Mathematics All Around (6th Edition)
6th Edition
ISBN: 9780134434681
Author: Tom Pirnot
Publisher: PEARSON
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Chapter 10.3, Problem 36E
To determine
The method (Jefferson’s apportionment method or Adam’s apportionment method) that violates quota rule in apportioning 400 representatives among six states A, B, C, D, E and F.
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2. The acreage of five county parks in Hillsborough County is shown in
the table below. Suppose the county wishes to distribute 75 new park
rangers among these five parks.
Lake Park
E. G. Simmons
Lettuce Lake
Lithia Springs
Eureka Springs
600
470
240
160
30
a. Find the modified quota for each park using the divisor 20.5
b. Find the number of rangers that should be allocated to each park
using Adam's method.
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…
Chapter 10 Solutions
Mathematics All Around (6th Edition)
Ch. 10.1 - Sharpening your Skills In Exercises 1-6, use the...Ch. 10.1 - Sharpening your Skills In Exercises 1-6, use the...Ch. 10.1 - Sharpening your Skills In Exercises 1-6, use the...Ch. 10.1 - Sharpening your Skills In Exercises 1-6, use the...Ch. 10.1 - Sharpening your Skills In Exercises 1-6, use the...Ch. 10.1 - Prob. 6ECh. 10.1 - Sharpening Your Skills If the American Nurses...Ch. 10.1 - Prob. 8ECh. 10.1 - Sharpening your Skills Which state is more poorly...Ch. 10.1 - Prob. 10E
Ch. 10.1 - Sharpening your Skills Recall that on a 10-member...Ch. 10.1 - Sharpening your Skills Redo Exercise 11 for Aroco...Ch. 10.1 - Sharpening your Skills Apportioning...Ch. 10.1 - Sharpening your Skills Apportioning...Ch. 10.1 - Applying What Youve Learned The Alabama paradox....Ch. 10.1 - Applying What Youve Learned The Alabama paradox....Ch. 10.1 - Applying What Youve Learned The Alabama paradox...Ch. 10.1 - Prob. 18ECh. 10.1 - Prob. 19ECh. 10.1 - Prob. 20ECh. 10.1 - Prob. 21ECh. 10.1 - Prob. 25ECh. 10.1 - Prob. 26ECh. 10.1 - Prob. 27ECh. 10.1 - Prob. 28ECh. 10.2 - Prob. 1ECh. 10.2 - Prob. 2ECh. 10.2 - Prob. 3ECh. 10.2 - Prob. 4ECh. 10.2 - Prob. 5ECh. 10.2 - Prob. 6ECh. 10.2 - Prob. 7ECh. 10.2 - Prob. 8ECh. 10.2 - Prob. 9ECh. 10.2 - Prob. 10ECh. 10.2 - Prob. 11ECh. 10.2 - Prob. 12ECh. 10.2 - Prob. 13ECh. 10.2 - Prob. 14ECh. 10.2 - Prob. 15ECh. 10.2 - Prob. 16ECh. 10.2 - Prob. 17ECh. 10.2 - Prob. 18ECh. 10.2 - Prob. 19ECh. 10.2 - Prob. 20ECh. 10.2 - Prob. 21ECh. 10.2 - Prob. 22ECh. 10.2 - Prob. 23ECh. 10.2 - Prob. 24ECh. 10.2 - Prob. 25ECh. 10.2 - Prob. 26ECh. 10.2 - Prob. 27ECh. 10.2 - Prob. 28ECh. 10.2 - Prob. 29ECh. 10.2 - Prob. 30ECh. 10.2 - Prob. 31ECh. 10.2 - Prob. 32ECh. 10.2 - Prob. 33ECh. 10.2 - Prob. 34ECh. 10.3 - In Exercises 1-4, we give you a total population,...Ch. 10.3 - Prob. 2ECh. 10.3 - In Exercises 1-4, we give you a total population,...Ch. 10.3 - Prob. 4ECh. 10.3 - Prob. 5ECh. 10.3 - Use the Jefferson method to assign the seats on...Ch. 10.3 - Prob. 7ECh. 10.3 - Prob. 8ECh. 10.3 - Choosing representatives on a negotiations...Ch. 10.3 - Prob. 10ECh. 10.3 - Prob. 11ECh. 10.3 - Use the Webster method to apportion the members of...Ch. 10.3 - Prob. 13ECh. 10.3 - Prob. 14ECh. 10.3 - Prob. 15ECh. 10.3 - Prob. 16ECh. 10.3 - Prob. 17ECh. 10.3 - Prob. 18ECh. 10.3 - Prob. 19ECh. 10.3 - Prob. 20ECh. 10.3 - Prob. 21ECh. 10.3 - Prob. 22ECh. 10.3 - Prob. 23ECh. 10.3 - Use the Webster method to assign the number of...Ch. 10.3 - Prob. 25ECh. 10.3 - Prob. 26ECh. 10.3 - Prob. 27ECh. 10.3 - In Exercises 25-32, we use the Hamilton method to...Ch. 10.3 - Prob. 29ECh. 10.3 - Prob. 30ECh. 10.3 - In Exercises 25-32, we use the Hamilton method to...Ch. 10.3 - In Exercises 25-32, we use the Hamilton method to...Ch. 10.3 - Exercises 33-36Illustrate that the Jefferson and...Ch. 10.3 - Prob. 34ECh. 10.3 - Prob. 35ECh. 10.3 - Prob. 36ECh. 10.3 - Prob. 37ECh. 10.3 - Prob. 38ECh. 10.3 - Prob. 39ECh. 10.3 - Prob. 40ECh. 10.3 - Prob. 43ECh. 10.3 - Prob. 44ECh. 10.3 - Prob. 45ECh. 10.3 - Prob. 46ECh. 10.3 - Prob. 47ECh. 10.4 - Identify each situation as dealing with either...Ch. 10.4 - Identify each situation as dealing with either...Ch. 10.4 - Use the method of sealed bids to complete the...Ch. 10.4 - Prob. 4ECh. 10.4 - Use the method of sealed bids to complete the...Ch. 10.4 - Prob. 6ECh. 10.4 - Prob. 7ECh. 10.4 - Prob. 8ECh. 10.4 - Prob. 9ECh. 10.4 - Use the method of sealed bids to complete the...Ch. 10.4 - Prob. 11ECh. 10.4 - Prob. 12ECh. 10.4 - Prob. 13ECh. 10.4 - Prob. 14ECh. 10.4 - Prob. 15ECh. 10.4 - In Exercises 15 and 16, use the method of sealed...Ch. 10.4 - Prob. 17ECh. 10.4 - Prob. 18ECh. 10.4 - Prob. 19ECh. 10.4 - Prob. 20ECh. 10.4 - Prob. 21ECh. 10.4 - Prob. 22ECh. 10.4 - Prob. 23ECh. 10.4 - Prob. 24ECh. 10.4 - Prob. 25ECh. 10.4 - Prob. 26ECh. 10.4 - Prob. 27ECh. 10.4 - Prob. 28ECh. 10.CR - Prob. 1CRCh. 10.CR - Prob. 2CRCh. 10.CR - Prob. 3CRCh. 10.CR - Prob. 4CRCh. 10.CR - Prob. 5CRCh. 10.CR - Prob. 6CRCh. 10.CR - Prob. 7CRCh. 10.CR - Prob. 8CRCh. 10.CR - Prob. 9CRCh. 10.CR - Prob. 10CRCh. 10.CR - Prob. 11CRCh. 10.CR - Prob. 12CRCh. 10.CR - Prob. 13CRCh. 10.CR - Prob. 14CRCh. 10.CR - Prob. 15CRCh. 10.CR - Prob. 16CRCh. 10.CT - What is the Alabama paradox?Ch. 10.CT - Suppose state C has a population of 1,640,000 and...Ch. 10.CT - The Metropolitan Community College Arts Council...Ch. 10.CT - Prob. 4CTCh. 10.CT - Suppose that Arizona has a population of 5.23...Ch. 10.CT - Prob. 6CTCh. 10.CT - Prob. 7CTCh. 10.CT - Prob. 8CTCh. 10.CT - Prob. 9CTCh. 10.CT - Prob. 10CTCh. 10.CT - Prob. 11CTCh. 10.CT - Prob. 12CTCh. 10.CT - Prob. 13CTCh. 10.CT - Prob. 14CTCh. 10.CT - Three brothersLarry, Moe, and Curlyare dissolving...
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- Consider the apportionment problem for College Town. North : 5,500 , South : 4,500 , East : 7,600, West : 7,400 Suppose each council member is to represent approximately 2,100 citizens. Use Jefferson's plan assuming there must be 10 representatives.arrow_forwardThe apportionment method that requires rounding the standard quota down to the lower quota is called X a. Jefferson's method b. Adams' method c. Webster's method d. Hamilton's method Question 11 A group called Physicians Medical Organization provides 85 medical clinics. The organization has hired 85 doctors. Since the clinics do not serve all the same number of patients, the organization decides to apportion the 85 doctors based on the number of patients who visit each clinic in a given week. Clinic A В C E Total Patients 350 221 205 233 250 1259 Use Hamilton's method for apportionment to determine how many doctors each clinic receives. a. A: 24 doctors, B: 15 doctors, C: 14 doctors, D: 15 doctors, E: 17 doctors X b. A: 23 doctors, B: 14 doctors, C: 13 doctors, D: 15 doctors, E: 16 doctors C. A: 24 doctors, B: 14 doctors, C: 14 doctors, D: 16 doctors, E: 17 doctors d. A: 24 doctors, B: 15 doctors, C: 14 doctors, D: 16 doctors, E: 16 doctorsarrow_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
- Assume that 100 representatives must be apportioned to the following set of states with the given populations. Determine the number of representatives for each state using Hamilton’s method. Then assume that the number of representatives is increased to 101. Determine the new number of representatives for each state using Hamilton’s method. State whether the change in total number of representatives results in the Alabama paradox. State A: 950; State B: 670; State C: 246arrow_forwardQUESTION 12 Which method of apportionment always satisfies the quota condition? OA. Hill-Huntington B. Jefferson OC. Hamilton OD. Websterarrow_forwardA small country consists of three states, whose populations are listed below.A: 6,000 B: 6,000 C: 2,000a. If the legislature has 10 seats, use Hamilton’s method to apportion the seats.b. If the legislature grows to 11 seats, use Hamilton’s method to apportion the seats.c. Which apportionment paradox does this illustrate?arrow_forward
- Use Webster's method of apportionment to solve the following problem. 2. Suppose a nation has 5 states, with populations shown in the chart below. The representative body had 150 seats. Find: the standard divisor, the modified divisor, and the distribution of representatives to each state. Then complete the table. Round all standard and modified quotas to 7 decimal places if needed. You can use a spreadsheet to help you figure out an answer or calculate using a calculator. Representative Seats 150 State Population Standard Rounded Modified Modified Quotas Quotas Quotas Rounded Quotas A 1,895,500 1,234,500 845,200 В C 399,120 500,680 4,875,000 D E Total Standard Divisor Modified Divisorarrow_forwardA small country is comprised of five states, A, B, C, D, and E. The population of each state is given in the following table. Congress will have 58 seats divided among the five states according to their respective populations. Use Jefferson's method with d = 32,920 to apportion 58 seats. State A B D E Population 138,432 218,282 401,379 524.915 714,634 ..... State Number of Apportioned Seats A (Type an integer.)arrow_forwardSC Find the apportionment asked for. Show your work either by hand or Microsoft Excel (attach your work). 9) A small city has 50 police officers to be apportioned among 8 precincts based on the population of each precinct. The populations are given in the following table. Precinct total 25,95 4 6. 7 8 Population 2250 3800 3225 1800 4900 4025 2775 3175 a) Find the apportionment for each state using Hamilton's method. A COnd dour b) Find the apportionment for each state using Jefferson's method. round down to nearest round up nearest in c) Find the apportionment for each state using Webster's method. round UD d) Find the apportionment for each state using Adams' method.arrow_forward
- Consider the desired number of seats and the populations given below. 12 seats Population 1st Precinct 33,000 25,000 2nd Precinct 3rd Precinct 12,000 4th Precinct 49,000 TOTAL 119,000 (a) Find the standard divisor. (Round your answers to two decimal places.) (b) Find the standard quota for each precinct. (Round your answers to two decimal places.) 1st Precinct 2nd Precinct 3rd Precinct 4th Precinct (c) Find the total of the standard quotas, rounding the standard quotas down. (d) Find a modified divisor that will give modified quotas to produce the desired number of seats when the standard quotas are rounded down.arrow_forwardUse Webster's method of apportionment to solve the following problem. 2. Suppose a nation has 5 states, with populations shown in the chart below. The representative body had 150 seats. Find: • the standard divisor, the modified divisor, and • the distribution of representatives to each state. Then complete the table. Round all standard and modified quotas to 7 decimal places if needed. You can use a spreadsheet to help you figure out an answer or calculate using a calculator. Representative Seats State A B C Total Standard Divisor Modified Divisor 150 Population 1,895,500 1,234,500 845,200 399.120 500.680 4,875,000 Standard Rounded Modified Modified Quotas Quotas Rounded Quotas Quotasarrow_forwardThere is a country with six states. There are 300 states in the legislature, and the populations of the states are given in the table below. State A B C E F Population 14.25% 53.75% 5.35% 16.5% 6.25% 3.9% Under Webster's method, the apportionments to each state are State A: seats, State B: seats, State C: seats, State D: seats, State E: State F:arrow_forward
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