Table of yearly discharge (cubic kilometers of water) of the Mississippi river gives the volume of water discharged by the Mississippi River into th Gulf of Mexico for each year from 1954 to 2001. The units are cubic kilometers of water-the Mississippi is a big river.

(a) Make a graph of the distribution of water volume. Describe the overall shape of the distribution and any outliers.

(b) Based on the shape of the distribution, do you expect the mean to be close to the median, clearly less than the median, or clearly greater than the median? Why? Find the mean and the median to check your answer.

$$\begin{array}{cc|cc|cc} \text { YEAR } & \text { DISCHARGE } & \text { YEAR } & \text { DISCHARGE } & \text { YEAR } & \text { DISCHARGE } \\ \hline 1954 & 290 & 1970 & 540 & 1986 & 600 \\ \hline 1955 & 420 & 1971 & 480 & 1987 & 450 \\ \hline 1956 & 390 & 1972 & 600 & 1988 & 420 \\ \hline 1957 & 610 & 1973 & 880 & 1989 & 630 \\ \hline 1958 & 550 & 1974 & 710 & 1990 & 680 \\ \hline 1959 & 440 & 1975 & 670 & 1991 & 700 \\ \hline 1960 & 470 & 1976 & 420 & 1992 & 510 \\ \hline 1961 & 600 & 1977 & 430 & 1993 & 900 \\ \hline 1962 & 550 & 1978 & 560 & 1994 & 640 \\ \hline 1963 & 360 & 1979 & 800 & 1995 & 590 \\ \hline 1964 & 390 & 1980 & 500 & 1996 & 670 \\ \hline 1965 & 500 & 1981 & 420 & 1997 & 680 \\ \hline 1966 & 410 & 1982 & 640 & 1998 & 690 \\ \hline 1967 & 460 & 1983 & 770 & 1999 & 580 \\ \hline 1968 & 510 & 1984 & 710 & 2000 & 390 \\ \hline 1969 & 560 & 1985 & 680 & 2001 & 580 \\ \hline \end{array}$$

(c) Based on the shape of the distribution, does it seem reasonable to use $\bar{x}$ and s to describe the center and variability of this distribution? Why? Find $\bar{x}$ and s if you think they are a good choice. Otherwise, find the five-number summary.

A particle with charge $6.40 \times 10^{-19} \mathrm{C}$ travels in a circular orbit with radius $4.68 \mathrm{~mm}$ due to the force exerted on it by a magnetic field with magnitude $1.65 \mathrm{~T}$ and perpendicular to the orbit. $(a)$ What is the magnitude of the linear momentum $\vec{p}$ of the particle? $(b)$ What is the magnitude of the angular momentum $\vec{L}$ of the particle?

Polo Ralph Lauren Corporation designs, markets, and distributes a variety of apparel, home decor, accessory, and fragrance products. The company's products include such brands as Polo by Ralph Lauren, Ralph Lauren Purple Label, Ralph Lauren, Polo Jeans Co., and Chaps. Polo Ralph Lauren reported the following (in thousands) for two recent years:

$$\begin{array}{lrr} & \textbf{For the Period Ending} \\ & \textbf{ Year 2 } & \textbf{Year 1} \\ \hline \text{Sales} & \$ 6,859,500 & \$ 5,660,300 \\ \text{Accounts receivable} & 690,000 & 592,700 \end{array}$$

Assume that accounts receivable (in millions) were $\$ 486,200$ at the beginning of Year 1.

c. What conclusions can be drawn from these analyses regarding Ralph Lauren's efficiency in collecting receivables?

Consider the space X obtained from a seven-sided polygonal region by means of the labelling scheme $\text {abaaab}^{-1} a^{-1}$. Show that the fundamental group of X is the free product of two cyclic groups.

H.J. Heinz Company was founded in 1869 at Sharpsburg, Pennsylvania, by Henry J. Heinz. The company manufactures and markets food products throughout the world, including ketchup, condiments and sauces, frozen food, pet food, soups, and tuna. For two recent years, H.J. Heinz reported the following (in thousands):

$$\begin{array}{lcr} &\textbf{Year 2}&\textbf{Year 1}\\ \hline \text{Net sales}&\$10,706,588&\$10,494,983\\ \text{Accounts receivable}&1,265,032&1,045,338 \end{array}$$

Assume that accounts receivable (in millions) were $576,700 at the beginning of Year 1. Assume that the accounts receivable (in thousands) were$1,171,797 at the beginning of Year 1. a. Compute the accounts receivable turnover for Year 2 and Year 1. Round to one decimal place.

Helen earns $\$ 7.50$ an hour at her job, but if she works more than $35$ hours in a week, she is paid $1 \frac{1}{2}$ times her regular salary for the overtime hours worked. One week her gross pay was $\$ 352.50$. How many overtime hours did she work that week?

An x-ray photon of initial frequency $3.0 \times 10 ^ { 19 }$ Hz collides with a free electron at rest; the scattered photon moves off at $90 ^ { \circ }$. What is the frequency of the scattered photon?

T. G. Exter’s book Regional Markets, Vol. 2/Households (Ithaca, NY: New Strategist Publications, Inc.) provides information on U.S. households by region of the country. This problem gives data current at the time of the book’s publication. One table in the book cross-classifies households by race (of the householder) and region of residence. The table shows that 7.8% of all U.S. households are Hispanic. a. If race and region of residence are not associated, what percentage of Midwest households would be Hispanic? b. There are 24.7 million Midwest households. If race and region of residence are not associated, how many Midwest households would be Hispanic? c. In fact, there are 645 thousand Midwest Hispanic households. Given this information and your answer to part (b), what can you conclude?

Given the following voltage transfer function:

$$H(s) = (Vo/Vi) = ((25 × 10^6)/(s² + 1000s + 25 × 10^6)).$$

a) At what frequencies (in radians per second) is the magnitude of the transfer function equal to unity? b) At what frequency is the magnitude of the transfer function maximum? c) What is the maximum value of the transfer function magnitude?

A straight wire segment of length 25 cm carries a current of 33.0 A and is immersed in a uniform external magnetic field. The magnetic force on the wire segment has magnitude 4.12 N. (a) What is the minimum possible magnitude of the magnetic field? (b) Explain why me given information enables you to calculate only the minimum possible field magnitude.

A force $\overrightarrow{\mathrm{F}}_1$ of magnitude $6.00$ units acts on an object at the origin in a direction $30.0^{\circ}$ above the positive $x$ axis. A second force $\overrightarrow{\mathbf{F}}_2$ of magnitude 5.00 units acts on the object in the direction of the positive y-axis. Graphically find the magnitude and direction of the resultant force $\overrightarrow{\mathrm{F}}_1+\overrightarrow{\mathrm{F}}_2$.

The force $\mathbf{F}=30 \mathbf{i}+20 \mathbf{j}-10 \mathbf{k}\ (\mathrm{N})$ (a) Determine the magnitude of the moment of $\mathbf{F}$ about $A$. (b) Suppose that you can change the direction of $\mathbf{F}$ while keeping its magnitude constant, and you want to choose a direction that maximizes the moment of $\mathbf{F}$ about $A$. What is the magnitude of the resulting maximum moment?

In the given Fig., particle $P$ is in uniform circular motion, centered on the origin of an $x y$ coordinate system. (a) At what values of $\theta$ is the vertical component $r_{y}$ of the position vector greatest in magnitude? (b) At what values of $\theta$ is the vertical component $v_{y}$ of the particle's velocity greatest in magnitude? (c) At what values of $\theta$ is the vertical component $a_{y}$ of the particle's acceleration greatest in magnitude?

Waldum Company purchased packaging equipment on January 5, 2012, for $135,000. The equipment was expected to have a useful life of three years, or 18,000 operating hours, and a residual value of$13,500. The equipment was used for 8,600 hours during 2012, 5,300 hours in 2013, and 4,100 hours in 2014.

Instructions

1. Determine the amount of depreciation expense for the years ended December 31, 2012, 2013, and 2014, by (a) the straight-line method, (b) the units-of-output method, and (c) the double-declining-balance method. Also determine the total depreciation expense for the three years by each method. The following columnar headings are suggested for recording the depreciation expense amounts:

$$\begin{array}{lcccc} \hspace{40pt}&\underline{\hspace{65pt}{\textbf{Depreciation Expense}\hspace{65pt}}}\\ \end{array}$$

$$\begin{array}{lcccc} {\textbf{}}&\textbf{Straight-}\hspace{15pt}&\textbf{Units-of-}\hspace{15pt}&\textbf{Double-Declining}\\ {\textbf{}}&\textbf{Line}\hspace{15pt}&\textbf{Output}\hspace{15pt}&\textbf{Balance}\\ {\textbf{Year}}\hspace{15pt}&\textbf{Method}\hspace{15pt}&\textbf{Method}\hspace{15pt}&\textbf{Method}\\\hline \end{array}$$

2. What method yields the highest depreciation expense for 2012?
3. What method yields the most depreciation over the three-year life of the equipment?