4. Which of the following options is correct? Statement 1: The initial state of DFA is a subset of the initial state of NFA. Statement 2: The final state of NFA is a combination of only the final states of the DFA. a. Statement 1 is true and Statement 2 is true b. Statement 1 is true and Statement 2 is false c. Statement 1 can be true and Statement 2 is true d. Statement 1 is false and Statement 2 is also false None of the above e

4. Which of the following options is correct? Statement 1: The initial state of DFA is a subset of the initial state of NFA. Statement 2: The final state of NFA is a combination of only the final states of the DFA. a. Statement 1 is true and Statement 2 is true b. Statement 1 is true and Statement 2 is false c. Statement 1 can be true and Statement 2 is true d. Statement 1 is false and Statement 2 is also false None of the above e

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A starting lineup in basketball consists of two guards, two forwards, and a center. (a) A certain college team has on its roster four centers, five guards, four forwards, and one individual (X) who can play either guard or forward. How many different starting lineups can be created? [Hint: Consider lineups without X, then lineups with X as guard, then lineups with X as forward.] lineups (b) Now suppose the roster has 5 guards, 5 forwards, 4 centers, and 2 "swing players" (X and Y) who can play either guard or forward. If 5 of the 16 players are randomly selected, what is the probability that they constitute a legitimate starting lineup? (Round your answer to three decimal places.)
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2. A new pill is touted to improve the memory retention capability of teenagers aging 13 to 16 years old. To test this claim, twenty teenagers of the same age range are randomly picked to read the first two chapters of the book "Harry Potter and the Philosopher's Stone" after which they are asked to enumerate the number of verbs they remember from those chapters. Then they are given the new pill to be taken once daily for 7 days. At the end of 7 days, they are asked to read the same two chapters and enumerate the number of verbs they remember. The results are tabulated below: Number of verbs remembered Number of verbs remembered Тeen before taking the pill (X1) after taking the pill (X2) 1 6. 7 10 3 14 15 4 7 9. 8 12 4 10 7 5 7 8 3 9. 9 9 10 10 10 12 11 6. 12 8 9 13 4 10 14 8 8 15 9 13 16 6. 9. 17 11 13 18 7 6 19 20 8 At the 1% level of significance, what can you conclude? Assume normality of the differences.
1.
1. Imagine you are at a school with 100 lockers, all shut. • • • Suppose the first student goes along and opens every locker. The second student then shuts every other locker, beginning with locker number 2. The third student changes the state of every third locker, beginning with locker number 3. (If the locker is open, the student shuts it, and if the locker is closed, the student opens it.) The fourth student changes the state of every fourth locker, beginning with number 4. Imagine that this continues until the 100 students have followed the pattern with the 100 lockers. At the end, which lockers will be open and which will be closed? Which lockers have been switched the most often? How many lockers, and which ones, were touched exactly five times? Hint: You might initially think about the problem with a small number of lockers and then generalize if possible
15. Suppose that the members of a student governance committee will be selected from the 40 members of the student senate. There are 18 sophomores, 12 juniors and 10 seniors who are members of the student senate. In how many ways can the governance committee be selected, if it must be made up of 2 sophomores, 2 juniors and 3 seniors? Assume that each of the sophomores, each of the juniors and each of the seniors is equally likely to be selected for the committee. a. 339 b. 1211760 c. 2160 d. 18643560 e. 25920
A starting lineup in basketball consists of two guards, two forwards, and a center. a. A certain college team has on its roster three centers, four guards, four forwards, and one individual (X) who can play either guard or How many different starting lineups can be created? [ Hint. Consider lineups without X, then lineups with X as guard, then lineups with X as forward.] b. Now suppose the roster has 5guards, 5 forwards, 3 centers, and 2 "swing players"(X and Y) who can play either guard or forward. If 5 of the 15 players are randomly selected, what is the probability that they constitute a legitimate starting lineup?
1. Among 10 000 students, the result of a survey for face-to-face classes show thefollowing are ready: 52% are enrolled in Mathematics in the Modern World (MMW),45% are enrolled in Understanding the Self (UTS) and 60% are enrolled in ArtAppreciation (AA). In addition, 25% are enrolled in both MMW and UTS, 28% areenrolled in both AA and UTS and 30% are enrolled in both MMW and AA while 6%are not enrolled in any of the three subjects (a) Draw the Venn Diagram.(b) How many students ready for face-to-face classes are enrolledall the three subjects: (MMW, UTS, and AA)?(c) Find the number of students who are enrolled in only onesubject.(d) Find the number of students who are enrolled in at least twosubjects.