Suppose there exists a Facebook group of n profiles, where n > 2. Within this group,there are some friendship connections. A member of the group could be friends with any othermember, or none at all. Prove that, no matter how these friendships are distributed, there willbe at least two members with the same number of friends.

Answered: Image /qna-images/answer/0cf1dcec-1727-42c1-aa98-4f23128b1ba2.jpg

Answered: Suppose there exists a Facebook group…

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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From time to time, the UTM Human Resource (UTMHR) department observes various employees fortheir work productivity. Recently UTMHR wanted to check whether the four employees at theDepartment XYZ counters, serve on average the same number of customers per hour. The HR managerobserved each of the four employees for a certain number of hours. The following Table 5 gives thenumber of customers served by the four employees during each of the observed hours. employee a employee b employee c employee d 19 14 11 24 21 16 14 19 26 14 21 21 24 13 13 26 18 17 16 20 employee a employee b employee c employee d mean 21.6 14.8 15.0 22.0 s 3.4 ? 3.8 ? c) Find variance between sample,d) Find variance within sample, e) Calculate the test statistic, F.f) Determine the numerator and denominator.g) Find the critical value of F at the 5% significance level, and test the claim that the mean numberof customers served per hour by each of these four employees is…
From time to time, the UTM Human Resource (UTMHR) department observes various employees fortheir work productivity. Recently UTMHR wanted to check whether the four employees at theDepartment XYZ counters, serve on average the same number of customers per hour. The HR managerobserved each of the four employees for a certain number of hours. The following Table 5 gives thenumber of customers served by the four employees during each of the observed hours. employee a employee b employee c employee d 19 14 11 24 21 16 14 19 26 14 21 21 24 13 13 26 18 17 16 20 a) Define the hypothesis null, H0 and hypothesis alternative, H1.b) Given below are means and standard deviation for some of the employees. Calculate thestandard deviation for Employee B and D.
Which of the following is a benefit of a within-groups design over a between-groups design?
A certain company sends 50% of its overnight mail parcels via express mail service E1. Of theseparcels, 1% arrive after the guaranteed delivery time (denote the event late delivery by L). Supposethat 10% of the overnight parcels are sent via express mail service E2 and the remaining 40% are sentvia E3. Of those sent via E2 only 2% arrive late, whereas 5% of the parcels handled by E3 arrive late.a. Draw a tree diagram for this problem.b. If a record of an overnight mailing is randomly selected from the company’s file, what is theprobability that the parcel went via E2 and was late?c. What is the probability that a randomly selected parcel arrived on time?d. If a randomly selected parcel has arrived late, what is the probability that is was not sent via E1?
A certain company sends 50% of its overnight mail parcels via express mail service E1. Of theseparcels, 1% arrive after the guaranteed delivery time (denote the event late delivery by L). Supposethat 10% of the overnight parcels are sent via express mail service E2 and the remaining 40% are sentvia E3. Of those sent via E2 only 2% arrive late, whereas 5% of the parcels handled by E3 arrive late.a. Draw a tree diagram for this problem.b. If a record of an overnight mailing is randomly selected from the company’s file, what is theprobability that the parcel went via E2 and was late?c. What is the probability that a randomly selected parcel arrived on time?d. If a randomly selected parcel has arrived late, what is the probability that is was not sent via E1? part c and d please
With reference to Figure 15, verify that events A, B, C, and D are independent. Note that the region repre-senting A consists of two circles, and so do the regions representing B and C.
Given the following fictitious data 40% of all undergraduates at XYZ University are from Florida and60% from out of state. 22% are freshmen, and 78% are not. Out of all freshmen, 36% are from Florida,and 64% from out of state. Determine the probability a randomly selected XYZ University undergraduate:Suggestion: Make a tree diagram with the first branches being freshmen or not.a) is from Florida and a freshman. b) is from Florida and not a freshman.c) is from out of state and not a freshman. d) is a freshman given the student is from Florida.
Suppose that 50% of households in a certain city subscribe to the morning newspaper, 70% of the household subscribe to the afternoon newspaper, and 80% of the household subscribe to at least one of the two newspapers. What proportion of the households subscribe to both newspapers?
Suppose that for each prime p, Zp is the homomorphic image of agroup G. What can we say about |G|? Give an example of such agroup.
For the following relation on S = {1, 2, 3, 4, 5, 6}: p = {(1, 2), (1, 6), (2, 1), (3, 5), (4, 5), (6, 3), (6, 6)} Draw the directed graph and find the adjacency matrix.
Find six numbers, five of which are smaller than the mean of the group.
in a certain city, 60% of the heads of household own the house in which they reside, and 80% of the heads of the household have full-time employment when considering what percentage of heads of household both own their home and have a full-time job, a student estimates that 48% of heads of household fit both requirements, stating that (0.60) (0.80)=0.48. is this student correct in his approach?

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