Someone who has consumed a lot of alcohol: A. Is not capable of giving true consent B. Is never to blame for being sexually assaulted C. May need help getting out of a potentially dangerous situation D. All of the above

If Mozart’s life span was exactly 35 years, what is the number of molecules he exhaled in that period (given that an average person breathes 12 times per minute)? a) $2 \times 10^8$ b) $2 \times 10^{29}$ c) $1\times 10^{29}$ d) $3 \times 10^{30}$

Write the complex number in standard form. $-i -(\sqrt{-23})^{2}$

Find the real and imaginary parts of the complex number.

$$5-7 i$$

Write the complex number in standard form. $i^{2}+3 i$

The following transactions occurred during 2021 for the Beehive Honey Corporation:

Feb 1. Borrowed $12,000 from a bank and signed a note. Principal and interest at 10% will be paid on January 31, 2022. Apr. 1. Paid$3,600 to an insurance company for a two-year fire insurance policy. July 17. Purchased supplies costing $2,800 on account. The company records supplies purchased in an asset account. At the year-end on December 31, 2021, supplies costing$1,250 remained on hand. Nov. 1. A customer borrowed $6,000 and signed a note requiring the customer to pay principal and 8% interest on April 30, 2022.

1. Record each transaction in general journal form. Omit explanations.

2. Prepare any necessary adjusting entries at the year-end on December 31, 2021. No adjusting entries were recorded during the year for any item.

Simplify the complex number and write it in standard form.

$$1/i^3$$

The suggested retail price of a new car is p dollars. The dealership advertised a factory rebate of $2000 and a 9(a) Write a function R in terms of p giving the cost of the car after receiving the rebate from the factory. (b) Write a function S in terms of p giving the cost of the car after receiving the dealership discount. (c) Form the composite functions (R$\circ$S)(p) and (S$\circ$R)(p) and interpret each. (d) Find (R$\circ$S)(24,795) and (S$\circ$ R)(24,795). Which yields the lower cost for the car? Explain.

Write $32.5$ billion in scientific notation.

Solve the problem.

The percentages of the U.S. Recommended Daily Allowances for phosphorus, magnesium, and calcium for a $1$-oz serving of Kix are $4$, $2$, and $4$, respectively. The percentages of the U.S. Recommended Daily Allowances for phosphorus, magnesium, and calcium in $1 / 2$ cup of milk are $11$,$4$ , and $16$ , respectively. Write a $1 \times 3$ matrix $K$ giving the percentages for $1 \mathrm{oz}$ of Kix and a $1 \times 3$ matrix $M$ giving the percentages for $1 / 2$ cup of milk. Find the matrix $K+2 M$; indicate what its entries represent.

At a gymnastics meet, three judges evaluate the balance beam performances of five gymnasts. The judges use a scale of $1$ to $10$ , where $10$ is a perfect score.

$$\begin{array}{|c|c|c|c|c|} \hline 1 & 8.0 & 8.5 & 8.2 & \bar{\chi}_{\text {Gymnast } 1}=8.2 \\ \hline 2 & 9.5 & 9.2 & 9.7 & \bar{\chi}_{\text {Gymnas } 2}=9.5 \\ \hline 3 & 7.3 & 7.5 & 7.7 & \bar{\chi}_{\text {Gymnast } 3}=7.5 \\ \hline 4 & 8.3 & 8.7 & 8.5 & \bar{\chi}_{\text {Gymnas }_4=8.5} \\ \hline 5 & 8.8 & 9.2 & 9.0 & \bar{\chi}_{\text {Gymnas } 5}=9.0 \\ \hline \text { Means } & \bar{\chi}_{\text {Judge } 1}=8.4 & \bar{\chi}_{\text {Judge } 2}=8.6 & \bar{\chi}_{\text {Judge } 3}=8.6 & \\ \hline \end{array}$$

A statistician wants to examine the objectivity and consistency of the judges. She performs a two-way ANOVA analysis without interaction using $\alpha=0.01$ and obtains the following results:

$$\begin{array}{|l|c|c|c|c|c|c|} \hline \begin{array}{l} \text { Source of } \\ \text { Variation } \end{array} & \text { SS } & \text { of } & \text { MS } & F & p \text {-value } & \text { Fcrit } \\ \hline \text { Rows } & 6.742 & 4 & 1.686 & 44.75 & 1.62 \mathrm{E}-05 & 7.006 \\ \hline \text { Columns } & 0.192 & 2 & 0.096 & 2.55 & 0.1392 & 8.649 \\ \hline \text { Error } & 0.301 & 8 & 0.038 & & & \\ \hline & & & & & & \\ \hline \text { Total } & 7.235 & 14 & & & & \\ \hline \end{array}$$

b. At the $1 \%$ significance level, can you conclude that average scores differ by gymnast?

How many 2.25-pound containers can you make with 24.75 pounds of almonds?

In a study of the vacancies occurring in the U.S. Supreme Court, it has been determined that the time elapsed between successive resignations is an exponential random variable with expected value 2 years.

Suppose that the average life span of an electronic component is 72 months and that the life spans are exponentially distributed.

(a) Find the probability that a component lasts for more than 24 months.

(b) The reliability function r(t) gives the probability that a component will last for more than t months. Compute r(t) in this case.

Last season, a baseball player scored 14 runs in 18 games. This season, the baseball player scored 12 runs in 15 games. Find the number of runs scored per game in each season. Round your answers to the nearest hundredth. Then identify the season in which the player scored more runs per game.