Iris rolled a five-sided number cube numbered 1 through 5. Find the probability that a roll will result in each of the following. Write your answer using probability notation. P(odd). P(not odd). P(4). P(not 4).

$$\begin{array} { l } { \text { Determine all homomorphisms from } Z \text { onto } S _ { 3 } \text { . Determine all } } \\ { \text { homomorphisms from } Z \text { to } S _ { 3 } } \end{array}$$

Use the product rule to simplify the expression. Assume that variables represent nonnegative real numbers.

$$\sqrt { 125 x ^ { 2 } }$$

The most popular pizza at Pavone's Pizza is the 10-inch personal pizza with one topping. What is the area of a pizza with a diameter of 10 inches? Round your answer to the nearest hundredth.

Determine which of the following probability experiments represents a binomial experiment. If the probability experiment is not a binomial experiment, state why. A random sample of 15 college seniors is obtained, and the individuals selected are asked to state their ages.

Compute each. Assume the values of the variables are restricted so that the expressions are defined.

$$\frac { ( n - 1 ) ! } { ( n + 1 ) ! }$$

The solubility of

$$\mathrm { MnSO } _ { 4 } \cdot \mathrm { H } _ { 2 } \mathrm { O }$$

in water at

$$20 ^ { \circ } \mathrm { C }$$

is 70 g per 100 mL of water. Given a solution of

$$\mathrm { MnSO } _ { 4 } \cdot \mathrm { H } _ { 2 } \mathrm { O }$$

of unknown concentrati on, what experiment could you perform to determine whether the new solution is saturated, supersaturated, or unsaturated?

Solve. If an equation has no real solution, say so.

$$2 \sqrt [ 3 ] { x } = \sqrt [ 3 ] { x ^ { 2 } }$$

For each prove each statement that is true and find a counterexample for each statement that is false. Assume all sets are subsets of a universal set U. For all sets A, B, and C,

$$( A - B ) \cap ( C - B ) = A - ( B \cup C )$$

.

At room temperature and pressure Rbl crystallizes with the NaCl-type structure. Use this value to estimate the density.

Tell whether the quotient is positive or negative without dividing. 5. 12 ÷ 4

Solve. 3y + 4y + 6 = 20

What does Momaday's account of the Kiowa's migration offer you that a description in a history book might not? Explain, citing specific lines of the selection that support your answer.

Explain how to write terms of a sequence if the formula for the general term is given.