Write a c++ function named multi_table to print out multiplication table for a given number of rows and columns. Your program should print a header row and a header column to represent each row and column number. For example your function call multi_table(4, 4) would print below to the command line:

1 | 1 2 3 4

_________

2 | 2 4 6 8

3 | 3 6 9 12

4 | 4 8 12 16

Test your function in a driver program for 12 by 12 multiplication table.

A potential new project would cost $1000 today. The 1st stage of the project would last 2 years. There are 2 possible scenarios for Stage 1 net cash flows in years 1 and 2: 1) $1,060 per year, with 50% probability; or 2) $0 per year, with 50% probability. If the 1st stage outcome is good (with non-zero outcomes), the firm will reinvest an equal amount in year 2 (the same amount invested at year 0) and extend the project into Stage 2 (years 3 and 4). The possible Stage 2 outcomes are either: 1) net cash flows in years 3 and 4 doubling relative to the good Stage 1 outcome (with probability of 50%), or 2) net cash flows of 0 in years 3 and 4 (with probability of 50%). If the Stage 1 outcome is bad, the firm will abandon the project at the conclusion of Stage 1.

The cost of capital is 9%. The overall expected NPV of the project (at year 0), considering Stage 1 and the option to expand the project into Stage 2, is $_______.

Find the general solution of the given second-order differential equation.

1. 4?'' + 9? = 15

2. (1/4) ?'' + ?' + ? = ?² − 3x

Solve the differential equation by variation of parameters.

3. ?'' + ? = sin(x)

In C++ please.

7. Provided that c1, c2 and c3 are of appropriate ranges. Use transform()
   algorithm so that it copies the larger of the corresponding elements
   from c1 and c2 to c3. That is, if

   c1 = {1, 2, 3, 4, 5} and   c2 = {5, 4, 3, 2, 1}

   then c3 should become c3={5, 4, 3, 4, 5}

Suppose that a certain random variable, X, has the following cumulative distribution function (cdf):

F(x) = 0 x < 2

  0.25x2 – x + 1 2 ≤ x ≤ 4

1 4 < x

Find P(X > 2.5) (Round your answer to 4 decimal places)

2. A serial dilution of patient serum is done: Tube #1 Tube #2 Tube #3 Tube #4 Tube #5 Tube #6

1:2 1:4 1:8 1:16 1:32 1:64

One milliliter of RBCs is added to each tube and the following is noted:

Tube #1 No agglutination

Tube #2 No agglutination

Tube #3 Agglutination

Tube #4 Agglutination

Tube #5 Agglutination

Tube #6 Agglutination

a. What has happened in Tubes #1 and 2?

b. What is the antibody titer?

3. You suspect that an individual has been infected with the Nasty Virus, a highly contagious virus that has been reported in your city. Describe how you could use the Western blot procedure to confirm that this individual has been infected. (Please list the steps of the Western Blot procedure)

A water-to-water system is used to test the effects of changing tube length, baffle spacing, tube pitch, pitch layout, and tube diameter. Cold water at 25°C and 100,000 kg/hr is heated by hot water at 100°C , also at 100,000 kg/hr. The exchanger has a 31 in. ID shell. Perform calculations on this 1–2 shell-and-tube heat exchanger for the following conditions, as outlined in the examples, and put together an overall comparison chart. a. 3/4 in. OD tubes, 12 BWG laid out on a 1 in. triangular pitch; 3 baffles per meter of tube length. Analyze the exchanger for tube lengths of 2, 3, 4, and 5 m. b. 3/4 in. OD tubes, 12 BWG laid out on a 1 in. triangular pitch; 2 m long. Analyze for baffle placement of 1 baffle per meter of tube length, 2 baffles per meter of tube length, 3 baffles per meter of tube length, 4 baffles per meter of tube length, and 5 baffles per meter of tube length. c. 3/4 in. OD tubes, 12 BWG; 2 m long; 4 baffles per meter of tube length. Analyze the exchanger for tube layouts of 15/16 in. triangular pitch, 1 in. triangular pitch, and 1 in. square pitch. d. 1 m OD tubes, 12 BWG; 4 m long; 9 baffles. Analyze the exchanger for tube layouts of 1.25 in. triangular pitch and 1.25 in. square pitch. e. 3/4 in. OD tubes, 12 BWG laid out on a 1 in. triangular pitch; 2 m long; 4 baffles per meter of tube length. Analyze the exchanger for 2, 4, 6, and 8 tube passes, and compare to the case of true counterflow (i.e., 1 tube pass).

1) Solve each of the following differential equations.

a)16y"-8y'+y=0

b) (d^4y)/(dx^4)-13((d^2y)/(dx^2))+36y=0

2) use Variation of Parameters to solve y"+16y=(1/3)csc4t

3) use undetermined coefficients to solve y"-5y'+4y=3e^(3t)-5e^(2t) with y'(0)=-1 and y(0)=1

4) Explain why the product (A+B)(A-B) not equal A^2-B^2 fro two NXN matrices A and B. what is the product of (A+B)(A-B)?

how to find the first, second, third quantile of a column in a dataset with R?

the dataset is like this:

columns values

a. 1. 2. 3. 5. 6. 7. 4. 7. 8. .........

b 5. 6. 7. 3. 8. 0. 4. 7. 4. 7. .........

c    1. 2. 3. 5. 6. 7. 4. 7. 8. .........

d 6. 3. 1. 0. 8. 3. 6. 6. 3.........