What can you say about the determinant of an $n \times n$ matrix with the following form?

$$\left[\begin{array}{ccccc}{0} & {0} & {\cdots} & {0} & {1} \\ {0} & {0} & {\cdots} & {1} & {0} \\ {\vdots} & {\vdots} & {} & {\vdots} & {\vdots} \\ {0} & {1} & {\cdots} & {0} & {0} \\ {1} & {0} & {\cdots} & {0} & {0}\end{array}\right]$$

A manufacturer produces custom steel products from recycled steel in which each ton of the product must contain 4 pounds of chromium, 8 pounds of tungsten, and 7 pounds of carbon. The manufacturer has three sources of recycled steel: Source l: Each ton contains 2 pounds of chromium, 8 pounds of tungsten, and 6 pounds of carbon. Source 2: Each ton contains 3 pounds of chromium, 9 pounds of tungsten, and 6 pounds of carbon. Source 3: Each ton contains 12 pounds of chromium, 6 pounds of tungsten, and 12 pounds of carbon. Let x, y, and z denote the percentages of the first, second, and third recycled steel sources that will be melted down for one ton of the product. Find (but do not solve) a linear system in x, y, and z whose solution tells the percentage of each source that must be used to meet the requirements for the finished product.

When would it be beneficial to use exclusive distribution rather than intensive distribution?

For each x in [0, 1], let $f(x) = x$ if x is rational, and let $f(x) = 1- x$ if x is irrational. Prove that: (a) $f(f(x))=x$ for all x in [0, 1]. (b) $f(x)+f(1-x)=1$ for all x in [0, 1]. (c) f is continuous only at the point $x=\frac{1}{2}$. (d) f assumes every value between 0 and 1. (e) $f(x+y)-f(x)-f(y)$ is rational for all x and y in [0, 1].

find the area of the region bounded by the line y+3=x,x=1,x=5.

$$800 \div 16$$

Prove Theorem 5-6: All right angles are congruent. Given: Angle 1 and angle 2 are right angles. Prove: $\angle 1 \cong \angle 2$

Suppose you plan to save $12 per week. You have already saved$7.50. In how many weeks will you have saved at least $100?

Find the inverse of the matrices.

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

Match (by letter) the following items with the description or example that best fits. Each letter is used only once.

$$\begin{matrix} \text{Terms}\\ \hline \text{\_\_\_\_\_ 1. Vertical analysis.}\\ \text{\_\_\_\_\_ 2. Horizontal analysis.}\\ \text{\_\_\_\_\_ 3. Liquidity.}\\ \text{\_\_\_\_\_ 4. Solvency.}\\ \text{\_\_\_\_\_ 5. Discontinued operations.}\\ \text{\_\_\_\_\_ 6. Quality of earnings.}\\ \text{\_\_\_\_\_ 7. Conservative accounting practices.}\\ \text{\_\_\_\_\_ 8. Aggressive accounting practices.}\\ \end{matrix}$$

$$\begin{matrix} \text{Descriptions}\\ \hline \text{a. A company's ability to pay its current liabilities.}\\ \text{b. Accounting choices that result in reporting lower income, lower assets, and higher liabilities.}\\ \text{c. Accounting choices that result in reporting higher income, higher assets, and lower liabilities.}\\ \text{d. The ability of reported earnings to reflect the company's true earnings as well as the}\\ \text{usefulness of reported earnings to help investors predict future earnings.}\\ \text{e. A tool to analyze trends in financial statement data for a single company over time.}\\ \text{f. The sale or disposal of a significant component of a company's operations.}\\ \text{g. A means to express each item in a financial statement as a percentage of a base amount.}\\ \text{h. A company's ability to pay its long-term liabilities.}\\ \end{matrix}$$

What is the significance of the change in Gibbs free energy $(\Delta G)$ for a reaction?

Why did the Phoenicians develop a writing system?

Graph each line.

$$y - 3 = \frac { 1 } { 3 } ( x - 3 )$$

Show that a moving electron cannot spontaneously change into an x-ray photon in free space. A third body (atom or nucleus) must be present. Why is it needed? (Hint:Examine the conservation of energy and momentum.)