A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a 1-hour flight is $.02$. What is the probability that (a) both will fail? (b) Neither will fail? (c) One or the other will fail? Show all steps carefully.

Identify the business units as a cost, revenue, profit, or investment center:

A corporation's subsidiary that is independent and whose manager makes decisions regarding capital investments.

Describe and illustrate in a graph what happened in the economy in Table 1 if in year 1, capital per hour of labor was 30 and in year 2 it was 40.

In 1978, Geoff Capes of Great Britain threw a heavy brick a horizontal distance of 44.5 m. Find the approximate speed of the brick at the highest point of its flight, neglecting any effects due to air resistance. Assume the brick landed at the same height it was launched.

A plane descends to sea level from $12,000 \mathrm{ft}$ after being airborne for $1 \frac{1}{2} \mathrm{hr}$. The entire flight time is $2 \mathrm{hr} 10 \mathrm{~min}$. Find the average rate of descent of the plane.

Use the Cobb-Douglas production function to show that if both the number of units of labor and the number of units of capital are doubled, the production level is also doubled.

The following statement contains an italicized vocabulary word or related form. Decide whether the sentence is true or false, and write True or False on the answer line.

Some people who live beneath the flight paths of airplanes never become inured to the noise level. __________________________

Suppose that photons of blue light (430 nm) are used to locate the position of a 2.80-g Ping Pong ball in flight and that the uncertainty in the position is equal to one wavelength. What is the minimum uncertainty in the speed of the Ping-Pong ball? Comment on the magnitude of your result.

Airplane flight plan An airplane flying at a speed of $400 \mathrm{mi} / \mathrm{hr}$ flies from a point $A$ in the direction $153^{\circ}$ for $1$ hour and then flies in the direction $63^{\circ}$ for $1$ hour.

How long will it take to get back to point $A$ ?

A small steel ball is projected horizontally off the top of a long flight of stairs. The initial speed of the ball is $3.0 \mathrm{~m} / \mathrm{s}$. Each step is $0.18 \mathrm{~m}$ high and $0.30 \mathrm{~m}$ wide. Which step does the ball strike first?

Insert colons where they are needed in the following items.

Example 1. The 8 : 15 flight was full, so I reserved a seat on the 9 : 10 .

2. I just finished Undaunted Courage Meriwether Lewis, Thomas Jefferson, and the Opening of the American West.

Prove these statements: $(a)$ As long as you can neglect the effects of the air, if you throw anything vertically upward, it will have the same speed when it returns to the release point as when it was released. $(b)$ The time of flight will be twice the time it takes to get to its highest point.

A manufacturer has modeled its yearly production function P (the monetary value of its entire production) as a so-called Cobb-Douglas function $P(L, K)=1.47 L^{0.65} K^{0.35}$ where L is the number of labor hours (in thousands) and K is the invested capital (in millions of dollars). If both the amount of labor and the amount of capital are doubled, verify that the production is also doubled.

A man of mass $80 \mathrm{~kg}$ runs up a flight of stairs $20 \mathrm{~m}$ high in $10 \mathrm{~s}$. (a) how much power is used to lift the man? (b) If the man's body is $25 \%$ efficient, how much power does he expend?