The following represents a project that should be scheduled using CPM:

                             IMMEDIATE                                TIMES (DAYS)

                            PREDECESSORS

ACTIVITY                                                                  a           m         b

A                                   —                                          1           4          7

B                                   —                                          3           5          10

C                                  A 2          5          8

D                                  A                                            4           6          11

E                                   B                                           1            2          3

F                                 C,D 3          5          7

G                                D,E                                         1            2          6

H                                F,G                                         2            5          6

b. What is the critical path?

            A-D-F-H

            B-E-G-H

            A-C-F-H

            A-D-G-H

c. What is the expected project completion time?

Project completion time __________ days

d. What is the probability of completing this project within 22 days?

Probability _________          

Let f(x,y)= (3/2)(x^2+y^2 ) in 0≤x≤1, 0≤y≤1.

(a) Find V(X)

(b) Find V(Y)

1. A call option priced at $6 with a stock price of $45 and an exercise price of $46 allows the holder to buy the stock at

$46

$45

$52

$51

$40

2.A put option has a strike price of $75 and the cost of the option is $6. If the current price of the stock is $73 then the breakeven price for the option is:

$69

$75

$67

$81

$79

3. A call option has a strike price of $62 and the cost of the option is $4. If the current price of the stock is $73 then the breakeven price for the option is:

$58

$62

$77

$66

$69

4. You bought a call option with a strike of $65 for $3 when the stock price was $58. If at expiration the stock price is $62, your gain/loss at expiration is:

loss of $3

gain of $1

Breakeven (no gain or loss)

loss of $2

gain of $4

5. You bought a put option with a strike of $60 for $4 when the stock price was $59. If at expiration the stock price is $52, your gain/loss at expiration is:

gain of $4

loss of $4

loss of $1

Breakeven (no gain or loss)

gain of $5

Jojo the wizard is currently on a dragon’s lair. To escape from the lair, Jojo needs to defeat the elder dragon. Jojo is currently a wizard under training, so he knows only one spell : the fireball spell. The dragon’s body can be represented as an array of size N , where each part of the dragon’s body, from its head to its tail, is numbered with integer from 1 to N. Each body part has its sensitivity to fire a i . If a i is positive, then the fireball spell will deal a i damage to the dragon. If a i is negative, it will heal the dragon by − a i health points instead.

The fireball spell is a spell which deals damage to the dragon’s body on exactly K consecutive body parts. That is, if Jojo casts the spell on i-th body part, then the fireball will attack the parts [i, i+1, i+2, ..., i + K −1]. For example, if the dragon’s body is [1 , 2 , − 2 , 4 , 5], and K is 3, then Jojo may cast the spell on 1st, 2nd, and 3rd body part, which deals 1, 4, and 7 damage respectively. Jojo can’t cast the spell on 4 or 5 since the fireball must hit exactly K body parts of the dragon. As Jojo can only cast the spell one time, Help Jojo determine the maximum damage output he can deal to the dragon.

Format Input

The first line of the input contains two integers N and K, the number of the dragon’s body part and the range of the fireball spell. The next line consists of N integers a i , the sensitivity of each body part.

Format Output

Output the maximum damage Jojo can deal to the elder dragon. If Jojo can’t deal any damage, output 0 instead.

Constraints

• 1 ≤ K ≤ N ≤ 10³

• 0 ≤ | a i | ≤ 10⁹

Sample Input 1 (standard input)

5 3

1 2 -2 4 5

Sample Output 1 (standard output)

7

Sample Input 2 (standard input)

5 1

-1 -2 -3 -4 -5

Sample Output 2 (standard output)

0

Explanation

On the second sample, no matter where Jojo choose to cast his fireball spell, it will heal the dragon. So, the answer to the second sample is 0.

NOTE: USE C LANGUAGE, DONT USE FUNCTION(RESULT,RETURN),VOID,RECURSIVE, USE BASIC CODE AND CODE IT UNDER int main (){, constraint must be the same

On January 1, 2007 Brown issued 10 million stock options that would permit key executives to buy 10 million shares of the Brown’s $1 par value common stock at an exercise price of $15. The options vest after 5 years and expire in 15 years. The fair value of these options on the grant date was estimated at $4 each.

During 2010 Brown Company reacquired 15 million common shares as follows:

       2/1/2010       3 million shares at $10 each

       4/15/2010     4 million shares at $20 each

       6/1/2010       8 million shares at $30 each

On January 1, 2012 the stock price was $32 per share, and half the executives exercised their options. On Feb 1, 2013 the stock price was $45 per share, and the other half of the executives exercised their options.

Assume that Brown reissues treasury shares to executives that exercise options, and that it is using the first-in first-out cost flow method.

Required:

1. Prepare the journal entry for compensation expense in 2007.

2. Prepare the journal entries to record the shares repurchase during 2010.

3. Prepare the journal entries to record the exercise of the options on 1/1/2012 and on 2/1/2013.

Jamal owns two 10-year bonds that both have a yield to maturity of 4% that pay interest annually. One bond has a 4% coupon and trades at 100% (par). The other bond has a 2% coupon and trades at 83.78%.

1. What is the current yield of the 4% bond?
2. What is the current yield of the 2% bond?
3. If yields in general were to drop by 1% from 4% to 3%, how much would each bond change in price?

4. Which, if either, bond would perform the best in this scenario?

Exhibit 5-4

A local bottling company has determined the number of machine breakdowns per month and their respective probabilities as shown below.

Refer to Exhibit 5-4. The expected number of machine breakdowns per month is?

2. The probability of at least 3 breakdowns in a month is

3. The probability of no breakdowns in a month is

4.The expected number of new clients per month is

5. The variance is

6. The standard deviation is

J.M. is seen at the outpatient clinic for her first prenatal visit at 15 weeks of gestation. Her obstetric history indicates that she has had one ectopic pregnancy (no RhIG was given) and one full-term pregnancy (RhIG was given). The last child required phototherapy. Results of prenatal testing indicate a group O, D-negative type with a positive antibody screen. An antibody panel identifies anti-D. Parallel titers are performed on the samples from 15 weeks and 20 weeks of gestation. The following results are obtained:

Amniocentesis performed at 24 weeks shows a DOD of 0.10. J.M. continues to be closely monitored throughout her pregnancy. She delivers a girl weighing 4 lb. 10 oz. at 37 weeks. The hemoglobin is 13 g/dL, and the bilirubin is 5.2 mg/dL. The following evening, J.M.’s infant has a bilirubin value of 17.4 mg/dL, and an exchange transfusion is requested. Results of cord blood testing are as follows:

Does this infant have HDFN? If so, what is the cause? Use laboratory data to support your conclusions.

Take Three

Jojo just graduated and moved up to grade 4. Today is his first day in 4th grade. Unfortunately, the lessons are held online because of pandemic. So that the quality of learning remains good, Jojo’s teacher gives a hard task for 4th grader. After the 4th graders finished their first task which is prime factorization. Jojo’s teacher set up a game for the stundets. The game is very simple. Given N colored balls, each student has to take 3 balls randomly. If a student got 3 balls with the same color, then the student counted as winner. Jojo is angry because he knows that this game is just pure luck to reach its goal. On the other hand, Jojo wants to know the number of possibilities to get 3 balls with the same color. As a good friend of Jojo, help Jojo to count the number of possibilities to get 3 balls with the same color.

Format Input:

There are T testcases. Every testcase contains two rows. The first row consists of one integer N which indicates the number of balls. The second row consists of N integers A 1, A 2, A 3, ..., A n where A i describes i-th ball’s color.

Format Output:

Output T line with format “Case # X: ”, where X indicates the testcase number and then followed by an integer describes the number of possibilities to get 3 balls with the same color.

Constraints

• 1 ≤ T ≤ 10

• 3 ≤ N ≤ 10 5

• 1 ≤ A i ≤ 1000

Sample Input (standard input) :

5

5

1 1 2 2 2

5

1 2 2 2 2

10

1 3 3 3 3 3 2 2 2 2

5

1 2 2 3 3

10

2 2 2 2 2 2 2 2 2 2

Sample Output (standard output):

Case #1: 1

Case #2: 4

Case #3: 14

Case #4: 0

Case #5: 12

note : use C language, integer must be the same as the constraint, DONT USE VOID/RESULT/QSORT/RETURN(RECURSIVE), (the output must be the same, print the "Case.." too)code it under int main (){

Take Three

Jojo just graduated and moved up to grade 4. Today is his first day in 4th grade. Unfortunately, the lessons are held online because of pandemic. So that the quality of learning remains good, Jojo’s teacher gives a hard task for 4th grader. After the 4th graders finished their first task which is prime factorization. Jojo’s teacher set up a game for the stundets. The game is very simple. Given N colored balls, each student has to take 3 balls randomly. If a student got 3 balls with the same color, then the student counted as winner. Jojo is angry because he knows that this game is just pure luck to reach its goal. On the other hand, Jojo wants to know the number of possibilities to get 3 balls with the same color. As a good friend of Jojo, help Jojo to count the number of possibilities to get 3 balls with the same color.

Format Input:

There are T testcases. Every testcase contains two rows. The first row consists of one integer N which indicates the number of balls. The second row consists of N integers A 1, A 2, A 3, ..., A n where A i describes i-th ball’s color.

Format Output:

Output T line with format “Case # X: ”, where X indicates the testcase number and then followed by an integer describes the number of possibilities to get 3 balls with the same color.

Constraints

• 1 ≤ T ≤ 10

• 3 ≤ N ≤ 10 5

• 1 ≤ A i ≤ 1000

Sample Input (standard input) :

5

5

1 1 2 2 2

5

1 2 2 2 2

10

1 3 3 3 3 3 2 2 2 2

5

1 2 2 3 3

10

2 2 2 2 2 2 2 2 2 2

Sample Output (standard output):

Case #1: 1

Case #2: 4

Case #3: 14

Case #4: 0

Case #5: 12

note : use C language, integer must be the same as the constraint, DONT USE VOID/RESULT/QSORT, (the output must be the same, print the "Case.." too)code it under int main (){