

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.

A recently graduated mechanical engineer wants to build a reserve fund as a safety net to pay his expenses in the unlikely event that an unexpected emergency arises. His aim is to have $45,000 developed over the next 3 years, with the proviso that the amount must have the same purchasing power as$45,000 today. If the expected market rate on investments is 8% per year and inflation is averaging 2% per year, find the annual amount necessary to meet his goal.