An office employs six customer service repres entatives. Each day, two of them are randomly selected and their customer interactions are monitored for the purposes of improving customer relations. In how many ways can the repres entatives be chosen?

What is the capacitance of an oscillating LC circuit if the maximum charge on the capacitor is

$$2.40 \mu \mathrm { C }$$

and the total energy is

$$140 \mu J$$

?

Evaluate the indefinite integral.

$$\int x ^ { 2 } \sin \left( x ^ { 3 } + 1 \right) d x$$

How many ways can you arrange two of the first three letters of the alphabet?

Compute the first-order partial derivatives.

$$w = \frac { x } { y + z }$$

three siblings are three different ages. The oldest is twice the age of the middle sibling, and the middle sibling is six years older than one-half the age of the youngest. Write a composite function that gives the oldest sibling’s age in terms of the youngest. Explain how you arrived at your answer.

Simplify each sum or difference.

$$( 9 x - 3 y ) - ( 3 x - 9 y )$$

In a certain community, 36 percent of the families own a dog and 22 percent of the families that own a dog also own a cat. In addition, 30 percent of the families own a cat. What is (a) the probability that a randomly selected family owns both a dog and a cat? (b) the conditional probability that a randomly selected family owns a dog given that it owns a cat?

An athletic store sells about 200 pairs of basketball shoes per month when it charges $120 per pair. For each$2 increase in price, the store sells two fewer pairs of shoes. How much should the store charge to maximize monthly revenue? What is the maximum monthly revenue?

Use the extended Euclidean algorithm to find the greatest common divisor of the given numbers and express it as a linear combination of the two numbers. 4158 and 1568

Solve each equation by factoring. $3 x^{2}-x-2=0$

A carton of milk is poured into a bowl. Describe the changes that occur in the milk's shape and volume.

Use the most appropriate method to solve each equation on the interval

$$[0,2\pi).$$

Use exact values where possible or give approximate solutions correct to four decimal places.

$$3 \tan ^ { 2 } x - \tan x - 2 = 0$$

A farmer drew a picture of his fields to the scale of 1 inch equals 250 feet. If the drawing of the pumpkin patch is 0.5 inches wide, how wide is the actual patch?