Show that the radius r of the moon’s orbit can be determined from the radius R of the earth, the acceleration of gravity g at the surface of the earth, and the time $\tau$ required for the moon to complete one full revolution about the earth. Compute r knowing that $\tau$= 27.3 days, giving the answer in both SI and U.S. customary units.

Write each system of equations in triangular form using Gaussian elimination. than solve the system.

$$\begin{aligned} &-3 xy+6 x=15\\ &2 x 2 and-5 x=9\\ &4 x-5 and+2 x=-3 \end{aligned}$$

Apply the Pauli exclusion principle to determine the number of electrons that could occupy the quantum states described by n = 4.

Urn I contains five red chips and four white chips; urn II contains four red and five white chips.Two chips are drawn simultaneously from urn I and placed into urn II. Then a single chip is drawn from urn II. What is the probability that the chip drawn from urn II is white?

Marcos traveled in his car from Phoenix to Flagstaff, a distance of 155 miles. a. Determine the amount of time required for Marcos to travel from Phoenix to Flagstaff if his average speed for the trip was 68 miles per hour. b. Construct a possible distance-time graph of Marcos's trip from Phoenix to Flagstaff. Be sure to label your axes. c. On the same axes, construct a graph that represents, the distance-time graph that represents another car traveling at a constant speed for the entire trip.

The IQs of nine randomly selected people are recorded. Let $\bar{Y}$ denote their average. Assuming the distribution from which the $Y_{i}$'s were drawn is normal with a mean of 100 and a standard deviation of 16, what is the probability that $\bar{Y}$ will exceed 103? What is the probability that any arbitrary $Y_{i}$ will exceed 103? What is the probability that exactly three of the $Y_{i}$'s will exceed 103?

The number of bacteria in a colony were growing exponentially. Approximately how many bacteria were there at 7 P.M? F. 15.700. G. 159.540. H. 1.0011.929. J. 6.372.392.

$$\begin{array}{|c|c|} \hline \text { Thule } & \text { Number of Bacteria } \\ \hline 2 \text { P.M. } & 100 \\ \hline 4 \text { P.M. } & 4000 \\ \hline \end{array}$$

Find the exact value of each expression. $\csc 390^{\circ}$

A lake is stocked with bass by the U.S. Park Service. The population of bass is given by $P(t)=\frac{3000}{1+2 e^{-0.37 t}},$ where t is the time in years after the lake was stocked. a. Evaluate P(0) and interpret its meaning in the context of this problem. b. Use the function to predict the bass population 2 yr after being stocked, Round to the nearest whole unit. c. Use the function to predict the bass population 4 yr after being stocked. d. Determine the number of years required for the bass population to reach 2800. Round to the nearest year. e. What value will the term $\frac{2}{e^{0.37 t}}$ approach as $t \rightarrow \infty.$ f. Determine the limiting value of P(t).

In the New York state lottery game "Lotto," a player wins the grand prize by choosing the same group of 6 numbers from 1 through 59 as is chosen by the computer. What is the probability that a player will win the grand prize by playing 5 different tickets?

After a 5-yr slump in the real estate market, housing prices stabilize and even begin to appreciate in value. One homeowner buys a house for $140,000 and finds that the value of the property increases by 3% per year thereafter. Assuming that the trend continues, find the value of the home 15 yr later. Round to the nearest$1000.

Suppose three points are picked randomly from the unit interval. What is the probability that the three are within a half unit of one another?

a. Graph the function. b. Write the domain in interval notation. c. Write the range in interval notation. d. Write an equation of the asymptote. $f(x)=\left(\frac{5}{2}\right)^{x}$

Solve each logarithmic equation. $36+3 \log _{3} x=60$