Recall that in class we defined, for any set A, P(A) := {B : B ⊆ A}, which we called the power set of A.

a) (10) Show that, if a set A has n elements (where n ∈ {0, 1, 2, 3, 4, . . .}), P(A) has exactly 2 n elements.

b) (10) Use #4(any infinite set S has a countably infinite subset) to show that, if A is an infinite set, P(A) is uncountable.

An engineering system consisting of n components is said to be a k-out-of-n
system (k ≤ n) if the system functions if and only if at least k of the n components
function. Suppose that all components function independently of each other.
(a) If the ith component functions with probability Pi , i=1, 2, 3, 4, compute
the probability that a 2-out-of-4 system functions.
(b) Repeat (a) for a 3-out-of-5 system.

The age in years of 11 children and the number of words in their vocabulary is given below

Ages 1 2    3    4    5 6 3    5 2    4 6

voc. size 125    220 565 1110 2300 3500 730    2365 260    1200    2551

Now used it to predict the vocabulary size for a child A.) 7 yrs old    B.) 11 years old round to the nearest whole number

A random sample of ten professional athletes produced the following data where X is the number of endorsements the player has and Y is the amount of money made (in millions of dollars). What is the slope of the line of best fit? What does it represent?

2. The firm is expected to distribute the following dividend over the follow years:

Year 1 D₁ = $1.5;

Year 2 D₂ = $2.0;

Year 3 D₃ = $2.2;

Starting from year 4, the dividend will be growing at 5% for two years, and then the growth rate will drop to 2%

1. List the annual dividend payment for year 4-8
2. Calculate the present value of the dividends as the price of the stock (as of today), assume the discount rate is 10%

Assume the spot rates for one-, two-, and three-year zero coupon bonds are 2%, 3%, and 4%. (a)Calculate P(1), P(2), and P(3).(b)Calculate the price of a three-year 8% coupon bond, with interest paid annually.(c)Calculate ?1,1, ?1,2, and ?2,1(d)Calculate F(1,1), F(1,2), and F(2,1).(e)If ?1,3= 5%, calculate P(4).

Consider University of Minnesota as a business.

1.Who are University of Minnesota’s customers? Explain your answers.

2.What is/are University of Minnesota’s product(s)? Explain your answers.

3.Describe University of Minnesota’s supply chain in relation to your answer for #2.

4.List three or four Critical Success Factors for University of Minnesota

5.For each CSF from #4 identify three Key Performance Indicators

x, y, z, w, u and t are integer variables, what will their value be after the execution of the statements below. Give the final value of each variable

x = 7;

y = x + 1;

z = x % (y – 2) + 4;

y = (y + z ) % (x + 4) ;

w = (x * y) / (z – 3);

x = x + x;

u = w - 3;

t = z + (x + y + 2) % w;

During 2019, its first year of operations, A Company purchased 4 available-for-sale investments as follows:
Security Shares Purchased Total Cost
Co 1 3500 $67000
Co 2 2215   $72620
Co 3 1000 $21550
Co 4 2250    $58000

Assume that as of November 30, 2019, the Co 1 stock had a market value of $23 per share, Co 2. stock had a market value of $23 per share, Co 3 stock had a market value of $38 per share and Co 4 stock had a market value of $18 per share. A Company had $36,550 shares of no par stock outstanding that was issued for $900,000. For the year ending November 30, 2019. A Company had a net income of $275,000 No dividends were paid.

1) Prepare the Stockholders’ Equity section of the balance sheet as of November 30, 2019

2) Prepare the Current Assets section of the balance sheet presentation for the available-for-sale securities as of November 30, 2020.

Q1. One benefit of hydroponic agriculture is the…

Q2. FM stations are assigned frequencies in the

Q3. what are doctors hesitant to give out antibiotics to sick patients?

Q4. Cancer is

Q5. Selective photothermolysis is used for