Use Laplace transforms to solve the initial value problem

x′′+4x′+3x=t,x(0)=0,x′(0)=3,

where primes indicate derivatives with respect to t.

6. You’re given with the following information for the bank’s stock portfolio. Suppose that there are three mutually independent funds in your portfolio. The standard deviations of these fund are provided in the following table 1.  

                                                            Table 1:

Answer the following questions:

a) Suppose your allocations for the portfolio are given as 1/6 for asset one, 1/3 for asset two, 1/2 for asset three, what is the standard deviation for this portfolio?

b) Suppose that your portfolio has initial value as $300 million, given that your confidence level as 95% and assuming the normal distribution for asset returns, what is the VaR (Value at Risk) for your portfolio? What is the meaning of VaR? Is the normality assumption appropriate for the assessment of VaR?

(TCO D) Compare and contrast each of the following pairs: a. Primary Market versus Secondary Market b. IPO versus Private Placement c. Stop-Loss Order versus Short Sale

Because money is neutral, monetary policy has no influence on output and should not be used. Is it true?

Consider a two level system interacting with a radiation field. Write down the differential equations defining the Einstein A and B coefficients. Define all terms in your equations.

a. Solve for the time varying upper state population density for the case of no external radiation present.

b. In steady state, solve for the photon energy density.

c. What other concept is required to predict the possibility of laser action?

Scott and Linda have been saving to pay for their daughter Casie's college education. Casie just turned 10 at (t = 0), and she will be entering college 8 years from now (at t = 8). College tuition and expenses at State U. are currently $14,500 a year, but they are expected to increase at a rate of 3.5% a year. Ellen should graduate in 4 years¾if she takes longer or wants to go to graduate school, she will be on her own. Tuition and other costs will be due at the beginning of each school year (at t = 8, 9, 10, and 11). So far, Scott and Linda have accumulated $15,000 in their college savings account (at t = 0). Their long-run financial plan is to add an additional $5,000 in each of the next 4 years (at t = 1, 2, 3, and 4). Then they plan to make 3 equal annual contributions in each of the following years, t = 5, 6, and 7. They expect their investment account to earn 9%. How large must the annual payments at t = 5, 6, and 7 be to cover Casie's anticipated college costs?

a. $2,412.76

b. $2,177.51

c. $1,965.21

d. $2,292.12

e. $2,068.64

Dakota Inc. and Jersey & Company are two large companies that manufacture and sell equipment used in the construction, mining, agricultural, and forestry industries. The companies reported the following data (in millions) for two recent years:

a. Determine the earnings per share in Year 2 and Year 1 for each company. Round your answers to two decimal places.

b. Evaluate the relative profitability of the two companies.

earnings per share for Year 1 and Year 2 are higher than . However, from Year 1 to Year 2, the earnings per share for both companies . The slowing world economy contributed to the from Year 1 to Year 2. Overall, appears to be the more profitable company.

According to the financial statements for Global Telecom Inc., the firm has total assets valued at $320 million and total liabilities of $200 million. Last year, the company had a total after tax earnings of $12million. Company records indicate that the firm has issued 2 million shares of stock and it has a current market value of $65 a share.

1. Based on the market to book ratio of the company, will you recommend buying the shares? Why? (8 points)
2. Calculate one more ratio from the information given and explain how you will use the information. (6 points)
3. The firm is in fact one of the first movers in the 5G business. Will your answer to a) change given this new piece of information? Explain the potential pitfall of using the market to book ratio in this situation. (6 points)

What is the age distribution of patients who make office visits to a doctor or nurse? The following table is based on information taken from a medical journal.

Age group, years Under 15 15-24 25-44 45-64 65 and older

Percent of office visitors 20% 15% 25% 20% 20%

Suppose you are a district manager of a health management organization (HMO) that is monitoring the office of a local doctor or nurse in general family practice. This morning the office you are monitoring has eight office visits on the schedule. What is the probability of the following?

(a) At least half the patients are under 15 years old. (Round your answer to three decimal places.)

Explain how this can be modeled as a binomial distribution with 8 trials, where success is visitor age is under 15 years old and the probability of success is 20%?

Let n = 8, p = 0.80 and compute the probabilities using the binomial distribution.

Let n = 8, p = 0.20 and compute the probabilities using the binomial distribution.

Let n = 8, p = 0.35 and compute the probabilities using the binomial distribution.

Let n = 15, p = 0.20 and compute the probabilities using the binomial distribution.

(b) From 2 to 5 patients are 65 years old or older (include 2 and 5). (Round your answer to three decimal places.)

(c) From 2 to 5 patients are 45 years old or older (include 2 and 5). (Hint: Success if 45 or older. Use the table to compute the probability of success on a single trial. Round your answer to three decimal places.)

(d) All the patients are under 25 years of age. (Round your answer to three decimal places.)

(e) All the patients are 15 years old or older. (Round your answer to three decimal places.)

Poison Corporation holds 70 percent of Snake Company’s voting common shares but none of its preferred shares. Summary balance sheets for the companies on December 31, 20X1, are as follows:

Neither of the preferred issues is convertible. Poison’s preferred pays a 9 percent annual dividend and Snake’s preferred pays a 10 percent dividend. Snake reported net income of $48,000 and paid a total of $20,000 of dividends in 20X1. Poison reported $62,000 of income from its separate operations and paid total dividends of $46,000 in 20X1.

Required:
Compute 20X1 consolidated EPS. Ignore any tax consequences. (Round your answer to 2 decimal places.)
  

Discuss any security situations that you have personally encountered and how they were handled by the business organization. Do you feel comfortable with how businesses are safekeeping your data and transaction activities?

1. Can one use energy conservation with electricity concepts?

2. Write down a phenomenon that involves potential or potential difference?

3. How is potential in static electricity related to potential in current-carrying circuits?

1.A 0.40-kg mass, attached to the end of a 0.75-m string, is whirled around in a circular horizontal path. If the maximum tension that the string can withstand is 450 N, then what maximum linear speed can the mass have if the string is not to break?

A.370 m/s

B.22 m/s

C.19 m/s

D.29 m/s

2.A point on the rim of a 0.25-m-radius rotating wheel has a centripetal acceleration of 4.0 m/s². What is the angular speed of the wheel?

A.1.0 rad/s

B.2.0 rad/s

C.3.2 rad/s

D.4.0 rad/s

3. An object of mass 0.50 kg is transported to the surface of Planet X where the object's weight is measured to be 20 N. The radius of the planet is 6.0 × 10⁶ m. What is the mass of Planet X? (G = 6.67 × 10⁻¹¹ N ⋅ m²/kg²)

A.1.80E+18 kg

B.5.40E+24 kg

C.2.16E+25 kg

D.1.80E+18 kg

4.The escape speed from the surface of the Earth is 11.2 km/s. Estimate the escape speed for a spacecraft from the surface of the Moon. The Moon has a mass 1/81 that of Earth and a radius 0.25 that of Earth.

A.2.5 km/s

B.4.0 km/s

C.5.6 km/s

D.8.7 km/s