A vase U1 contains 2 white balls, a vase U2 contains 2 red balls, a vase U3 contains 2 white balls and 2 red balls and vase U4 contains 3 white balls and 1 red ball. The probability of choosing vase U1, U2, U3, and U4 are respectively 1/2, 1/4, 1/8 and 1/8. A vase is chosen and we retrieve the ball inside. Determine

a) The probability that the retrieved ball is white

b) Knowing the retrieved ball is white what is the probability that the ball was retrieved from vase U3.

Consider three different US Treasury securities with maturities T = 1, 2 and 3 years, all with principal of $100. As usual convention, today is time t=0.

1. One year Treasury bill trades at price ? = $97. 1

2. Two year Treasury note which pays 4% coupon annually, trades at ? ₂= $100.60

3. Three year Treasury note which pays 5% coupon 5% annually, trades at ? ₃= $101.9

• Compute one period forward rates at times T=1, 2 and 3. Assume that the price of 4 year zero coupon bond price is $0.82.

• You are thinking of starting a business on year two (T=2) when you might need to borrow money. You believe interest rates are low today. What interest rate can you lock in today for borrowing on year two, assuming you want to borrow only for a period of 2 years?

1. Locate a root of sin(x)=x2 where x is in radians. Use a graphical technique and bisection with
the initial interval from 0.5 to 1. Perform the computation until ea is less than es=2%. Also
perform an error check by substituting your final answer into the original equation.
2. Determine the positive real root of ln(x
2
)=0.7 using three iterations of the bisection method,
with initial interval of [0.5:2].
3. Determine the lowest positive root of f(x)=7sin(x)e
-x
-1 using (a) the Newton-Raphson
method (three iterations, xi=0.3). (b) the secant method (five iterations, xi-1=0.5 and xi=0.4). (c)
the modified secant method (three iterations, xi=0.3, δ=0.01).
4. Use the Newton-Raphson method to find the root of f(x)=e
-0.5x
(4-x)-2. Employ initial guesses
of (a) 2, (b) 6, and (c) 8. Explain your results.

Perdue Company purchased equipment on April 1 for $82,620. The equipment was expected to have a useful life of three years, or 5,940 operating hours, and a residual value of $2,430. The equipment was used for 1,100 hours during Year 1, 2,100 hours in Year 2, 1,800 hours in Year 3, and 940 hours in Year 4. Required: Determine the amount of depreciation expense for the years ended December 31, Year 1, Year 2, Year 3, and Year 4, by (a) the straight-line method, (b) units-of-output method, and (c) the double-declining-balance method.

1. Consider the three vectors, u and v are 10 degrees above and below the x-axis respectively, and ||u|| = 1, ||v|| = 2, and ||w|| = 3. Arrange the dot products taken among these vectors from least to greatest

2. Let A be a 4 x 6 matrix. Find the elimination matrix E that corresponds with the row operation "switch rows 1 and 3, and scale row 4 by a factor of 6.

3. Find the formula for the entry in the ith row and j column of the product AB in terms of the entries of A and B. Assume A is m x n and B is n x p.

1.

As a business owner, you find that your resource prices are increasing often. Because these costs are rising, you find it necessary to change your prices frequently. This best describes
1.a price confusion problem.
2.money illusion.
3.future price uncertainty.
4.hyperinflation.
5.menu costs.

9.Arguably, the increases in housing prices in 2005–2006 caused
1.a price confusion problem for producers.
2.a menu cost problem for producers.
3.a money illusion problem for producers.
4.a money illusion problem for consumers.
5.future price uncertainty for producers.

1. Point-of-Sale System: We have two companies that can implement a point-of-sale system. Both with cost $200,000 to implement. Company A says we will receive the following returns on our investment: Year 1: $85,000; Year 2: $25,000; Year 3: $30,000; Years 4–10: $10,000. Company B says we will receive the following returns on our investment: Year 1: $30,000; Year 2: $25,000; Year 3: $85,000; Years 4–10: $10,000. Using the payback method, which company should we use and Why?

The initial rate of the reaction of species A and B A + 2 B → C was measured at a temperature of 25 °C for various initial concentrations of A and B. Data are collected in the table. Determine the rate equation from these data. What is the overall order of the reaction? What is the value of the rate constant? (Give the appropriate units of k.)

Please solve this problem, in c++ (algoritms) write code and explaination how to solve it!

1) N numbers are given. The first K of them are sorted in ascending order, the remaining NK are also sorted in ascending order. Sort numbers in ascending order in O (N).

Input data format N - number of numbers, K - number of numbers in the first half (sorted).

Example input

10 6

1 2 5 6 8 9 3 4 7 12

Sample Output

1 2 3 4 5 6 7 8 9 12