Motocar Co. produces and sells automobile parts. On the first day of its fiscal year, Motocar Co. issued $\$15,000,000$ of five-year, $15\%$ bonds at an effective interest rate of $13\%$, with interest payable semiannually. Compute the following, presenting figures used in your computations.

$\hspace{20pt}$ The amount of cash proceeds from the sale of the bonds. (Use the tables of present values. Round to the nearest dollar.)

Ware Co. produces and sells motorcycle parts. On the first day of its fiscal year, Ware Co. issued $35,000,000 of five-year, 12% bonds at a market (effective) interest rate of 10%, with interest payable semiannually. Compute the (b) amount of premium to be amortized for the first semiannual interest payment period, using the interest method. Round to the nearest dollar. Present figures used in your computations.

Benny the Barber owns a one-chair shop. At barber college, they told Benny that his customers would exhibit a Poisson arrival distribution and that he would provide an exponential service distribution. His market survey data indicate that customers arrive at a rate of two per hour. It will take Benny an average of 20 minutes to give a haircut. Based on these figures, find the following:. The average number of customers waiting.

Evans Co. produces and sells motorcycle parts. On the first day of its fiscal year, Evans Co. issued $50,000,000 of five-year, 14% bonds at a market (effective) interest rate of 12%, with interest payable semiannually. Compute the following, presenting figures used in your computations. b. The amount of premium to be amortized for the first semiannual interest payment period, using the interest method. Round to the nearest dollar.

(a) A strongly connected digraph is a digraph in which, given any pair of distinct vertices, there is a directed path (of some length) from each of these two vertices to the other. Determine whether the digraphs in the said figures and are strongly connected.

(b) Prove that a digraph with $n$ vertices having adjacency matrix $\mathbf{A}$ is strongly connected if and only if $\mathbf{A}+\mathbf{A}^2+\mathbf{A}^3+\cdots+\mathbf{A}^{n-1}$ has the property that all entries not on the main diagonal are nonzero.

The table below shows the historical minimum wage (in dollars per hour) for the State of New York.

$$\begin{matrix} \text{Year (x)} & \text{Wage (y)}\\ \text{1962} & \text{1.15}\\ \text{1968} & \text{1.60}\\ \text{1974} & \text{2.00}\\ \text{1978} & \text{2.65}\\ \text{1981} & \text{3.35}\\ \text{1990} & \text{3.80}\\ \text{1991} & \text{4.25}\\ \text{2000} & \text{5.15}\\ \text{2005} & \text{6.00}\\ \text{2012} & \text{7.25}\\ \end{matrix}$$

Construct a scatter plot of the data.

The program of earlier figures illustrated three recursive methods of traversing a binary tree—inorder, preorder and postorder traversals. This exercise presents the level-order traversal of a binary tree, in which the node values are printed level by level, starting at the root node level. The nodes on each level are printed from left to right. The level-order traversal is not a recursive algorithm. It uses a queue object to control the output of the nodes. The algorithm is as follows:

a) Insert the root node in the queue.

b) While there are nodes left in the queue, do the following:

Get the next node in the queue.

Print the node’s value.

If the reference to the left child of the node is not null:

Insert the left child node in the queue.

If the reference to the right child of the node is not null:

Insert the right child node in the queue.

Write method levelOrder to perform a level-order traversal of a binary tree object. Modify the program of earlier figures to use this method.

A memoir is a personal account of events from the author's past. It is usually written from the first-person point of view, using the pronoun $l$; this point of view allows the reader to see events as the author did. While an autobiography usually tells the story of a person's entire life, a memoir-like "Living Well. Living Good. ${ }^\pi$-typically focuses on a single incident or a particular period in a person's life. Unlike a historical account, which is objective and emphasizes facts, a memoir usually includes the author's personal observations and responses to people and events.

Could Angelou have converted this essay into an autobiography? Explain.

If necessary round all dollar figures to the nearest cent and round percents to the nearest hundredth of a percent. The city of Bradenton is offering simple interest loans to start-up businesses at a rate of 3.5%. Mr. Cannata obtains one of these loans of $6000 for 3 years to help pay for start-up costs of his restaurant, Ortygia. Determine the amount of money Mr. Cannata must repay the city after 3 years.

Home Building Inc. (HBI) seeks to schedule manual labor for 18 new homes being constructed. Historical data leads HBI to apply a 92% learning curve rate to the manual labor portions of the project. If the first home requires 3500 manual labor hours to build, estimate the time required to build (a) the filth house, (b) the tenth house, (c) all 18 houses. What would the manual labor estimate be for all 18 of the HBI houses in the problem above if the learning curve rate is (d) 70%, (e) 75%, (f) 80%

In the earlier exercise. we saw that in 2007 Harvard accepted about 9% of its applicants, Stanford 10%, and Penn 16%. Jorge has applied to all three. He figures that his chances of getting into at least one of the three must be about 35%.

a. How has he arrived at this conclusion?

b. What assumption is he making?

c. Do you agree with his conclusion?

Area Use the Trapezoidal Rule to estimate the number of square meters of land in a lot, where $x$ and $y$ are measured in meters, as shown in the figures. The land is bounded by a stream and two straight roads that meet at right angles.

In the given figures are shown ray diagrams for different types of contact lenses. Which of the following statements correctly describes the images formed by these contact lenses?

(a) A properly designed contact lens always forms a real image.

(b) A properly designed contact lens always forms a virtual image.

(c) A properly designed contact lens can form a real or virtual image, depending on the type of lens.

The precise definition of the left-hand limit, $\lim _{x \rightarrow a^{-}} f(x)=L$, may be stated as follows: For every number $\varepsilon>0$ there exists a number $\delta>0$ such that $|f(x)-L|<\varepsilon$ whenever $a-\delta<x<a$. Similarly, for the right-hand limit, $\lim _{x \rightarrow a^{+}} f(x)=L$ if for every number $\varepsilon>0$ there exists a number $\delta>0$ such that $|f(x)-L|<\varepsilon$ whenever $a<x<a+\delta$. Explain, with the aid of figures, why these definitions are appropriate.