Factor the polynomial.

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

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

Among all positive numbers a, b whose sum is 8, find those for which the product of the two numbers and their difference is largest.

Determine the null space of the given matrix A.

$$A = \left[ \begin{array} { r r r } { 1 } & { - 2 } & { 1 } \\ { 4 } & { - 7 } & { - 2 } \\ { - 1 } & { 3 } & { 4 } \end{array} \right]$$

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

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. _____

Complete the square and factor the resulting perfect square trinomial.

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

Find the exact value of each expression.

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

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?

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?

Suppose that a student has 500 vocabulary words to learn. If the student learns 15 words after 5 minutes, the function $L(t) = 500(1 - e^{-0.0061t})$ approximates the number of words L that the student will learn after t minutes. How many words will the student learn after 60 minutes?

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