Solve each equation or inequality. $2 ^ { x - 1 } = 5$

(a) How do copyright laws protect property rights? (b) Some consumers download music or videos from Internet sites not authorized by the copy right holder. Do those actions violate copyright laws? (c) Do you think people who do this should be punishable under the law? Why or why not?

If $f(x)=x^{3}$, find in simplest form: f(x + 1)

What happens to the total resistance of a parallel circuit as more branches are added? Why?

Compressed air can be pumped underground into huge caverns as a form of energy storage. The volume of a cavern is

$$5.6 \times 10 ^ { 5 } \mathrm { m } ^ { 3 }$$

and the pressure of the air in it is

$$7.7 \times 10 ^ { 6 } \mathrm { Pa }.$$

Assume that air is a diatomic ideal gas whose internal energy U is given by

$$U = \frac { 5 } { 2 } n R T$$

If one home uses

$$30.0 \mathrm { kW } \cdot \mathrm { h }$$

of energy per day, how many homes could this internal energy serve for one day?

Let p be a prime integer. (a) Prove Fermat's Theorem: For every integer a, a^p = a modulo p. (b) Prove Wilson's Theorem: (p-1)! = -1 (modulo p).

Use a number line to find the product. -2 (-3.4).

Solve each equation.

$$\left( x ^ { 2 } - 1 \right) ^ { 2 } - 11 \left( x ^ { 2 } - 1 \right) + 24 = 0$$

A large discount store has built its reputation on offering consumers low prices. However, its customers come from many different income levels. Recently, the store began offering higher priced jewelry and consumer electronic products. What signal might this send to producers of other premium products who have never sold in discount store before?

Use the given annual interest rate r and the compounding period to find i, the interest rate per compounding period. 3.84% compounded monthly.

Predict wh ich will experience more weathering, a rock in the Sonoran Desert in southern Arizona or the same rock on a beach in North Carolina.

Plot the given points, and find the distance between them. P(0, 2, 4), Q(1, 3, 0)

A partially inflated weather balloon has a volume of $1.56 \times 10 ^ { 3 }$ L and a pressure of 98.9 kPa. What is the volume of the balloon when the balloon is released to a height where the pressure is 44.1 kPa?

Perform the indicated operations and simplify the result. Leave your answer in factored form. $\frac{4+\frac{1}{x^{2}}}{3-\frac{1}{x^{2}}}$