Find the equation for the conic in standard form. Hyperbola: center (-5,0), one focus is (-5,3), one vertex is (-5,2)

Factor the polynomial.

$$3 z ^ { 2 } - 27$$

Make an appropriate u-substitution, and then use the Endpaper Integral Table to evaluate the integral.

$$\int \cos \sqrt { x } d x$$

What does correlation tell you about the relationship between two variables?

Write the negation of each statement. The lunch was served at noon.

Find the exact value of each expression.

$$\sin \frac { 3 \pi } { 8 }$$

If $\mathbf{F}(x, y)=P(x, y) \mathbf{i}+Q(x, y) \mathbf{j}$ is a vector field in a domain D with div F = 0 and curl F = 0, then the complex function $g(z)=P(x, y)+i Q(x, y)$ is analytic in D. _____

The third floor of a house is 8 m above street level. How much work is needed to move a 150-kg refrigerator to the third floor?

Complete the square and factor the resulting perfect square trinomial.

$$x ^ { 2 } + 24 x$$

Whitney deposits $9,000 for two years. She compares two different banks. State Bank will pay her 4.1% interest, compounded monthly. Kings Savings will pay her 4.01% interest, compounded continuously. How much interest does State Bank pay?

The integers below represent the monthly gains and losses in the value of an investment over one year. Find the mean of the integers. -$190,$75, -$65,$100, $72, -$ 54, -$62 , -$87, $92,$81, -$73,$63

A humor piece published in the British Medical Journal ("Parachute use to prevent death and major trauma related to gravitational challenge: systematic review of randomized control trials," Gordon, Smith, and Pell, BMJ, 2003:327) notes that we can't tell for sure whether parachutes are safe and effective because there has never been a properly randomized, double-blind, placebo-controlled study of parachute effectiveness in skydiving. (Yes, this is the sort of thing statisticians find funny . ... ) Suppose you were designing such a study: How would you randomize this "experiment"? How would you make the experiment double-blind?

Suppose that f is a continuous additive function on

$$\mathbb{R}.$$

If c := f (1), show that we have f(x) = cx for all

$$x \in \mathbb{R}.$$

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?