91Ó°ÊÓ

A letter of the alphabet is selected at random; one of the remaining letters is selected at random.

Find any points of discontinuity for each rational function. $$ y=\frac{x^{2}+4 x+3}{2 x^{2}+5 x-7} $$

Draw a graph of each function. Describe properties of the graph. \(y=\frac{8}{x}\)

Multiply. State any restrictions on the variables. $$ \frac{4 x^{2}}{5 y} \cdot \frac{7 y}{12 x^{4}} $$

Solve each equation. Check each solution. $$ \frac{2}{3 x-5}=\frac{4}{x-15} $$

Two standard number cubes are tossed. State whether the events are mutually exclusive. Explain your reasoning. The sum is a prime number; the sum is less than 4

The weight \(P\) in pounds that a beam can safely carry is inversely proportional to the distance \(D\) in feet between the supports of the beam. For a certain type of wooden beam, \(P=\frac{9200}{D} .\) Use a graphing calculator and the Intersect feature to find the distance between supports that is needed to carry each given weight. 1200 \(\mathrm{lb}\)

Solve each equation. Check each solution. $$ \frac{5 x}{4}-\frac{3}{x}=\frac{1}{4} $$

A standard number cube is tossed. Find each probability. \(P(3 \text { or odd })\)

A standard number cube is tossed. Find each probability. \(P(4 \text { or even })\)