1. Derive the coordinate transformation changes form the spherical to Cartesian

Problem 3. Consider the unit interval [0, 1], and let ξ be fixed real number with ξ ∈ (0, 1) (note that the case ξ = 1/3 corresponds to the regular Cantor set we learned in our lectures). In stage 1 of the construction, remove the centrally situated open interval in [0, 1] of length ξ. In stage 2 remove the centrally situated open intervals each of relative length ξ (i.e. if the interval has length a you remove an interval of length ξ × a), one in each of the remaining intervals after stage 1, and so on. Let C_ξ denote the set which remains after applying the above procedure indefinitely

(a) Prove that C_ξ is compact.

(b) Prove that C_ξ is totally disconnected and perfect.

(c) Atually, prove that the complement of C_ξ in [0, 1] is the union of open intervals of total length equal to 1.

Let A be a finite set. Say A has five elements.

(a) Can you find a function g : A → A which is injective but not surjective? Explain your answer.

(b) Can you find a function f : A → A which is surjective but not injective? Explain your answer

Planning a festival. The Earth Day Committee has begun planning for an Earth Day festival. We list the subtasks for this project and the dependencies among them in the following table. Draw a PERT diagram for this project and construct a schedule for the tasks.

28. calculate  the present value of the annuity. (Round your answer to the nearest cent.)

$1300 monthly at 6.3% for 30 years.

29. determine the payment to amortize the debt. (Round your answer to the nearest cent.)

Monthly payments on $130,000 at 4% for 25 years.

You took a short futures position in 10 contracts, covering each 100 ounces of gold at a price of $276.5 per ounce. The initial and the maintenance margin requirement are respectively $1500 and is $1100 per contract. No withdrawal in any excess margin will be made. Ignore any interest on the balance.

The settlement prices per ounce of gold at the end of days 1, 2 and 3 are respectively $278, $281 and $276.

(c) Calculate your total gain or loss at the end of day 3, and the annualized return. [5]

21. the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period.

Find the required payment for the sinking fund. (Round your answer to the nearest cent.)

Monthly deposits earning 4% to accumulate $3000 after 10 years.

22. the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period.

Find the required payment for the sinking fund. (Round your answer to the nearest cent.)

Yearly deposits earning 12.9% to accumulate $2500 after 12 years.

Big Retailer (BR) follows a moderate current asset investment policy, but is now considering a change, perhaps to a restricted or maybe to a relaxed policy. BR’s annual sales are $1,400,000; its fixed assets are $950,000; its target capital structure calls for 40% debt and 60% equity; its EBIT is $500,000; the interest rate on debt is 8%; and its tax rate is 20%. With a restricted policy, current assets will be 20% of sales, while under a relaxed policy, current assets will be 35% of sales. What is the difference in the projected ROEs between the restricted and relaxed policies?

Whitson Co. is looking for ways to shorten its cash conversion cycle. It has annual sales of $45,625,000, or $125,000 a day on a 365-day basis. The firm's cost of goods sold is 65% of sales. On average, the company has $7,500,000 in inventory, $5,750,000 in accounts receivable, and $2,750,000 in accounts payable. Its CFO has proposed new policies that would result in a 25% reduction in both average inventories and accounts receivable, and a 10% increase in average accounts payable. She also anticipates that these policies would reduce sales by 5%. What effect would these policies have on the company's cash conversion cycle?

Solve the congruence: 1287x ≡ 447 (mod 516)

Please explain what we mean by Time Complexity and Space Complexity. Please provide a short survey of Complexity classes.

Suppose we use the ElGamal signature scheme with p = 65539, ?=2,?=33384. We send signed messages (m, r, s): (809, 18357, 1042) = hi and (22505, 18357, 26272) = bye. (a). Show that the same value of k was used for each signature. (b). Use this fact to find this value of k and to find the value of “a” such that ?≡?? (??? ?).

Make up a Bayes example from DAILY life(Create your own exaample)

First write question and analyze your question.

Explain the differences between conditional probabilities;explain the meaning of those conditional probabilities.

You may assign probabilities to events in the question or may use historical observations for empirical probabilities.

PharmaPlus operates a chain of 30 pharmacies. The pharmacies are staffed by licensed pharmacists and pharmacy technicians. The company currently employs 100 full-time-equivalent pharmacists (combination of full time and part time) and 175 full-time-equivalent technicians. Each spring management reviews current staffing levels and makes hiring plans for the year. A recent forecast of the prescription load for the next year shows that at least 280 full-time-equivalent employees (pharmacists and technicians) will be required to staff the pharmacies. The personnel department expects 10 pharmacists and 30 technicians to leave over the next year. To accommodate the expected attrition and prepare for future growth, management states that at least 15 new pharmacists must be hired. In addition, PharmaPlus’s new service quality guidelines specify no more than two technicians per licensed pharmacist. The average salary for licensed pharmacists is $35 per hour and the average salary for technicians is $15 per hour.

1. Determine a minimum-cost staffing plan for PharmaPlus. How many pharmacists and technicians are needed

1. Let P	=	number of full-time equivalent pharmacists
   T	=	number of full-time equivalent technicians

Min or Max ___P+____T

____P+____T _____ (less than or equal to, greater than or equal to, equal) ____ Full-time -equivalent employees_

____P- ____T _____ (less than or equal to, greater than or equal to, equal) ____ Quality Guideline

____P ____ (less than or equal to, greater than or equal to, equal) ____ Number of pharmacists

The optimal solution requires ____ full-time equivalent pharmacists and ____ full-time equivalent technicians. The total cost is $ ____ per hour.

b. Given current staffing levels and expected attrition, how many new hires (if any) must be made to reach the level recommended in part (a)?

What will be the impact on the payroll?

The payroll cost will ____ by $ ____ per hour.