Use the following data:

$$\begin{matrix} x_i& \text{1} & \text{2} & \text{3} & \text{4} & \text{5}\\ y_i & \text{3} & \text{7} & \text{5} & \text{11} & \text{14}\\ \end{matrix}$$

Use the $t$ test to test the following hypotheses $( \alpha = .05 ) :$

$$H _ { 0 } : \beta _ { 1 } = 0$$

$$H _ { \mathrm { a } } : \beta _ { 1 } \neq 0$$

Identify each of the following word groups as a sentence or a sentence fragment.

If the Third Amendment pertains specifically to the quartering of soldiers in private homes.

At which of the following times was there $110$ mass extinction?

a. The end of the Cretaceous period

b. The end of the Devonian period

c. The end of the Permian period

d. The end of the Triassic period

e. The end of the Silurian period

What is the speed of light in diamond if the index of refraction is 2.42?

Find the prime factori zations of eighty four and one hundred and sixty two. What do they share in common?

What is the difference between an SI base unit and a derived unit? Give some examples of each type of unit.

In the discussion of the Lindemann mechanism, it was assumed that the rate of activation by collision with another reactant molecule A was the same as collision with a nonreactant molecule $\mathrm{M}$ such as a buffer gas. What if the rates of activation for these two processes are different? In this case, the mechanism becomes

$$\begin{aligned} & \mathrm{A}+\mathrm{M} \underset{k_{-1}}{\stackrel{k_1}{\rightleftharpoons}} \mathrm{A}^*+\mathrm{M} \\ & \mathrm{A}+\mathrm{A} \underset{k_2}{\underset{k_2}{\rightleftharpoons}} \mathrm{A}^*+\mathrm{A} \\ & \mathrm{A}^* \stackrel{\mathrm{k}_3}{\longrightarrow} \mathrm{P} \end{aligned}$$

a. Demonstrate that the rate law expression for this mechanism is

$$R=\frac{k_3\left(k_1[\mathrm{~A}][\mathrm{M}]+k_2[\mathrm{~A}]^2\right)}{k_{-1}[\mathrm{M}]+k_{-2}[\mathrm{~A}]+k_{-3}}$$

b. Does this rate law reduce to the expected form when $[\mathrm{M}]=0 ?$

Extend the reasoning of the previous problems to argue that a positive function is either analytic and nonzero at $\infty$ or has a simple pole or a simple zero there. What does this say about the degrees of its numerator and denominator polynomials?

Graphite and diamond are both made of the element carbon.

Compare the conditions needed to form graphite with the conditions needed to form diamond.

Why do you think graphite is more common?

Information from Mrs. Shah’s Cookies’ statement of owner’s equity for 2014 follows.

$$\begin{array}{lr} \text{Withdrawals} & \$\hspace{30pt} 0\\ \text{Net income} & ?\\ \text{Owner’s equity, January 31, 2014} & 159,490\\ \text{Owner’s equity, January 31, 2013} & 102,403\\ \end{array}$$

Prepare Mrs. Shah’s Cookies’ statement of owner’s equity. You will need to solve for the amount of net income. What is owner’s equity? Why might the owner decide not to make any withdrawals from the company?

Mark the following statement as true or false:

• To use a predefined function in a program, you need to know only the name of the function and how to use it.

Explain the major outcomes for society of the marketing process and consumers' responses to it.

What are some things that your family usually does on Saturdays around the same time? For each time given below, describe something that a family member may have just done.

11h00 du soir

You are writing a college-level textbook on finite mathematics, and are trying to come up with the best combination of word problems. Over the years, you have accumulated a collection of amusing problems, serious applications, long complicated problems, and “generic” problems. Before your book is published, it must be scrutinized by several reviewers who, it seems, are never satisfied with the mix you use. You estimate that there are three kinds of reviewers: the “no-nonsense” types who prefer applications and generic problems, the “dead serious” types, who feel that a college-level text should be contain little or no humor and lots of long complicated problems, and the “laid-back” types, who believe that learning best takes place in a light-hearted atmosphere bordering on anarchy. You have drawn up the following chart, where the payoffs represent the reactions of reviewers on a scale of -10 (ballistic) to +10 (ecstatic):

$$\begin{matrix} & \text{} & \text{} & \text{Reviewers}\\ & \text{} & \text{No-Nonsense} & \text{Dead Serious} & \text{Laid-Back} & \text{Laid-Back}\\ & \text{Amusing} & \text{-5} & \text{-10} & \text{10}\\ \text{You} & \text{Serious} & \text{5} & \text{3} & \text{0}\\ & \text{Long} & \text{-5} & \text{5} & \text{3}\\ & \text{Generic} & \text{5} & \text{3} & \text{-10}\\ \end{matrix}$$

a. Your first draft of the book contained no generic problems, and equal numbers of the other categories. If half the reviewers of your book were “dead serious” and the rest were equally divided between the “no-nonsense” and “laid-back” types, what score would you expect? b. In your second draft of the book, you tried to balance the content by including some generic problems and eliminating several amusing ones, and wound up with a mix of which one eighth were amusing, one quarter were serious, three eighths were long, and a quarter were generic. What kind of reviewer would be least impressed by this mix? c. What kind of reviewer would be most impressed by the mix in your second draft?