Mathematics: A Practical Odyssey
8th Edition
ISBN: 9781305104174
Author: David B. Johnson, Thomas A. Mowry
Publisher: Cengage Learning
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Chapter 6.2, Problem 38E
To determine
To find:
The apportion of the bureau seats by using Hill-Huntington Method.
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The Republic of Tropicana is a small country consisting of five states (A, B, C, D, and E). The total population of Tropicana is 27.4 million. According to the Tropicana constitution, the seats in parliament (i.e. the legislature) are apportioned to the states according to their population. The table below shows each state's standard quota
A
B
C
D
E
Standard Quota
41.2
31.9
24.8
22.6
16.5
(a) Find the number of seats in the Tropicana Legislature: Answer
(b) Find the standard divisor: Answer
(c) Find the population of each state and fill in the table below. (Hint: Write the equation for the standard divisor. Can you use it to find populations?)
A
B
C
D
E
Population
Answer
Answer
Answer
Answer
Answer
(d) Find the apportionment under Adam's method of the republic of Tropicana parliament (i.e. legislature). (Hint: Look for suitable divisors in the interval 205,000 to 206,000.)
A gets Answer seats, B…
1. World's Richest. Each year, Forbes magazine publishes a list of the world's richest people. In
2009, the six richest people, their citizenship, and their wealth (to the nearest billion dollars)
Wealth ($ billion)
Citizenship
United States
Name
Willlam Gate (G)
Warren Buffett (B)
Carlos Slim Helu (H)
40
United States
38
Мexico
35
United States
Lawrence Ellison (E)
Karl Albrecht (A)
23
Sweden
22
Ingvar Kamprad (K)
Germany
22
a. Calculate the mean wealth, µ, of the six people.
For samples of size 2, construct a table and calculate the means for samples of size 2.
c. For a random sample of size 2, what is the chance that the sample mean will equal the
population mean?
d. For a random sample of size 2, determine the probability that the mean wealth of the two
people obtained will be within 2 (i.e., $2 billion) of the population mean. Interpret your result in
terms of percentages.
b.
Twenty sections of bilingual math courses, taught in both English and Spanish, are to be offered in introductory algebra, intermediate algebra, and liberal arts math.
The preregistration figures for the number of students planning to enroll in these bilingual sections are given in the following table. Use Webster's method with
d = 29.6 to determine how many bilingual sections of each course should be offered.
Course
Introductory Algebra
Intermediate Algebra
Liberal Arts Math
Enrollment
139
271
182
.....
Course
Introductory Algebra
Number of Apportioned Sections
(Type an integer.)
Course
Intermediate Algebra
Number of Apportioned Sections
9
(Type an integer.)
Course
Liberal Arts Math
Number of Apportioned Sections
(Type an integer.)
Chapter 6 Solutions
Mathematics: A Practical Odyssey
Ch. 6.1 - Four candidates, Alliotti, Baker, Cruz, and Daud,...Ch. 6.1 - Prob. 2ECh. 6.1 - Prob. 3ECh. 6.1 - Prob. 4ECh. 6.1 - Prob. 5ECh. 6.1 - Prob. 6ECh. 6.1 - Prob. 7ECh. 6.1 - Number of Ballots Cast 6 8 7 10 15 1st choice C C...Ch. 6.1 - Prob. 9ECh. 6.1 - Prob. 10E
Ch. 6.1 - Prob. 11ECh. 6.1 - Four candidates, Harrison H, Lennon L, McCartney...Ch. 6.1 - Prob. 13ECh. 6.1 - Five candidates, Fino F, Gempler G, Holloway H,...Ch. 6.1 - Prob. 15ECh. 6.1 - Prob. 16ECh. 6.1 - Prob. 17ECh. 6.1 - Prob. 18ECh. 6.1 - Prob. 19ECh. 6.1 - Prob. 20ECh. 6.1 - In an election, there are seven candidates. a....Ch. 6.1 - Prob. 22ECh. 6.1 - Prob. 23ECh. 6.1 - Prob. 24ECh. 6.1 - Prob. 25ECh. 6.1 - Prob. 26ECh. 6.1 - Prob. 27ECh. 6.1 - Prob. 28ECh. 6.1 - Prob. 29ECh. 6.1 - Prob. 30ECh. 6.1 - What is Arrows Impossibility Theorem?Ch. 6.2 - A small country consists of three states, A, B and...Ch. 6.2 - A small country consists of three states, A, B and...Ch. 6.2 - Suppose that the governors of three Middle...Ch. 6.2 - Suppose that the governors of three midwestern...Ch. 6.2 - Prob. 5ECh. 6.2 - Prob. 6ECh. 6.2 - Prob. 7ECh. 6.2 - Prob. 8ECh. 6.2 - A local school district contains four middle...Ch. 6.2 - A local school district contains four elementary...Ch. 6.2 - Prob. 11ECh. 6.2 - In J.R.R. Tolkiens Middle Earth, the regions in...Ch. 6.2 - Prob. 13ECh. 6.2 - Prob. 14ECh. 6.2 - Prob. 15ECh. 6.2 - Prob. 16ECh. 6.2 - Prob. 17ECh. 6.2 - Prob. 18ECh. 6.2 - Prob. 19ECh. 6.2 - Prob. 20ECh. 6.2 - Prob. 21ECh. 6.2 - Prob. 22ECh. 6.2 - Prob. 23ECh. 6.2 - Prob. 24ECh. 6.2 - Prob. 25ECh. 6.2 - Prob. 26ECh. 6.2 - Prob. 27ECh. 6.2 - Prob. 28ECh. 6.2 - Prob. 29ECh. 6.2 - Prob. 30ECh. 6.2 - Prob. 31ECh. 6.2 - Prob. 32ECh. 6.2 - Use the Hill-Huntington Method to determine how...Ch. 6.2 - Prob. 34ECh. 6.2 - Prob. 35ECh. 6.2 - Prob. 36ECh. 6.2 - Prob. 37ECh. 6.2 - Prob. 38ECh. 6.2 - Prob. 39ECh. 6.2 - Prob. 40ECh. 6.2 - Prob. 41ECh. 6.2 - Prob. 42ECh. 6.2 - Prob. 43ECh. 6.2 - Prob. 44ECh. 6.2 - Prob. 45ECh. 6.2 - Prob. 46ECh. 6.2 - Prob. 47ECh. 6.2 - Prob. 48ECh. 6.2 - What is apportionment?Ch. 6.2 - Prob. 50ECh. 6.2 - Prob. 51ECh. 6.2 - Prob. 52ECh. 6.2 - Prob. 53ECh. 6.2 - Prob. 54ECh. 6.2 - Prob. 55ECh. 6.2 - Prob. 56ECh. 6.2 - Prob. 57ECh. 6.2 - Since the founding of the United States, what...Ch. 6.2 - Prob. 59ECh. 6.2 - Prob. 60ECh. 6.3 - A small country consists of three states: A, B,...Ch. 6.3 - Prob. 2ECh. 6.3 - Prob. 3ECh. 6.3 - Prob. 4ECh. 6.3 - A small country consists of four states: A, B, C,...Ch. 6.3 - Prob. 6ECh. 6.3 - Prob. 7ECh. 6.3 - Prob. 8ECh. 6.3 - Prob. 9ECh. 6.3 - Prob. 10ECh. 6.3 - A small country consists of three states:A, B, and...Ch. 6.3 - Prob. 12ECh. 6.3 - Prob. 13ECh. 6.3 - Prob. 14ECh. 6.3 - Prob. 15ECh. 6.3 - What is the Alabama Paradox? Explain its meaning.Ch. 6.3 - Prob. 17ECh. 6.3 - Prob. 18ECh. 6.3 - Prob. 19ECh. 6.CR - Prob. 1CRCh. 6.CR - Prob. 2CRCh. 6.CR - Prob. 3CRCh. 6.CR - Prob. 4CRCh. 6.CR - Prob. 5CRCh. 6.CR - Prob. 6CRCh. 6.CR - Prob. 7CRCh. 6.CR - Prob. 8CRCh. 6.CR - Prob. 9CRCh. 6.CR - Prob. 10CRCh. 6.CR - Prob. 11CRCh. 6.CR - Prob. 12CRCh. 6.CR - Prob. 13CRCh. 6.CR - Prob. 14CRCh. 6.CR - Prob. 15CRCh. 6.CR - Prob. 16CRCh. 6.CR - Prob. 17CRCh. 6.CR - A small country consists of three states: A, B,...Ch. 6.CR - Prob. 19CRCh. 6.CR - Prob. 20CRCh. 6.CR - Prob. 21CRCh. 6.CR - Prob. 22CRCh. 6.CR - Prob. 23CRCh. 6.CR - Prob. 24CRCh. 6.CR - Prob. 25CRCh. 6.CR - Prob. 26CRCh. 6.CR - Prob. 27CRCh. 6.CR - Prob. 28CRCh. 6.CR - What is the New States Paradox? Explain its...Ch. 6.CR - Prob. 30CRCh. 6.CR - Prob. 31CRCh. 6.CR - Prob. 32CRCh. 6.CR - Prob. 33CRCh. 6.CR - Prob. 34CRCh. 6.CR - What method of appointment for the House of...
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- 1. World's Richest. Each year, Forbes magazine publishes a list of the world's richest people. In 2009, the six richest people, their citizenship, and their wealth (to the nearest billion dollars) Name Citizenship Wealth ($ billion) Willlam Gate (G) Warren Buffett (B) Carlos Slim Helu (H) Lawrence Ellison (E) Karl Albrecht (A) United States 40 United States 38 Мexico 35 United States 23 Sweden 22 Ingvar Kamprad (K) Germany 22 Calculate the mean wealth, µ, of the six people. а. b. For samples of size 2, construct a table and calculate the means for samples of size 2. С. For a random sample of size 2, what is the chance that the sample mean will equal the population mean? d. For a random sample of size 2, determine the probability that the mean wealth of the two people obtained will be within 2 (i.e., $2 billion) of the population mean. Interpret your result in terms of percentages.arrow_forwardA small country is comprised of four states, A, B, C, and D. The population of each state is given in the following table. State A B Total 144,000 208,000 432,000 496,000 1,280,000 3.6 5.2 10.8 12.4 Population Standard quota According to the country's constitution, the congress will have 32 seats, divided among the four states according to their respective populations. Determine each state's apportionment using Hamilton's method where the standard divisor is 40. Complete the table below. State Population Allocated seats B D 144,000 208,000| 432,000 496,000 5 (Type integers or simplified fractions.) Total 1,280,000 32 Elearrow_forward3. Using Jefferson plan method (JP), What leisure activities do you participate in? In the table below are five activities and the approximate number of participants (in millions) in each. EXERCISE SPORTS CHARITY WORK 150 90 85 HOME REPAIR COMPUTER 130 80 PARTS Suppose you wish to allocate $100 million to pro- mote leisure activities on the basis of the number of participants. A) Find the modified quota for each activity using the divisor 5.25. B) Find how much money should be apportioned to each activity using Jefferson's method.arrow_forward
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