Show the hash table of size 11 after inserting entries with keys 34, 29, 53, 44, 120, 39, 45, and 40, using quadratic probing.

Let $A^{+}$denote the pseudoinverse of a matrix $A$. Prove that $A^{+} A$ is symmetric.

Prove that if $A$ is an $m \times n$ matrix, then $A^T A$ and $A A^T$ are symmetric.

Solve. Round answer to the nearest cent.

$$\$30.39 - \$17.91$$

Solve. Round answer to the nearest hundredth.

$$\$795 -\$412$$

The density property of rational numbers states that no matter how close two rational numbers are, there is a rational number between them.

Find a real number between $\sqrt{10}$ and $\sqrt{11}$.

Write an equation in point-slope form for the line.

Through $(3,-6)$ and parallel to $y=5 / 4(x+10)$

Solve. Round answer to the nearest cent.

$$\$19- \$9.88$$

Show that if A is an $m \times n$ matrix, then $\mathbf{A} \mathbf{A}^{T}$ is symmetric.

Suppose S is spanned by the vectors (1, 2, 2, 3) and (1, 3, 3, 2). Find two vectors that span

$$S^⊥.$$

This is the same as solving Ax = 0 for which A?

Say whether the reaction will shift to the reactants or to the products to re-establish equilibrium.\

Increase the volume of the following reaction: $\mathrm{H}_2(\mathrm{~g})+\mathrm{I}_2(\mathrm{~g}) \leftrightarrow 2 \mathrm{HI}(\mathrm{g})$

Round answer to the nearest cent.

$$\$1,650,000 \div 360$$

Choose the verb in parentheses that correctly completes each of the sentences on the following page.

EXAMPLE:(Has, Have) you or your sister ever been in a play? Have

(There's, There are) still openings for the stage crew.

Explain why an even function is symmetric with respect to the $y$-axis.