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.

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:

a. The average number of customers waiting.

b. The average time a customer waits.

c. The average time a customer is in the shop.

d. The average utilization of Benny's time.

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.

A maser is a laser-type device that produces electromagnetic waves with frequencies in the microwave and radio-wave bands of the electromagnetic spectrum. You can use the radio waves generated by a hydrogen maser as a standard of frequency. The frequency of these waves is 1,420,405,751.786 hertz. (A hertz is another name for one cycle per second.) A clock controlled by a hydrogen maser is off by only 1 s in 100,000 years. For the following questions, use only three significant figures. (The large number of significant figures given for the frequency simply illustrates the remarkable accuracy to which it has been measured.) (a) What is the time for one cycle of the radio wave? (b) How many cycles occur in 1 h? (c) How many cycles would have occurred during the age of the earth, which is estimated to be $4.6 \times 10^{9}$ years? (d) By how many seconds would a hydrogen maser clock be off after a time interval equal to the age of the earth?

Use the Table for the exercise.

$$\begin{matrix} \text{ } & \text{Regional Historical Museum} & \text{ } & \text{ } & \text{ } & \text{ } & \text{ }\\ \text{Year} & \text{0} & \text{2} & \text{4} & \text{6} & \text{8} & \text{10}\\ \text{Visitors} & \text{980} & \text{1251} & \text{1667} & \text{1785} & \text{2110} & \text{2056}\\ \text{Gift Shop Sales(\$)} & \text{8890} & \text{12365} & \text{15100} & \text{18060} & \text{20650} & \text{22600}\\ \end{matrix}$$

For the relationship between the year and the number of visitors. Interpret the meaning of the slope and the y-intercept.

Refer to plane figures.

Consider the following problem: Given a point $A$ and a line $k$, what is the locus of points 3 cm from $A$ and 1 cm from $k$ ? a. The locus of points 3 cm from $A$ is b. The locus of points 1 cm from $k$ is ? c. Draw diagrams to show five possibilities with regard to points that satisfy both conditions (a) and (b). d. Give a one-sentence solution to the problem.

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.

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.

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?

(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 gives the population of India, in millions, for the second half of the 20th century.

$$\begin{array}{|c|c|} \hline\text{Year} & \text{Population}\\ \hline1951 & 361\\ 1961 & 439\\ 1971 & 548\\ 1981 & 683\\ 1991 & 846\\ 2001 & 1029\\ \hline \end{array}$$

Use the exponential model and the census figures for 1951 and 1961 to predict the population in 2001. Compare with the actual figure.

Lewis Co. produces and sells aviation equipment. On the first day of its fiscal year, Lewis Co. issued $60,000,000 of five-year, 10% bonds at a market (effective) interest rate of 13%, with interest payable semiannually. Compute the following, presenting figures used in your computations. c. The amount of discount to be amortized for the second semiannual interest payment period, using the interest method. Round to the nearest dollar.

Using the points shown below to draw the following figures:

$$\begin{array}{l} \hspace{.2cm}E\bullet\hspace{1cm}\bullet\text{U}\\ D\bullet\hspace{1.4cm}\bullet\text{C}\\ \hspace{.35cm}I\bullet\hspace{1cm}\bullet\text{L} \end{array}$$

(a) $\stackrel{\longleftrightarrow}{EL}$
(b) $\stackrel{\longrightarrow}{LC}$
(c) $\overline{LD}$
(d)$\overline{DL}$

A giant thunderstorm is moving toward a weather station at $45.0\ \mathrm{~mi} / \mathrm{~h}(20.1 \mathrm{~m} / \mathrm{~s})$. If the station sends a radar beam of frequency $200.0\ \mathrm{~MHz}$ toward the storm, what is the difference in frequency between the emitted beam and the beam reflected back from the storm? Be careful to carry plenty of significant figures! (Hint: The storm reflects the same frequency that it receives.)