Find the apportionment under Adams’s method of the Margarita Congress described in Exercise 10. (Hint: Express the modified divisors in terms of percents of the total population and look for suitable divisors in the interval 0.81% to 0.82%.) 10. The small island nation of Margarita is made up of four islands: Aleta, Bonita, Corona, and ( A , B , C , and D for short ) . There are 125 seats in the Margarita Congress, which are apportioned among the islands according to their populations. The table 4-28 gives the island populations as percentages of the total population of Margarita. Table 4-28 Island A B C D Population Percentage 6.24 26.16 28.48 39.12
Find the apportionment under Adams’s method of the Margarita Congress described in Exercise 10. (Hint: Express the modified divisors in terms of percents of the total population and look for suitable divisors in the interval 0.81% to 0.82%.) 10. The small island nation of Margarita is made up of four islands: Aleta, Bonita, Corona, and ( A , B , C , and D for short ) . There are 125 seats in the Margarita Congress, which are apportioned among the islands according to their populations. The table 4-28 gives the island populations as percentages of the total population of Margarita. Table 4-28 Island A B C D Population Percentage 6.24 26.16 28.48 39.12
Find the apportionment under Adams’s method of the Margarita Congress described in Exercise 10. (Hint: Express the modified divisors in terms of percents of the total population and look for suitable divisors in the interval 0.81% to 0.82%.)
10. The small island nation of Margarita is made up of four islands: Aleta, Bonita, Corona, and
(
A
,
B
,
C
,
and
D
for short
)
. There are 125 seats in the Margarita Congress, which are apportioned among the islands according to their populations. The table 4-28 gives the island populations as percentages of the total population of Margarita.
7. [10 marks]
Let G = (V,E) be a 3-connected graph with at least 6 vertices. Let C be a cycle in G
of length 5. We show how to find a longer cycle in G.
(a) Let x be a vertex of G that is not on C. Show that there are three C-paths
Po, P1, P2 that are disjoint except at the shared initial vertex and only intersect
C at their final vertices.
(b) Show that at least two of P0, P1, P2 have final vertices that are adjacent along C.
(c) Combine two of Po, P1, P2 with C to produce a cycle in G that is longer than C.
1. Let X and Y be random variables and suppose that A = F. Prove that
Z XI(A)+YI(A) is a random variable.
30. (a) What is meant by the term "product measur"?
AND
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