Events A and B are independent. Find the missing probability.

$$P ( \mathrm { A } ) = \frac { 2 } { 5 }$$

,

$$P ( \mathrm { B } ) = \frac { 1 } { 6 }$$

, P(A and B)=___

Find the volume of the solid that results when the region enclosed by y=x² and y=x³

Determine whether the following statement is true or false. If false, give a counterexample. If true, give an argument to support your conclusion. If the sum of two acute angles of a triangle is greater than 90, then the triangle is acute.

Use the Binomial Theorem to expand each binomial and express the result in simplified form.

$$( x - 3 y ) ^ { 5 }$$

Explain how organelles increase the efficiency of the cell:

The table displays the amounts the Jackson family spent on vacations during the years 1996-2006.

$$\begin{matrix} \text{Jackson Family Vacation Costs }\\ \text{Year} & \text{Cost} & \text{Year} & \text{Cost}\\ \text{1996} & \text{\$1000} & \text{2002} & \text{\$2750}\\ \text{1997} & \text{\$1750} & \text{2003} & \text{\$3200}\\ \text{1998} & \text{\$1750} & \text{2004} & \text{\$2900}\\ \text{1999} & \text{\$2000} & \text{2005} & \text{\$3100}\\ \text{2000} & \text{\$2200} & \text{2006} & \text{\$3300}\\ \text{2001} & \text{\$2700}\\ \end{matrix}$$

Make a scatter plot of the data.

What is a random variable? Give an example of a discrete random variable and a continuous random variable. Justify your answer.

The Environmental Protection Agency is examining the relationship between the ozone level (in parts per million) and the population (in millions) of U.S. cities. Part of the regression analysis is shown. Dependent variable is: Ozone R-squared = 84.4%, s = 5.454 with 16 - 2 = 14 df

$$\begin{array} { l l l } { \text { Variable } } & { \text { Coefficient } } & { \text { SE(coeff) } } \\ { \text { Intercept } } & { 18.892 } & { 2.395 } \\ { \text { Pop } } & { 6.650 } & { 1.910 } \end{array}$$

Find the sum.

$$\left[\begin{array}{rr}{3} & {2} \\ {-1} & {5}\end{array}\right]+\left[\begin{array}{rr}{8} & {-5} \\ {3} & {0}\end{array}\right]$$

Read the brief report of statistical research, and identify whether it was an observational study or an experiment. If it was an observational study, identify (if possible) 130 patients with eligible lacerations randomly assigned to have the wound closed either with Octylcyanoacrylate Tissue Adhesive (essentially superglue) or with traditional sutures. When evaluated at the end of the study, the two treatments worked equally well with regard to scarring, and the adhesive was less painful and worked faster.

Identify the period and tell where two asymptotes occur for each function. $y=\tan 4 \theta$

Solve the initial-value problem.

$$\frac { d y } { d t } = 1 + \frac { 2 } { t } , t \gt 0 , y = 5 \text { when } t = 1$$

-¿Son nuestros cepillos? (ours) -No, los cepillos no son __________.

Determine the LU factorization of the given matrix. Verify your answer by computing the product LU.

$$A = \left[ \begin{array} { r r r } { 3 } & { - 1 } & { 2 } \\ { 6 } & { - 1 } & { 1 } \\ { - 3 } & { 5 } & { 2 } \end{array} \right].$$