A project consists of 8 activities. The activity completion times and the precedence relationships are as follows: Activity. Completion time Days. immediate predecessor activities.

A. 5 -
B. 7 -
C. 6 -
D. 3 A
E. 4 B, C
F. 2 C
G. 6 A, D
H. 5 E, F

1. Draw the network diagram using AON model notations:

2. What is the critical path?

3. Calculate: Early Start, Early finish, Late start, Late finish, slack, critical path.

4. What is the minimum time to complete the projects?

1. If activity E is delayed by 3 days how is the project completion time affected? Why is this the case?

2. If activity F is delayed by 3 days how is the project completion time affected? Why is this the case? Will the critical path change, why or why not?

3. If you want to shorten (crash) the overall time of this project, how do you pick which activity to shorten? What information, if any, do you need?

4. Once you shorten (crash) an activity, do you need to redo the AON, yes or no? Why or why not?

Show that there is a language a ⚆ {0, 1} â— with the following properties: 1. for all x â a, |x| ≤ 5. 2. no dfa with fewer than 9 states recognizes a. hint: you don’t have to define a explicitly; just show that it has to exist. count the number of languages satisfying (1) and the number of dfas satisfying (2), and argue that there aren’t enough dfas to recognize all those languages. to count the number of languages satisfying (1), think about writing down all the strings of length at most 5, and then to define such a language, you have to make a binary decision for each string about whether to include it in the language or not. how many ways are there to make these choices? to count the number of dfas satisfying (2), consider that a dfa behaves identically even if you rename all the states, so you can assume without loss of generality that any dfa with k states has the state set {q1, q2, . . , qk}. now think about how to count how many ways there are to choose the other four parts of the dfa.

What is a rush associated with alcohol?

One subtask in the game is to roll the dice. explain why is roll the dice an abstraction.