Determine the water of hydration for the following hydrates and write the chemical formula.

Ni(NO$_{3}$)$_{2}$ $\sdot$ XH$_{2}$O is found to contain $37.2$% water.

Define the linear transformation $T: R^{n} \rightarrow R^{m}$' by T(v) = Av. Find the dimensions of $R^n$ and $R^m$.

$$A=\left[\begin{array}{rrrr} {1} & {0} & {0} & {0} \\ {0} & {-1} & {0} & {0} \\ {0} & {0} & {1} & {0} \\ {0} & {0} & {0} & {2} \end{array}\right]$$

Determine whether each series is convergent or divergent. $\frac{1}{10}+\frac{2}{100}+\frac{6}{1000}+\frac{24}{10,000}+\cdots$

What variables must be known in order to use the Hardy-Weinberg equation?

Determine whether the geometric series $3 - 4 + \frac{16}{3} - \frac{64}{9} + \cdots$ is convergent or divergent. If it is convergent, find its sum.

How do you decide to shade above or below a boundary line? What does this shading represent?

Find an eigenbasis for each of the matrices A, and thus diagonalize A.

$$A=\left[\begin{array}{rrr} 1 & -1 & 1 \\ -1 & 1 & -1 \\ 1 & -1 & 1 \end{array}\right]$$

In the previous figure, what is the value of $k$ ?

Graph each of the following functions: $y=\frac{x^{2}-1}{x-1}$. $y=\frac{x^{3}-1}{x-1}$. $y=\frac{x^{4}-1}{x-1}$. $y=\frac{x^{5}-1}{x-1}$. Is x = 1 a vertical asymptote? Why not? What is happening for x = 1? What do you conjecture about $y=\frac{x^{n}-1}{x-1}$, $n \geq 1$ an integer, for x = 1?

Solve the boundary-value problem, if possible.

$$y’’-8y’+17y=0, y(0)=3, y(π)=2$$

Find the lexicographic ordering of these n-tuples: a) (1, 1, 2), (1, 2, 1) b) (0, 1, 2, 3), (0, 1, 3, 2) c) (1, 0, 1, 0, 1), (0, 1, 1, 1, 0)

Use a Karnaugh map to find the minimal sum-of-products form for the truth functions shown.

$$\begin{array}{|c|c|c|c|c|} \hline x_{1} & x_{2} & x_{3} & x_{4} & f\left(x_{1}, x_{2}, x_{3}, x_{4} )\right. \\ \hline 1 & 1 & 1 & 1 & 1 \\ \hline 1 & 1 & 1 & 0 & 1 \\ \hline 1 & 1 & 0 & 1 & 1 \\ \hline 1 & 1 & 0 & 0 & 1 \\ \hline 1 & 0 & 1 & 1 & 0 \\ \hline 1 & 0 & 1 & 0 & 1 \\ \hline 1 & 0 & 0 & 1 & 0 \\ \hline 1 & 0 & 0 & 0 & 1 \\ \hline 0 & 1 & 1 & 1 & 1 \\ \hline 0 & 1 & 1 & 0 & 1 \\ \hline 0 & 1 & 0 & 1 & 1 \\ \hline 0 & 1 & 0 & 0 & 1 \\ \hline 0 & 0 & 1 & 1 & 0 \\ \hline 0 & 0 & 1 & 0 & 0 \\ \hline 0 & 0 & 0 & 1 & 0 \\ \hline 0 & 0 & 0 & 0 & 0 \\ \hline \end{array}$$

Identify each underlined verb by writing above it AV for action verb or LV for linking verb.

Example 1. I $\overset{\textit{\color{#c34632}{LV}}}{{\underline{\text{feel}}}\text{}}$ sleepy.

The Hanson brothers $\underline{\text{are}}$ the best hockey players in the state.

What is the meaning of a $[-100, 100, 50]$ by $[-100, 100, 10]$ viewing rectangle? Create a figure like the one in Figure $7$ that illustrates this viewing rectangle.