Find the mass of the solid bounded by the ??-plane, ??-plane, ??-plane, and the plane (?/2)+(?/4)+(?/8)=1, if the density of the solid is given by ?(?,?,?)=?+3?.

1-Exchange rate for Turkish Lira (TL) is $2

Exchange rate for Swiss Franc is $4

The cross rate between franc and TL is 3 francs per TL.

Is there an triangle arbitrage opportunity to make profit?

True

False

2-Exchange rate for Turkish Lira (TL) is $2

Exchange rate for Swiss Franc is $4

The cross rate between franc and TL is 3 francs per TL.

How much profit would you make at most if you have $100?

4. Draw the PROFIT graphs for the following:

Buy 1 100 call for $5

Sell 2 50 calls for $2

Buy 3 150 puts for $20

Sell 5 40 puts for $4

A hat contains a number of cubes: 3 red, 2 white, 1 blue, and 4 black.

1. If one cube is chosen at random, what is the probability that it is:

1. A red cube? (3 points)
2. Not a red cube? (3 points)
3. A cube that is white OR black? (4 points)
4. A cube that is neither white nor black? (4 points)
5. What do the answers to part a and part b add up to and why? (5 points)

2. If three cubes are chosen at random, with replacement, what is the probability that:

1. All three cubes are white? (4 points)
2. None of the cubes are white? (4 points)
3. At least one of the cubes is white? (4 points)
4. The first cube is red, and the next two are black (4 points)

3. Explain how you could simulate this experiment using a random number table. (5 points)

In 1-2 sentences each, answer the following questions:

4. What is the controversial way that respect for autonomy may be applied to issues of
organ allocation, and what is one problem with this application? Explain.
5. What is the core idea of the “fair innings” argument and who does it tell us to prioritize?
6. What does it mean for a treatment option to be considered “futile care”? Provide one
example.

trace by using quicksort on the array : 4 6 5 3 2 7 1 using 7 as the pivot

a.) Assume the universal set is U = {1, 2, 3, 4, 5, 6}, like when rolling a single six-sided die.

Write two sets where the intersection is empty and the union is the universe.

b.) True or False: For any set A,

True or False: For any set A,

Some years ago X AG paid €15’000 for a vacant lot with planning permission. The plot could easily be sold today for 10 times that amount. X AG has however a project in mind that would occupy the plot and require investment of €200,000 but generate positive cash flows of €150,000 for the next 4 years. X AG will be able to sell the plot for € 100’000 at the conclusion of the project.

1. Calculate the relevant cash flows for years 1 through 4 and the appropriate initial investment value.

2. For the cash flows calculated above, suppose the firm uses the NPV decision rule. At a required return of 7 per cent, should the firm accept this project?

3. What if the required return was 15 percent?

4. What is the Cash Payback Period ? Should the firm accept if projects are required to payback within 2 years?

5. Calculate the PI ratio at 7 and 15 percent

3. Let X = {1, 2, 3, 4}. Let F be the set of all functions from X to X. For any relation R on X, define a relation S on F by: for all f, g ∈ F, f S g if and only if there exists x ∈ X so that f(x)Rg(x).

For each of the following statements, prove or disprove the statement.

(a) For all relations R on X, if R is reflexive then S is reflexive.

(b) For all relations R on X, if S is reflexive then R is reflexive.

(c) For all relations R on X, if R is symmetric then S is symmetric.

(d) For all relations R on X, if S is symmetric then R is symmetric.