A hot-air balloon is flying at a height of 600 feet and is directly above the Marshall Space Flight Center in Huntsville, Alabama. The pilot of the balloon looks down at the airport that is known to be 5 miles from the Marshall Space Flight Center. What is the angle of depression from the balloon to the airport?

Evaluate the expression when x = 2.

$$6 x + 8$$

A 12-foot ladder leaning against a wall makes an angle

$$\theta$$

with the floor. If the top of the ladder is h feet up the wall, express h in terms of

$$\theta$$

and then use dh to estimate the change in h if

$$\theta$$

changes from

$$60 ^ { \circ }$$

to

$$59 ^ { \circ }$$

.

A 12-foot ladder leans against a building. The top of the ladder leans against the wall 10.5 feet from the ground. What is the angle formed by the ground and the ladder?

Expand each expression. (4+2x)(4-2x)

Sketch the asymptotes and the graph of each equation. $y=\frac{1}{x-3}+4$

A 12-foot ladder leans against a building. The top of the ladder leans against the wall 10.5 feet from the ground. What is the angle formed by the ground and the ladder?

You are examining a free-living animal that has a thin, solid body with two surfaces. Into what phylum is this organism classified? Explain.

Reconstruct the table using the two categorical variables "letter listed first (S or Q)" and "ordering of letter chosen (listed first or second).”

What is happening to the U.S. real exchange rate in each of the following situations? Explain. a. The U.S. nominal exchange rate is unchanged, but prices rise faster in the United States than abroad. b. The U.S. nominal exchange rate is unchanged, but prices rise faster abroad than in the United States. c. The U.S. nominal exchange rate declines, and prices are unchanged in the United States and abroad. d. The U.S. nominal exchange rate declines, and prices rise faster abroad than in the United States.

Find the vertices, foci, center (if an ellipse or a hyperbola), and asymptotes (if a hyperbola).

$$16 x ^ { 2 } + 25 y ^ { 2 } - 64 x - 200 y + 64 = 0$$

If $g ( x ) = x ^ { 2 } – 5$ find the value(s) of x so that: a. g(x) = 20 b. g(x) = 6

Twenty sophomores are randomly selected from campus dormitories at a college, and 20 other sophomores are randomly selected from students who live off campus. The mean grade point averages of the two groups are compared. Does this comparison involve paired data or data from two independent samples?

A stick of length 1 is broken at a uniformly random point, yielding two pieces. Let $X$ and $Y$ be the lengths of the shorter and longer pieces, respectively, and let $R = X/Y$ be the ratio of the lengths $X$ and $Y$ . (a) Find the CDF and PDF of $R$. (b) Find the expected value of $R$ (if it exists). (c) Find the expected value of $1/R$ (if it exists).