Express each probability as a fraction reduced to lowest terms. you are dealt one card from a standard 52-card deck. Find the probability of being dealt a club.

The correlation between the number of visitors to the state of Florida and the number of shark attacks since 1990 is 0.946. Should the number of visitors to Florida be reduced in an attempt to reduce shark attacks? Explain your reasoning.

To determine premium, life insurance companies must compute the probable date of death. On the basis of a great deal of research, Mr. Duncan, age 36, is expected to live another 43.21 years. Does this determination mean that Mr. Duncan will live until he is 79.21 years old? If not, what does it mean?

Solve each equation. Check your solution.

$$z - 19 = 34$$

Both the forward reaction and the reverse reaction in the following equilibrium are believed to be elementary steps:

$$\mathrm { CO } ( g ) + \mathrm { Cl } _ { 2 } ( g ) \rightleftharpoons \operatorname { COCl } ( g ) + \mathrm { Cl } ( g )$$

At

$$25 ^ { \circ } \mathrm { C }$$

the rate constants for the forward and reverse reactions are

$$1.4 \times 10 ^ { - 28 } M ^ { - 1 } \mathrm { s } ^ { - 1 }$$

and

$$9.3 \times 10 ^ { 10 } \mathrm { M } ^ { - 1 } \mathrm { s } ^ { - 1 }$$

respectively. What is the value for the equilibrium constant at

$$25 ^ { \circ } \mathrm { C } ?$$

draw a scatter diagram

$$\begin{array}{ccccccc}{X} & {0} & {1.2} & {1.8} & {2.3} & {3.5} & {4.1} \\ \hline Y & {2} & {6.4} & {7} & {7.3} & {4.5} & {2.4} \\ \hline\end{array}$$

Find the value of k that would make the left side of each equation a perfect square trinomial. $25 x^{2}-k x+1=0$

Evaluate each determinant.

$$\left| \begin{array} { c c } { - 5 } & { - 1 } \\ { - 2 } & { - 7 } \end{array} \right|$$

Use the Intermediate Value Theorem and Rolle’s Theorem to prove that the equation has exactly one real solution. 2x² + 7x - 1 = 0

Use Pascal’s Triangle to find the binomial coefficient. $_7C_2$

Find the first five terms of each sequence described.

$$a _ { 1 } = 6 , a _ { n + 1 } = 3 a _ { n } - n$$

Suppose A is an orthogonal matrix. Then show that $\mathbf{A}^{-1}$ is orthogonal.

Use the standard normal distribution or the t-distribution to construct a 95% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results. If convenient, use technology to construct the confidence interval. In a random sample of 19 patients at a hospital's minor emergency department, the mean waiting time before seeing a medical professional was 23 minutes and the standard deviation was 11 minutes. Assume the waiting times are not normally distributed.

Work cooperatively. Use a graphing calculator to solve each system of inequalities.

$$\begin{array}{l}{y \geq 2 x+1} \\ {y \leq-x-1}\end{array}$$