Consider a uniform flow in the positive x direction combined with a free vortex located at the origin of the coordinate system. The streamline $\psi=0$ passes through the point x = 4, y = 0. Determine the equation of this streamline.

Identify the four types of tissue membranes found in the body.

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.

Mark Washington, CFA, is an analyst with BIC. One year ago, BIC analysts predicted that the U.S. equity market would most likely experience a slight downturn and suggested delta-hedging the BIC portfolio. As predicted, the U.S. equity markets did indeed experience a downturn of approximately 4% over a 12-month period. However, portfolio performance for BIC was disappointing, lagging its peer group by nearly 10%. Washington has been told to review the options strategy to determine why the hedged portfolio did not perform as expected.

BIC owns 51,750 shares of Smith & Oates. The shares are currently priced at $69. A call option on Smith & Oates with a strike price of$70 is selling at $3.50 and has a delta of .69. What is the number of call options necessary to create a delta-neutral hedge?

(a) What is the magnitude of the electric force between charges of 0.25 C and 0.11 C at a separation of 0.88 m? (b) If the separation between the charges is increased, does the magnitude of the force increase, decrease, or stay the same? Explain.

Your bank account has a balance of $-\$ 12$. You deposit $\$ 60$. What is your new balance?

Plot the magnitude of the resultant R of the three forces as a function of $\theta$ for $0 \leq \theta \leq 360^{\circ}$ and determine the value of $\theta$ which makes the magnitude R of the resultant of the three loads (a) a maximum and (b) a minimum. Record the magnitude of the resultant in each case. Use values of $\phi=75^{\circ} \text { and } \psi=20^{\circ}$.

The magnetic field at distance $x$ from the current in a long, straight conductor has magnitude $B$. What is the magnitude of the field at twice the distance from the conductor? $(a)$ $2 B$ $(b)$ $B$. $(c)$ $B / 4$. $(d)$ $4 B$. $(e)$ $B / 2$.

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?

How does the way that women view their body shape compare with the way that men view their body shape? How does this affect women?

Solve each problem.

According to T. Rowe Price Associates, a person who has a moderate investment strategy and $n$ years to retirement should have accumulated savings of $a_n$ percent of his or her annual salary. The geometric sequence defined by $a_n=1276(0.916)^n$ gives the appropriate percent for each year $n$.

Find $a_1$ and $r$.

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?

Mark Washington, CFA, is an analyst with BIC. One year ago, BIC analysts predicted that the U.S. equity market would most likely experience a slight downturn and suggested delta-hedging the BIC portfolio. As predicted, the U.S. equity markets did indeed experience a downturn of approximately 4% over a 12-month period. However, portfolio performance for BIC was disappointing, lagging its peer group by nearly 10%. Washington has been told to review the options strategy to determine why the hedged portfolio did not perform as expected.

Which of the following best explains a delta-neutral portfolio? A delta-neutral portfolio is perfectly hedged against:

a. Small price changes in the underlying asset.

b. Small price decreases in the underlying asset.

c. All price changes in the underlying asset.

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?