a) Show that if A is a real, non-singular nxn matrix, then A.(A^T) is positive definite.

b) Let H be a real, symmetric nxn matrix. Show that H is positive definite if and only if its eigenvalues are positive.

Save the Turtles is a non-for-profit organization that was incorporated in 20X0 and has a December 31 year end. Save the Turtles had the following transactions during 20X0.

1. Volunteers donated $20,000 in time to help with answering the phones, mailing materials, and other clerical activities.
2. A business donated rent-free office space to the organization that would normally rent for $35,000 per year.
3. Office furniture worth $10,600 and with an estimated 10-year life was donated to the organization.
4. A fund drive raised $215,000 in cash and $100,000 in pledges that will be paid within one year. A state government grant of $50,000 was received for program operating costs.
5. Save the Turtles paid salaries and fringe benefits of $208,560 during the year and had $22,400 of accrued salaries and benefits at the end of the year.
6. Utilities expense for the year totaled $8,300 and other expenses for the year included $5,600 for telephone, $4,300 for supplies, and $14,200 for printing. There were no supplies remaining at the end of the year and accounts payable totaled $4,400.
7. Office equipment with a useful life of 5 years was purchased for $12,000.
8. The organization claims a full year of depreciation on fixed assets.
9. Ninety percent of pledges for 20X1 are estimated to be collectible.
10. Expenses were allocated to program services and support services in the following percentages: Public education—45%, Veterinary services—20%, Management and general—20%, Fundraising—15%.

Required.

• Prepare a schedule of expenses by nature and function for the year ended December 31, 20X0.

Question 1

A non – dividend – paying stock with a current price of £52, the strike price is £50, the volatility is 30% pa, the risk free interest rate is 12% pa, and the time to maturity is 3 months?   

b) Calculate the price of a put option price on this stock?

b) Calculate the price of a call option on this stock

c) Is the put-call parity of these options hold?

If possible, please provide a detailed step by step as I would like to fully understand and not just copy answers. Thank you :)

A. Minimum Wage The non-economist’s view of the minimum wage seems to be that it forces greedy employers pay poor workers more money, making all workers better off. The “conventional” economic view of an increase in the minimum wage is that, as with most public policies, there are winners (those unskilled workers who keep their jobs and earn more) and losers (those workers who lose their jobs). What is the “unconventional” view and how does it alter that calculus of gains and losses?

A non – dividend – paying stock with a current price of $52, the strike price is $50, the risk free interest rate is 12% pa, the volatility is 30% pa, and the time to maturity is 3 months?

a) Calculate the price of a call option on this stock

b) What is the price of a put option price on this stock?

c) Is the put-call parity of these options hold?

(4 + 4 + 2 = 10 marks)

Please provide step by step answers, thank you!

Question 8

A non – dividend – paying stock with a current price of £104, the strike price is £100, the volatility is 30% pa, the risk-free interest rate is 12% pa, and the time to maturity is 3 months?  

a) Calculate the price of a call option on this stock?

b) Calculate the price of a put option price on this stock?

c) Is the put-call parity of these options hold?

If possible, please provide a detailed step by step and include an explanation as I would like to fully understand and not just copy answers. Thank you :)

​(Compound interest with​ non-annual periods)  Calculate the amount of money that will be in each of the following accounts at the end of the given deposit​ period:

PLEASE round to the nearest cent. Thank you.

1. The amount of money in Ted Logan’s account at the end of 6 years will be $__
2. The amount of money in Vern Coles account at the end of 3 years will be $__
3. The amount of money in Teena Elliott’s account at the end of 5 years will be $__
4. The amount of money in Wade Robinson’s account at the end of 4 years will be $__
5. The amount of money in Eunice Chang’s account at the end of 5 years will be $__
6. The amount of money in Kelli Craven’s account at the end of 5 years will be $__

Given a test in which there is overlap of the test results for diseased and non-diseased individuals (e.g., normal individuals are found who have test results ranging in value from 8 to 15, and diseased individuals are found who have test results ranging in value from 12 to 25, so that in the range of values 12 to 15 there are both normal and diseased individuals), if the current cutoff value lies in the range of this overlap and you move the cutoff value toward the normal population (lower numbers in this example), the true positive numbers will _____, the true negative numbers will ____, the false positive numbers will ____, the false negative numbers will ____, the sensitivity will ____, and the specificity will ____? (Please explain each)

1) An assumption of non parametric tests is that the distribution must be normal: (a) True (b) False

2) ​One characteristic of the chi-square tests is that they can be used when the data are measured on a nominal scale: (a) True (b) False

3) Which of the following accurately describes the observed frequencies for a chi-square test?​: (a) They are always whole numbers. (b) ​They can contain fractions or decimal values. (c) They can contain both positive and negative values. (d) ​They are always the same value.

4) The term expected frequencies refers to the frequencies ____.​ (a) ​found in the sample data (b) ​found in the population being examined (c) ​computed from the null hypothesis (d) ​that are hypothesized for the population being examined

5) For a given alpha level, what happens to the critical value for a chi-square test if the number of categories is increased?​: (a) The critical value also increases. (b) The critical value decreases. (c) ​The critical value depends on the sample size, not the number of categories. (d) ​the critical value is determined entirely by the alpha level.

6) A chi-square test for independence has df = 3. What is the total number of categories (cells in the matrix) that were used to classify individuals in the sample?​: (a) ​four (b) ​six (c) ​eight (d) nine

7) Suppose we wanted to explore the following research question: Are males more likely to choose a business course than females? Which groups are being compared here?

(a)Males and Females (b) Students enrolled in Business, Social Science and Other courses