A company's capital consists of 100 000 ordinary shares issued at $2 and paid to $1 per share.

On 1 September, a first call of 50c was made on the ordinary shares. By 30 September, the call money received amounted to $45 000. No further payments were received, and on 31 October, the shares on which calls were outstanding were forfeited. On 15 November, the forfeited shares were reissued as paid to $1.50 for a payment of $1 per share. The appropriate cash amount from the reissue was received on 19 November. Costs of reissue amounted to $1 500. The company's constitution provided for any surplus on resale, after satisfaction of unpaid calls, accrued interest and costs, to be returned to the shareholders whose shares were forfeited.

What is the remaining balance of the forfeited share account that is refundable to shareholders?

1. A management company must first decide whether to undertake a market research survey. If the market research study is conducted, the outcome will either be favorable (F) or unfavorable (U). Assume there are only two decision alternatives, D1 and D2, and two states of nature, S1 and S2. The payoff table showing profit is as follows:

1. Using the following probabilities, what is the optimal decision strategy?

P(F) = 0.56        P(S1/F) = 0.57               P(S1/U) = 0.18              P(S1) = 0.40

P(U) = 0.44       P(S2/F) = 0.43               P(S2/U) = 0.82             P(S2) = 0.60

2. Find the Efficiency of this market research. What would be your recommendation?
3. How much will this company be willing to pay for this market research?

A blind taste test is conducted to determine which of two​ colas, Brand A or Brand​ B, individuals prefer. Individuals are randomly asked to drink one of the two types of cola​ first, followed by the other​ cola, and then asked to disclose the drink they prefer. Results of the taste test indicate that 42 of 100 individuals prefer Brand A. Complete parts a through c. ​(a) Conduct a hypothesis test​ (preferably using​ technology) Upper H 0​: p equals p 0 versus Upper H 1​: pnot equalsp 0 for p 0equals0.31​, 0.32​, 0.33​, ​..., 0.51​, 0.52​, 0.53 at the alphaequals0.05 level of significance. For which values of p 0 do you not reject the null​ hypothesis? What do each of the values of p 0 ​represent? Do not reject the null hypothesis for the values of p 0 between nothing and nothing​, inclusively. ​(Type integers or decimals as​ needed.)

Your goal is to collect all 80 player cards in a game. The Player cards are numbered 1 through 80. High numbered cards are rarer/more valuable than lower numbered cards.

Albert has a lot of money to spend and loves the game. So every day he buys a pack for $100. Inside each pack, there is a random card. The probability of getting the n-th card is c(1.05)^-n, For some constant c. Albert buys his first pack on June 1st. What is the expected number of Player cards Albert will collect in June?(30 days)

a.) Find an exact, closed-form expression for c. (Answer should not include a summation symbol or integral sign).

b.)Find the expected number of unique Player cards Albert will collect in June. (Answer may include summation symbol or integral sign.

We have a solution of protein that has a concentration of 0.25 mg/ml.

a.We need 20 g of the protein for an experiment. What volume of the protein solution do we need?

b.Suppose we want a solution containing 150 g of the protein at a concentration of 0.50 mg/ml. To do this we will first evaporate the liquid from enough of the protein solution to get 150 g. How much solution do we need to start with? How much H₂O do we add to get the desired concentration?

d.Suppose we want 1 ml of a 10 g/ml solution. How much H₂O and protein stock must we add to get this?

e.Suppose we want 100 l of a 0.1 g/l solution. How much H₂O and protein stock must we add to get this?

From the data collected below, show how you have followed all 14 of the steps on page 340 to compute the chi-square test of difference by completing the information in the charts below. Answer the hypothesis and interpret your findings. You can use the abbreviations provided in the first chart in Labels column of the second chart. For example, reference Japanese individuals who primarily utilized an action-based strategy to resolve a conflict episode as AJ.

1. X²=
2. df =
3. Critical X²=
4. Interpretation =

(1)You have just taken out a $20 000 car loan with a 4% APR, compounded monthly. The loan is for five years. When you make your first payment in one month, how much of the payment will go toward the principal of the loan and how much will go toward interest? (Note: Be careful not to round any intermediate steps to fewer than six decimal places.)

2)You have just sold your house for $ 1 100 000 in cash. Your mortgage was originally a 30-year mortgage with monthly payments and an initial balance of $750 000.

The mortgage is currently exactly18.50years old, and you have just made a payment. If the interest rate on the mortgage is6.25%

(APR), how much cash will you have from the sale once you pay off the mortgage? (Note: Be careful not to round any intermediate steps to

Problem 15. Give an example of a two mutually exclusive events.

Problem 16. Give an example of three events E, F, and G so that each pair of events is mutually exclusive

Problem 17. Consider a situation where #(all) = 100, #(E) = 32, #(F) = 52, and #(E ∩ F) = 13. 1. Find P(E | F). 2. Calculate #(E ∩ F) #(F) and explain why this matches the value in part 1. Problem 18. Suppose we have 30 shuffled cards numbered 1-30. What is the probability of drawing an even value given that the value is greater than 9?

Problem 19. Suppose we roll a 6-sided die two times. What is the probability of the sum of the values being greater than 7 given that the first roll was a 5?

3. For the following analog signal:
x_a(t) = 3sin(40πt) + 3cos(50πt)
which is sampled at a rate of 100 samples/second.

a. Design an IIR digital filter that will pass the first component 3sin(40πt) with attenuation of
less than 1 dB and suppress the second component 3cos(50πt) at least 50 dB. The filter should be
monotonic in the passband and have ripple in the stopband.

b. Generate 500 samples of the sampled signal x_a(t) at the given sampling rate and use the
filter you designed to process the sampled signal using MATLAB’s "filter" command.

c. Plot the original signal and the output signal in one window using MATLAB’s subplot
command ( in either a 1 X 2 arrangement or a 2 X 1 arrangement. Remember to title all plots and
label all axes.

Please include Matlab code. EVEN JUST PART A HELPS