Write the numbers in given of the following sentences as decimals.
a. A flea has a body length about one sixteenth of an inch.
b. Venus orbits the sun about once every 224 and $\frac {7006} {10,000}$ days.

In the "Fosbury flop" method of high jumping, named for the track and field star Dick Fosbury, an athlete's center of mass may pass under the bar while the athlete's body passes over the bar. Explain how this is possible.

Using

$$f ( x ) = \cos x \text { or } f ( x ) = \sin x$$

as a guide, graph the function. Identify the period and asymptotes. j(x) = -2 csc x

Without a calculator, decide whether the quantities are positive or negative.

$$-4^3$$

Let $(a, b)=1$. Prove that $\left(a, b^n\right)=1$ for all positive integers $n$.

Let x be a binomial random variable with n=7 and p=.5. Find the values of the quantities.

$$P(x=4)$$

A museum had 275,608 visitors last year. What is this number rounded to the nearest thousand?

The Cobalt $({}_{27}^{57}\mathrm{Co})$ emits 122-keV gamma rays. If a 70-kg person swallowed 2.0 $\mu$Ci of ${}_{27}^{57}\mathrm{Co}$, what would be the dose rate (rad/day) averaged over the whole body? Assume that $50$ percent of the $\gamma$-ray energy is deposited in the body. $\it{[Hint:}$ Determine the rate of energy deposited in the body and use the definition of the rad.$]$

A segment that is 1/2 of an inch long is how many sixteenths of an inch long?

Write the equality and conversion factors for the following pair of unit: dimes and dollars.

Determine the cumulative distribution function of a binomial random variable with n=3 and p=1/4.

Answer true of false for each part.

a. When you flip a coin ten times, you are more likely to get the sequence HHHHHTTTTT than the sequence HHHHHHHHHH.

b. When you flip a coin ten times, you are more likely to get a sequence that contains five heads than a sequence that contains ten heads.

How can you find the conversion rate for milliliters to kiloliters?

Define a success in this context, and define the random variable X of interest. What is the probability of success?