Simplify.

$$\sqrt [ 3 ] { 32 }$$

To be rescued from the roof of a burning building, a 70-kg man must be able to jump straight up and catch hold of a rope ladder hanging from a helicopter. He has to raise his center of mass 2.00 m above the roof to do so. (a) If he crouches down such that his center of mass is 0.50 m above the roof and his feet leave the roof when his center of mass is 1.05 m above the roof, what minimum force must he exert on the roof to reach the ladder? (b) A typical candy bar contains about 850 kJ of food energy. How many candy bars does this jump require?

Calculate. $\int{\dfrac{dx}{1-\sqrt{x}}}$

Claim: The mean pulse rate (in beats per minute, or bpm) of adult males is equal to 69 bpm. For the random sample of 153 adult males the mean pulse rate is 69.6 bpm and the standard deviation is 11.3 bpm. Make subjective estimates to decide whether results are significantly low or significantly high, then state a conclusion about the original claim. For example, if the claim is that a coin favors heads and sample results consist of 11 heads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favors heads (because it is easy to get 11 heads in 20 flips by chance with a fair coin).

In a drama club, 7 of the 20 girls are seniors, and 4 of the 14 boys are seniors. What is the probability of randomly selecting a boy or a senior to represent the drama club at an arts symposium?

Some water is placed in a coffee cup calorimeter. When 1.0 g of an ionic solid is added, the temperature of the solution increases from $21.5 ^ { \circ } \mathrm { C }$ to $24.2 ^ { \circ } \mathrm { C }$ as the solid dissolves. For the dissolving process, what are the signs for $\Delta S _ {sys}, \Delta S _ {surr},$ and $\Delta S _ {univ}?$

Let P(x) be the cumulative distribution function for the household income distribution in the US in 2009. Values of P(x) are in the following table:

Income x (thousand $): 20, 40, 60, 75, 100 P(x) (%): 29.5, 50.1, 66.8, 76.2, 87.1

Is the statement "More than one-third of households made between$40,000 and $75,000" true or false?

Sandra is a 25-year old woman who weighs 120 lb. She burns 300 − 50t cal/hr while walking on her treadmill. Her caloric intake from drinking Gatorade is 100t calories during the tth hour. What is her net decrease in calories after walking for 3 hours?

If a function f has no limit as x approaches c, then we say that $\lim _{x \rightarrow c} f(x)$ _____ _____ _____.

Use synthetic division to find each quotient. $\frac{y^{3}+1}{y-1}$

The following list of prices is for a used original radio for a 1955 Thunderbird. The prices vary depending on the condition of the radio. $210,$210, $320,$200, $300,$10, $340,$300, $245,$325, $700,$250, $240,$200 Find the four quartiles.

Why is it important for everyone, even good swimmers, to know the technique of survival floating?

Solve the equation by completing the square. Round your solutions to the nearest hundredth, if necessary.

$$0.75 x ^ { 2 } + 1.5 x = 4$$

Find the indicated term(s) of the geometric sequence with the given description. The common ratio is

$$\frac { 1 } { 6 }$$

and the third term is 18. Find the first and seventh terms.