Question Solved1 Answer Question 21 (7 points) The coffee shop at the mall employs 19 people as full time, casual and/or weekend staff as shown in the table below. Employment Type Number of Employees Full Time Casual Weekend Full Time and Casual Full Time and Weekend Casual and Weekend Full Time, Casual & 1 Weekend A) Create a Venn-diagram, and then determine the probability that a randomly selected employee works full time or on weekends. B) Determine the probability that a randomly selected employee works only full time or only weekends or only casual. C) Determine the probability that a randomly selected weekend employee is also a casual employee. 13 9 7 4 3 4

In Exercises 17–27, let the universe be the set Z+. Let X = {1, 2, 3, 4, 5} and let Y be the set of positive, even integers. In set- builder notation, Y = {2n | n ∈ Z+}. In Exercises 18–27, give a mathematical notation for the set by listing the elements if the set is finite, by using set-builder notation if the set is infinite, or by using a predefined set such as ∅. X ∪ Y'

E13-6B Wood Corporation purchased from its stockholders 5,000 shares of its own previously issued stock for $250,000. It later resold 2,000 shares for $53 per share, then 2,000 more shares for $48 per share, and finally 1,000 shares for $43 per share. Instructions Prepare journal entries for the purchase of the treasury stock and the three sales of treasury stock

3. (Taken from Rossiti chap-ex 1.3) Customers arrive to a gas station with two pumps. Each pump can reasonably accommodate a total of two cars. If all the space for the cars is full, potential customers will balk (leave without getting gas). What measures of performance will be useful in evaluating the effectiveness of the gas station? Describe how you would collect the inter-arrival and service times of the customers necessary to simulate this system. 4. (Taken from Rossiti chap-ex 2.3) Consider the multiplicative congruential generator with (a = 13, m = 64, and seeds X0 = 1,2,3,4) a) Does this generator achieve its maximum period for these parameters? Use Theorem 2.1 to justify your answer. b) Generate a period's worth of uniform random variables from each of the supplied seeds. 5. (Taken from Rossiti chap-ex 2.4) Consider the multiplicative congruential generator with (a = 11, m = 64, and seeds X0 = 1,2,3,4) 0.409 a) Does this generator achieve its maximum period for these parameters? Use Theorem 2.1 to justify your answer. b) Generate a period's worth of uniform random variables from each of the supplied seeds. 6. (Taken from Rossiti chap-ex 2.5) Analyze the following LCG: Xi =(11Xil +5)(mod(16)), X0 = 1 using Theorem 2.1. a) What is the maximum possible period length for this generator? Does this generator achieve the maximum possible period length? Justify your answer. b) Generate 2 pseudo-random uniform numbers for this generator. 7. (Taken from Rossiti chap-ex 2.10) Consider the following sequence of (0,1) random numbers: 0.943 0.398 0.372 0.943 0.204 0.794 0.498 0.528 0.272 0.899 0.294 0.156 0.102 0.057 0.398 0.400 0.997 Test if the sequence is distributed U (0, 1) using both a K-S test and a Chi-Squared test. 8. (Taken from Rossiti chap-ex 2.15) Suppose that customers arrive at an ATM via a Poisson process with mean 7 per hour. Determine the arrival time of the first 6 customers using the data given in Exercise 2.10 (starting with the first row). Use the inverse transformation method. 9. (Taken from Rossiti chap-ex 2.17) The service times for an automated storage and retrieval system has a shifted exponential distribution. It is known that it takes a minimum of 15 seconds for any retrieval. The parameter of the exponential distribution is = 45. Using the sequence of (0,1) random numbers in Exercise 2.10 (starting with the first row) generate 2 service times for this situation. 10. (Taken from Rossiti chap-ex 2.20) The interest rate for a capital project is unknown. An accountant has estimated that the minimum interest rate will between 2% and 5% within the next year. The accountant believes that any interest rate in this range is equally likely. You are tasked with generating interest rates for a cash flow analysis of the project. Using the sequence of (0,1) random numbers in Exercise 2.10 (starting with the first row) generate 2 independent interest rate values for this situation. 11. (Taken from Rossiti chap-ex 2.21) Customers arrive at a service location according to a Poisson distribution with mean 10 per hour. The installation has two servers. Experience shows that 60% of the arriving customers prefer the first server. By using the first row of (0,1) random numbers given in Exercise 2.10, determine the arrival times of the first three customers at each server. 12. (Taken from Rossiti chap-ex 2.25) Consider the following probability density function: 05:55 f(x) = 25 otherwise a) Derive an inverse transform algorithm for this distribution. b) Using the first row of random numbers from chap-ex 2.10 generate 2 random numbers using your algorithm. 0

I'VE ALREADY DONE THE EXPERIMENT, I JUST NEED HELP WITH THE LAST3 QUESTIONS.Create a text file that is at least 64 bytes long.Encrypt the file using the AES-128 cipher.Unfortunately, a single bit of the 30th byte in the encryptedfile got corrupted. You can achieve this corruption using a hexeditor.Decrypt the corrupted file (encrypted) using the correct key andIV. 1. How much information can you recover by decrypting thecorrupted file, if the encryption mode is ECB, CBC, CFB, or OFB,respectively?2. Please explain why.3. What are the implication of these differences?

A rocket accelerates upward from rest, due to the first stage, with a constant acceleration of a1 = 71 m/s2 for t1 = 26 s. The first stage then detaches and the second stage fires, providing a constant acceleration of a2 = 45 m/s2 for the time interval t2 = 119 s.1.  Enter an expression for the rocket's speed, v1, at time t1 in terms of the variables provided. 2. Enter an expression for the rocket's speed, v2, at the end of the second period of acceleration, in terms of the variables provided in the problem statement. 3. Using your expressions for speeds v1 and v2, calculate the total distance traveled, in meters, by the rocket from launch until the end of the second period of acceleration.  acceleration twoa,acceleration onea,

5.) Given A = (10v2) ( ax + az) and B = 3( ay + az) , express the projection of B on A as a %3D vector in the direction of A.