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?

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 $r$.

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?

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. Washington considers a put option that has a delta of −.65. If the price of the underlying asset decreases by $6, then what is the best estimate of the change in option price?

Gruden Company produces golf discs which it normally sells to retailers for $7 each. The cost of manufacturing 20,000 golf discs is:

Gruden also incurs 5% sales commission ($0.35) on each disc sold. McGee Corporation offers Gruden $4.80 per disc for 5,000 discs. McGee would sell the discs under its own brand name in foreign markets not yet served by Gruden. If Gruden accepts the offer, its fixed overhead will increase from$40,000 to $46,000 due to the purchase of a new imprinting machine. No sales commission will result from the special order.

Instructions (c) What assumptions underlie the decision made in part (b)?

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.

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?

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.

Abbas Manufacturing produces wheels for cars. It holds high inventory levels so that one-off orders from major car manufacturers can be satisfied quickly. The world's big car manufacturers demand long credit periods from their suppliers of three months. Bruno has prepared the following cash flow forecast for the next three months:

$$\begin{matrix} \text{\$000} & \text{July} & \text{August} & \text{September}\\ \text{Cash inflows}\\ \text{Cash from debtors' payments} & \text{550} & \text{475} & \text{545}\\ \text{Sale of old equipment} & \text{0} & \text{0} & \text{50}\\ \text{Total cash in} & \text{550} & \text{475} & \text{595}\\ \text{Cash outflows} & \quad & \quad & \quad\\ \text{Materials purchased} & \text{160} & \text{175} & \text{170}\\ \text{Employee costs} & \text{185} & \text{185} & \text{190}\\ \text{New computers} & \text{0} & \text{145} & \text{0}\\ \text{Other costs} & \text{155} & \text{125} & \text{135}\\ \text{Total cash out} & \text{500} & \text{630} & \text{495}\\ \text{Opening bank balance} & \text{(75)} & \text{(25)} & \text{(180)}\\ \text{Net cash flow} & \text{50} & \text{(155)} & \text{x}\\ \text{Closing bank balance} & \text{(25)} & \text{(180)} & \text{y}\\ \end{matrix}$$

$$\begin{matrix} \text{a) What is meant by 'net cash flow'? } & \text{[2]}\\ \text{b) Identify two reasons why Abbas Manufacturing needs high amounts of cash or working capital.} & \text{[2]}\\ \text{c) Calculate the values for x and y in the cash flow forecast. Show your working.} & \text{[4]}\\ \text{d) Amend the cash flow forecast for July assuming cash from debtors and material costs are going to be 10 per cent higher than originally forecast. Show your working.} & \text{[6]}\\ \text{e) Using the cash flow forecast above, advise Abbas Manufacturing on the best ways for the business to reduce its bank overdraft (negative closing balance). Justify your advice.} & \text{[6]}\\ \end{matrix}$$

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

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? $(a)$ $2 B$ $(b)$ $B$. $(c)$ $B / 4$. $(d)$ $4 B$. $(e)$ $B / 2$.

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.

The magnitude of the force $\mathbf{F}$ is $0.2 \mathrm{~N}$ and its direction cosines are $\cos \theta_x=0.727, \cos \theta_y=-0.364$, and $\cos \theta_z=0.582$. Determine the magnitude of the moment of $\mathbf{F}$ about the axis $A B$ of the spool.

Use a graphing utility to find the magnitude and direction angles of the resultant of forces $\mathbf{F}_1$ and $\mathbf{F}_2$ with initial points at the origin. The magnitude and terminal point of each vector are given.