A chain email starts with a person sending an email out to five others. Each person who receives the email is asked to send it on to five other people. Some people do this, but others do not send any emails.

a) How many people have seen the email, including the first person, if no one receives more than one email and if the chain email ends after there have been one hundred people who read it but did not sent it out?

b) How many people sent out the email?

I'm supposed to use a tree to solve this problem, the 100 people in section a are not internal vertices(i) , they are leaves(l)

by using the rules l = i * (m-1) + 1 and n = m * i + 1 please answer the question

1. Suppose a raffle costs $4 to buy a ticket. there are 100 tickets and you buy one ticket. what is your expected winning if the following prizes are awarded: one first prize: $80 two second prizes of $40 twenty third prizes of $8

2. a student estimates that for each question of a ten question true/false test, he has about a 75% chance of getting the answer right. what are his chances of passing the test with a grade of 80 or better? Show the calculator input for your answer.

3. Mary is looking for someone with a change of $1. she estimates that each person she asks has a 25 probability of having the right change. what is the probability that Mary will have to ask at least four people in order to find one with the right change?

Benefit Cost Analysis:

You are trying to decide if you should place a solar panel on your apartment. You can buy the solar for 1000 dollars today, and it will reduce your electricity bill by

$300/year from today until you graduate four years from now (NOTE: this means it is a 4-year project). If you face an interest rate of 10%, should you buy the solar panel for your apartment?

Would a subsidy of of $100 in the first year affect your purchasing decision? How would a $200 fee to remove the solar panel when you graduate (T=3) affect your decision (assume there is still a subsidy)?

1. Suppose that for each of the next 10 years you will receive $250. If the opportunity cost of capital is 5% how much is this stream of cash flows worth today?  

2.Suppose that you deposit $450 in the bank at the end of each of the next 10 years. If the APR is 1% how much will be in your account at the end of 10 years?

3.Suppose that starting one year from now you will receive $100 a year at the end of every year. If the discount rate is 6% what is this stream of cash flows worth today?

4.Suppose that you will receive $200 at the end of every year starting 5 years from now (i.e. first payment EOY 5). What is this stream of cash flows worth if the cost of capital is 7%?

Efficiency

An ideal diatomic gas is used in a reversible heat cycle. The gas begins in state A with pressure 100 kPa, temperature300 K, and volume 0.50 L. It first undergoes an isochoric heating to state B with temperature 900 K. That is followed by an isothermal expansion to state C. Finally, an isobaric compression that returns the gas to state A.

(a)Determine the pressure, volume, and temperature of state B.

(b)Determine the pressure, volume, and temperature of state C.

(c)Compute the work and heat exchanged with the gas going from state A to B.

(d)Compute the work and heat exchanged with the gas going from state B to C.

(e)Compute the work and heat exchanged with the gas going from state C to A.

(f)Compute the efficiency of the heat cycle.

My first son was born on July 5, 2002. On the day he was born, I opened a 529 Plan for him and deposited $1,000. Every year on his birthday, I contributed $100 more than the previous year. I will make my last contribution this year on his 18^th birthday. As a conservative investor, I invested the money in a money market that paid 4% annually.

(b) How much money is in my son’s 529 Plan on his 18^th birthday (after I make my final contribution)?

(c) What single lump sum contribution could I have made on July 5, 2002, without any subsequent annual contributions, that would have resulted in the exact same account value on his 18^th birthday?

Theoretically speaking, suppose you, for some unknown reasons, decide to change a career path after a no-deal Brexit to become a consultant for the head of an underground enterprise, in which it plans to form a cartel with another operation ring in neighbouring region. The combined turnover would easily exceed €100 million in its first year together. The problem is, however, forming a cartel is difficult, not least maintaining it. Answer the following:

a. Why would it be difficult to form and maintain a cartel in general?

b. Explain in detail what the various challenges are, in this particular case, in order to succeed.

c. What will you give advice in order to successfully execute the project? Motivate. d. Give examples of two successful cartels in history. Are they still active? If not, what happened to them? What went wrong?

1)Find

Marginal Utility for x and determine if it is diminishing

Marginal utility for y and determine if its diminishing

Marginal rate of Substitution of x for y (MRS_xy) and determine if its diminishing

U (x, y) = 2x^2/3y^1/3

U (x, y) = x³ + 4y^1/4

2. Continental Long Distance Telephone service offer am optional package for in-stare calling whereby each month the subscriber gets the first 50 minutes of in-state calls free, the next 100 min at $0.25/min, and each additional time at the normal rate of $0.50/min. Draw the budget constraint for in-state phone calls and the composite good for a subscriber with an income of $400/month.

Composite goods imply all other goods: Assume it costs $1 and its on the horizontal axis.

A group of entrepreneurs want to purchase a rural hotel.

The renovation and purchase of the hotel has an estimated cost of €525,000.

This capital investment will be depreciated consistently over the next 5 years.

It is estimated that there will be 4,000 rooms total occupation per year, at a rate of €100 per room/night. Room occupation will rise by 5% year over year.

Running costs are estimated as €290,000 for the first year and will increase by 5% year over year.

The tax rate is 35%.

Step 1: Calculate the initial free cash flows correctly.

Step 2: If the partners require a minimum return of 8% on their investments, would you recommend that these businessmen buy the hotel? (Assume a continuous increase in cash flow of 1% from the 5^th year forwards). Why or why not?

a) A truck is bought for RO 30,000 and depreciation is charged at 10% p.a. by using written down value method, the amount of depreciation at the end of first year RO 3,000 and book value of the truck is RO 27,000. The amount of depreciation at the end of second year RO 2,700 and book value of the truck is RO 24.300 What does the amount book value of truck represent? Does this balance represent the original value of truck at the end of each year? Yes or no, comment on your answer. (Suggested: 80 – 100 words)
b) Truck is bought for RO 40,000 with an estimated useful life of 4 years. The expected scrap vahue at the end of its useful life is RO 2,000. Calculate the WDV Rate (Written Down Value method) and Prepare the Depreciation Schedule for 4 years.