Find a constant b such that h is continuous at x = 2, where

$$h ( x ) = \left\{ \begin{array} { l l } { x + 1 } & { \text { for } | x | < 2 } \\ { b - x ^ { 2 } } & { \text { for } | x | \geq 2 } \end{array} \right.$$

With this choice of b, find all points of discontinuity.

Chiko says, "There's an amazing fact about the number I'm thinking of. I call this fact the four 4's. Using my number, you can get four different answers if you add 4, subtract 4, multiply by 4 or divide by 4. That's not impressive, but if you add all the answers, you get 60." a. Is Chiko's number 12?
b. Is Chiko's number 8?
c. Find Chiko's number. Describe how to find it.

State the domain and range of the function. $f(x)=\sqrt{x-12}+4$

Find the inverse of the matrices.

$$\left[\begin{array}{rrr}{1} & {2} & {1} \\ {2} & {-1} & {3} \\ {2} & {2} & {1}\end{array}\right]$$

Give a pseudocode description of the algorithm for multiplying two upper triangular matrices.

At what point is the young man's fate actually decided? Explain.

a. Are the sets equivalent? Explain. b. Are the sets equal? Explain. $A=\{x | x \in \mathbf{N}$ and $200 \leq x \leq 206 \}$, $B=\{x | x \in \mathbf{N}$ and 199<x<207}

Find the curl and divergence of the given vector field. $y^{3} \mathbf{i}-x^{3} \mathbf{j}$

Perform the indicated operations and express the result in simplest radical form with rationalized denominators. $\sqrt{a^{-3} \sqrt[5]{b^{12}}}$

What made Watson and Crick realize that DNA was a double helix?

Let T be a linear operator on a vector space $V,$ and let $W_{1}, W_{2}, \ldots, W_{k}$ be T-invariant subspaces of $V .$ Prove that $W_{1}+W_{2}+\cdots+W_{k}$ is also a T-invariant subspace of $V$

Use your book or dictionary to define each term. Artificial selection _____.

Complete and balance the equations for the following reactions, and then identify each by type. a.

$$\text { zinc } + \text { sulfur } \longrightarrow$$

___, b. silver nitrate + potassium iodide

$$\longrightarrow$$

___, c. toluene,

$$\mathrm { C } _ { 7 } \mathrm { H } _ { 8 } +$$

oxygen

$$\longrightarrow$$

___, d. nonane,

$$\mathrm { C } _ { 9 } \mathrm { H } _ { 20 }$$

+oxygen

$$\longrightarrow$$

Vicki works at Apple Appliances. She earns d dollars per hour, but is also paid p% commission on all sales. Last week she sold w dollars worth of appliances in the h hours she worked. Write an expression that represents her salary for the week.