Express the answer to the following combination problem using combination notation $\left({ }_n C_k\right)$ and numerically. See the earlier examples.

Many lottery games are set up so that players select a subset of numbers from a larger set, and the winner is the person whose selection matches that chosen by some random mechanism. The order of the numbers is irrelevant. How many choices of six numbers can be made from the numbers 1 through 49?

Life on the Mississippi first appeared serially in the Atlantic Monthly magazine in 1875 . In 1874 , Twain wrote the magazines editor that he liked writing for the audience of the Atlantic "for the simple reason that it don't require a 'humorist' to paint himself striped and stand on his head every fifteen minutes." In other words, he liked an audience that appreciated subtle humor. Do you find this sensibility reflected in the selection you have just read? Explain.

A researcher receives 100 containers of oxygen. Of those containers, 20 have oxygen that is not ionized, and the rest are ionized. Two samples are randomly selected, without replacement, from the lot. a. What is the probability that the first one selected is not ionized? b. What is the probability that the second one selected is not ionized given that the first one was ionized? c. What is the probability that both are ionized? d. How does the answer in part (b) change if samples selected were replaced prior to the next selection?

Which of the following passages contributes most to the mood of this selection?

A "My great-grandfather on my mother's side ran a drugstore in a small town in central Illinois."

B "Some people drove all the way in from Decatur just to taste it."

C "As far as the family knew, the person who bought the recipe never used it."

D "The spin of my mother on the high stool with her whole life in front of her, something fine and fragrant still to happen."

(a) Using a chart like the one shown, analyze the author's perspective in the selection.

$$\begin{aligned} &\text { Author's Perspective }\\ &\begin{array}{|l|l} \hline \text { Types of Details Included } & \text { Examples of Each } \\ \hline \square \text { researched facts } & \\ \square \text { personal experiences } & \\ \square \text { opinions } & \\ \square \text { attitudes } & \\ \hline \end{array} \end{aligned}$$

(b) Referring to your chart, briefly describe Cox's perspective.

Which of the following represents an idea that Darwin learned from the writings of Thomas Malthus?

A. Earth has changed over the years through a series of massive geological events.

B. Earth is more than 10,000 years old.

C. Technological innovation in agricultural practices will permit exponential growth of the human population into the foreseeable future.

D. Populations tend to increase at a faster rate than their food supply allows.

E. The environment is responsible for natural selection.

Which of the following correctly states the order of events in humoral immunity? Let
1 = antigen display,
2 = antibody secretion,
3 = secretion of interleukin,
4 = clonal selection, and
5 = endocytosis of an antigen.
a. 3–4–1–5–2
b. 5–3–1–2–4
c. 3–5–1–4–2
d. 5–3–1–4–2
e. 5–1–3–4–2

New Zealand lamb breeders measure the following variance values for their herd.

a. Calculate the broad sense heritability (H$^{2}$) and the narrow sense heritability (h$^{2}$) for each trait in this lamb herd.

b. How would you characterize the potential response to selection ( R) for each trait?

Census data for a certain county show that 19% of the adult residents are Hispanic. Suppose 72 people are called for jury duty and only 9 of them are Hispanic. Does this apparent under representation of Hispanics call into question the fairness of the jury selection system? a) Write the null hypothesis. b) Write the alternative hypothesis. c) Check the assumptions and conditions for inference. d) Find the z-score for this sample proportion. e) Give the P-value for this test. f) State your conclusion (in context, of course).

In his research into the components of ethical decision making, Rest raised the following issue: Assuming someone possesses sound moral reasoning skills, “Why would they ever chose the moral alternative, especially if it involves sacrificing some personal value or suffering some hardship? What motivates the selection of moral values over other values?” How does Rest’s model deal with such a question? How would you answer it from the point of view of an accounting professional?

The Briggs and Stratton Commercial Division designs and manufactures small engines for golf turf maintenance equipment. A robotics-based testing system with support equipment will ensure that their new signature guarantee program entitled “Always Insta-Start” does indeed work for every engine produced. (a) Compare the annual worth values of the two systems at MARR = 10% per year. Select the better system. (b) Determine the salvage value for the Push System that will make the company indifferent between the two systems.

$$\begin{array}{lrr} & \text { Pull System } & \text { Push System } \\ \hline \text { Equipment first cost, } \$ & -1,500,000 & -2,250,000 \\ \text { AOC, } \$ \text { per year } & -700,000 & -600,000 \\ \text { Salvage value, } \$ & 100,000 & 50,000 \\ \text { Estimated life, years } & 8 & 8 \\ \hline \end{array}$$

(a) Using a chart like the one shown, analyze the author's perspective in the selection.

$$\begin{aligned} &\text { Author's Perspective }\\ &\begin{array}{l|l} \hline \text { Types of Details Included } & \text { Examples of Each } \\ \hline \square \text { researched facts } & \\ \square \text { personal experiences } & \\ \square \text { opinions } & \\ \square \text { attitudes } & \\ \hline \end{array} \end{aligned}$$

(b) Use your chart to briefly describe Angelou's point of view.

Which of the following is an incorrect match?

$$\textbf{\ \ a.}\text{ Lyell-suggested physical changes to Earth result from geologic processes occurring over long periods of time.}$$

$$\textbf{\ \ b.}\text{ Lamarck-proposed that organisms adapt to their environment.}$$

$$\textbf{\ \ c.}\text{ Darwin-developed the theory of natural selection as a mechanism of change in species}$$

$$\textbf{\ \ d.}\text{ Malthus-thought that characteristics acquired during an organism's lifetime can be passed on to the next generation.}$$

A regional infrastructure building and maintenance contractor is trying to decide whether to buy a new compact horizontal directional drilling (HDD) machine now or wait to buy it 2 years from now (when a large pipeline contract will require the new equipment). The HDD machine will include an innovative pipe loader design and maneuverable undercarriage system. The cost of the system is $68,000 if purchased now or$81,000 if purchased 2 years from now. At a real MARR of 10% per year and an inflation rate of 5% per year, determine if the company should buy now or later (a) without any adjustment for inflation and (b) with inflation considered.