Let V be a finite-dimensional vector space over C and T in L(V). Prove that the set of zeros of the minimal polynomial of T is exactly the same as the set of the eigenvalues of T.

Let Q:= {1,2,...,q}. Let G be a graph with the elements of Q^n as vertices and an edge between (a1,a2,...,an) and (b1,b2,...bn) if and only if ai is not equal to bi for exactly one value of i. Show that G is Hamiltonian.

Tom borrows $100 at annual effective interest rate of 4% and agrees to repay it with 30 annual installments. The amount of each payment in the last 20years is set at twice that in the first 10 years. At the end of 10 years, Tom has the option to repay the entire loan with a final payment $X, in addition to the regular payment. This will yield the lender an annual effective rate of 4.5% over the 10-year period. Calculate $X? (ANS: 108.88)

On a certain flight, from prior data, 70% of passengers will buy a meal. A typical row in the economy section of this flight seats 10 in "3-4-3" seating. Create an Excel spreadsheet. In your Excel spreadsheet, answer the following questions: a. What method was used to determine that 70% of passengers will buy a meal? b. Use the letter M to stand for your random variable. What is the meaning of M? The answer to this question begins, "Let M = ...." c. What probability distribution is appropriate to assign to M? d. Compute the probability mass function, pmf, of that probability distribution from (c) above using an Excel formula. The values of the pmf should be in one vertical column (see the attached PDF for an example). NOTE 1: You can put n and p somewhere on your Excel sheet. Then, in your computation of the pmf, using =BINOM.DIST(), you should reference (and "lock") the cells. NOTE 2: Looking below, you can see that you are asked to create the cdf adjacent to this pmf. If you lock the column here in (d), then you can copy the =BINOM.DIST() formula to the adjacent column, and simply change the FALSE to TRUE. Then, you can propagate the formula down and be done. e. Compute the cumulative distribution function, cdf, using an Excel formula. The values of the cdf should be in one vertical column, adjacent to the pdf. f. Verify Excel's formula in d. as follows: Create one column based on Excel's version of nCr = COMBIN(n, r) Create an adjacent column that computes the probability of the successes Create an adjacent column that computes the probability of the failures Multiply the three factors and verify that this matches the numerical value in d g. In a typical row in economy, how many passengers would you expect to purchase a meal? h. How likely is this to occur? i. Compute the interval one standard deviation, σ, above and one standard deviation below this expected value. j. What is the probability of the interval P(μ - σ ≤ M ≤ μ + σ) = ? k. What is the probability that at least one passenger buys a meal in a typical row in economy? l. What is the probability that no passenger buys a meal in a typical row in economy? Upload your Excel workbook file to this assignment. NOTE: Two OPTIONAL opportunities for extra credit: I. Create a graph of the probability mass function, pmf, the "comb" function. II. Create a graph of the cumulative probability distribution, cdf, the step function (HARDER). You may do either one or both for extra credit.

Are nursing salaries in Tampa, Florida, lower than those in Dallas, Texas? As reported by the Tampa Tribune, salary data show staff nurses in Tampa earn less than staff nurses in Dallas. Suppose that in a follow-up study of 41 staff nurses in Tampa and 51 staff nurses in Dallas you obtain the following results. Enter negative value as negative number.

a. Formulate hypothesis so that, if the null hypothesis is rejected, we can conclude that salaries for staff nurses in Tampa are significantly lower than for those in Dallas. Use a=.05

b. What is the value of the test statistic?

(to 3 decimals)

c. What is the p-value?

Degrees of freedom is ? Round degrees of freedom to previous whole number.

Consider the following results for independent samples taken from two populations.

a. What is the point estimate of the difference between the two population proportions (to 2 decimals)?

b. Develop a 90% confidence interval for the difference between the two population proportions (to 4 decimals). Use z-table.
?  to ?  

c. Develop a 95% confidence interval for the difference between the two population proportions (to 4 decimals). Use z-table.
?  to ?

Consider the following hypothesis test.

H0: u1 - u2 ≤ 0
Ha: u1 -u 2 > 0

Consider the following results for two independent random samples taken from two populations.

Use pooled estimator of p.

1. What is the value of the test statistic (to 2 decimals)?
   
2. What is the p-value (to 4 decimals)? Use z-table.

1. Find the quadratic product of each of the following
a) (x + 2)( x + 7) =
b) (x – 2)(x – 7 ) =
c) (x – 2 )(x + 7) =
d) (x + 2)( x – 7) =
e) (x + 7)(x – 7) =
2. Factorize the following
a) x²– 6x – 16 =
b) x² + 6x – 16 =
c) x² − 16 = (2, 2, 1 mark)
3. Find the equation of the line joining the points (1, 4) and (-3, -2)
( 5 marks)
4. Find the equation of the line passing through the point (2, 3) and
parallel to the line 4y = 5x + 2

Corporate valuation model

The corporate valuation model, the price-to-earnings (P/E) multiple approach, and the economic value added (EVA) approach are some examples of valuation techniques. The corporate valuation model is similar to the dividend-based valuation that you’ve done in previous problems, but it focuses on a firm’s free cash flows (FCFs) instead of its dividends. Some firms don’t pay dividends, or their dividends are difficult to forecast. For that reason, some analysts use the corporate valuation model.

Charles Underwood Agency Inc. has an expected net operating profit after taxes, EBIT(1 – T), of $14,200 million in the coming year. In addition, the firm is expected to have net capital expenditures of $2,130 million, and net operating working capital (NOWC) is expected to increase by $35 million. How much free cash flow (FCF) is Charles Underwood Agency Inc. expected to generate over the next year?

A. $12,035 million

B. $288,976 million

C. $12,105 million

D. $16,295 million

Charles Underwood Agency Inc.’s FCFs are expected to grow at a constant rate of 3.54% per year in the future. The market value of Charles Underwood Agency Inc.’s outstanding debt is $76,494 million, and its preferred stocks’ value is $42,496 million. Charles Underwood Agency Inc. has 525 million shares of common stock outstanding, and its weighted average cost of capital (WACC) equals 10.62%.

Using the preceding information and the FCF you calculated in the previous question, calculate the appropriate values in this table. Assume the firm has no nonoperating assets.

An Egyptian mummy is discovered in which the amount of Carbon-14 present is only about twenty-nine fiftieths the amount found in living human beings. a. Using the half-life of Carbon-14, determine the decay constant for Carbon-14 (answer in decimal form and scientific notation, accurate to the tenth decimal place)? b. About how long ago did the Egyptian die? c. If this is a royal tomb, which Pharaoh is in the sarcophagus? Which dynasty and regnal years are recorded for this Pharaoh? In addition to showing the calculations that lead to your solution, write a synopsis of the tactic(s) you used to arrive at your solution(s) to this series of questions. Use clear and concise sentence structure and grammar. Your answer should be labelled with appropriate units and reflect the context used in this question.

a.) Show that the DE is exact and find a general solution

2y - y^2sec^2(xy^2)+[2x-2xysec^2(xy^2)]y' = 0

b.) Verify that the equation is not exact. Multiply by integrating factor u(x, y) = x and show that resulting equation is exact, then find a general solution.

(3xy+y^2) + (x^2 + xy)dy/dx = 0

c.) Verify that the equation is not exact. Multiply by integrating factor u(x, y) = xy and show that resulting equation is exact, then find a general solution.

(-xysinx + 2y cosx) + 2xcosx(dy/dx) = 0

Look up and list the main properties of the acids formed in acid rain.

Determine whether the following categorical syllogisms are valid or invalid.

Categorical syllogism 1 No M are P. No M are S No S are P.

Categorical syllogism 2 Some M are not P. Some M are S. Some S are not P.

Categorical syllogism 3 Some M are not P. Some M are not S. Some S are P.

Categorical syllogism 4 All M are P. All S are M. All S are P.

Categorical syllogism 6 No M are P. No S are M. No S are P.

Categorical syllogism 8 All M are P. No M are S. Some S are not P.

Categorical syllogism 9 Some M are P. No S are M. Some S are not P.

Categorical syllogism 10 No P are M. No S are M. No S are P.

Categorical syllogism 13 All P are M. All S are M. All S are P.

Categorical syllogism 14 Some P are M. Some S are M. Some S are P.

Categorical syllogism 15 No M are P. All M are S. Some S are not P.

Categorical syllogism 16 Some M are P. No M are S. Some S are not P.

A nutritionist at the Medical Center has been asked to prepare a special diet for

certain patients. She has decided that the meals should be prepared from Foods A and B and that they

should contain a minimum of 400 mg of calcium, 10 mg of iron, and 40 mg of vitamin C. Each ounce of Food

A contains 30 mg of calcium, 1 mg of iron, 2 mg of vitamin C, and 3 mg of cholesterol. Each ounce of Food

B contains 25 mg of calcium, 0.5 mg of iron, 5 mg of vitamin C, and 5 mg of cholesterol.

(1) How many ounces of each type of food should be used in a meal so that the cholesterol content is

minimized and the minimum requirements of calcium, iron, and vitamin C are met? What is the

minimum cholesterol content?

(2) By how much can the cholesterol content of Food A vary before the optimal solution changes?

(3) By how much can the cholesterol content of Food B vary before the optimal solution changes?

What are some fourier series applications? Please list at least 5 applications from different field and take one as an example and do an example of it.