Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. -If f(x) = sin²(2x), then f’(x) = 2(sin 2x)(cos 2x).

If $X_1,X_2, . . .,X_n$ is a random sample from a beta distribution with parameters $\alpha = \beta = \theta > 0,$ find a best critical region for testing $H _ { 0 } : \theta = 1$ against $H _ { 1 } : \theta = 2$

What is the thermal energy associated with $5.6 \times 10 ^ { 18 }$ nitrogen molecules, $\mathrm { N } _ { 2 }$, at $100 ^ { \circ } \mathrm { F }$? Assume the nitrogen can be treated as an ideal gas.

Find the geometric mean of the pair of numbers.

$$6 \text { and } \frac { 3 } { 8 }$$

Find the x- and y-intercepts of the function

$$y = 2x + 1.$$

What are the intercepts of the inverse function?

Evaluate to the nearest hundredth. a)

$$\cos 34 ^ { \circ }$$

b)

$$\sec 10 ^ { \circ }$$

c)

$$\cot 75 ^ { \circ }$$

d)

$$\csc 45 ^ { \circ }$$

Make an order-of-magnitude estimate of the quantity. -The minimum work needed to assemble eight protons, one at each of the eight corners of a 5-mm cube.

At some colleges and universities, economics professors receive higher salaries than professors in some other fields. a. Why might this be true? b. Some other colleges and universities have a policy of paying equal salaries to professors in all fields. At some of these schools, economics professors have lighter teaching loads than professors in some other fields. What role do the differences in teaching loads play?

An American roulette wheel has 38 slots. Two of the slots are numbered 0 and 00, and the rest are numbered from 1 to 36. A player places a bet on a number between 1 and 36 and wins if a ball thrown into the spinning roulette wheel lands in the slot with the same number. Find the probability of winning on two consecutive spins of the roulette wheel.

Sketch the following sets of points.

$$\{ ( r , \theta ) : 0 \leq r \leq 4 , - \pi / 2 \leq \theta \leq - \pi / 3 \}$$

Determine the formula weights of each of the following compounds: nitric acid,

$$HNO_3$$

Use fraction strips to find the difference. Write your answer in simplest form.

$$\frac { 2 } { 3 } - \frac { 1 } { 4 }$$

A ball bounces up and down on the end of a spring. Describe the energy changes that take place during one complete cycle. Does the total mechanical energy change?

A factory manufactures two kinds of ice skates: racing skates and figure skates. The racing skates require 6 work-hours in the fabrication department, whereas the figure skates require 4 work-hours there. The racing skates require 1 work-hour in the finishing department, whereas the figure skates require 2 work-hours there. The fabricating department has available at most 120 work-hours per day, and the finishing department has no more than 40 work-hours per day available. If the profit on each racing skate is $10 and the profit on each figure skate is$12, how many of each should be manufactured each day to maximize profit? (Assume that all skates made are sold.)