Mathematical Excursions (MindTap Course List)

4th Edition

ISBN: 9781305965584

Author: Richard N. Aufmann, Joanne Lockwood, Richard D. Nation, Daniel K. Clegg

Publisher: Cengage Learning

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Textbook Question

Chapter 4.1, Problem 11ES

Medical Care A hospital district consists of six hospitals. The district administrators have decided that 48 new nurses should be apportioned based on the number of beds in each of the hospitals. The following table shows the number of beds in each hospital.

Chapter 4.1, Problem 11ES, Medical Care A hospital district consists of six hospitals. The district administrators have decided

a. Determine the standard divisor. What is the meaning of the standard divisor in the context of this exercise?

b. Use the Hamilton method to determine the number of nurses to be apportioned to each hospital.

c. Use the Jefferson method to determine the number of nurses to be apportioned to each hospital.

d. How do the apportionment results produced using the Jefferson method compare with the results produced using the Hamilton method?

Expert Solution & Answer

Chapter 4 Solutions

Mathematical Excursions (MindTap Course List)

Ch. 4.1 - Verify this apportionment using the Jefferson...Ch. 4.1 - Find the apportionment that would have resulted if...Ch. 4.1 - Prob. 3EE Ch. 4.1 - Find the apportionment that would have resulted if...Ch. 4.1 - Explain how to calculate the standard divisor of...Ch. 4.1 - Teacher Aides A total of 25 teacher aides are to...Ch. 4.1 - In the Hamilton apportionment method, explain how...Ch. 4.1 - Prob. 4ES Ch. 4.1 - Governing Boards The following table shows how the...Ch. 4.1 - Forest Rangers The table below shows how the...

Ch. 4.1 - Sales Associates The table below shows the number...Ch. 4.1 - Hospital Interns The table below shows the number...Ch. 4.1 - House of Representatives The U.S. House of...Ch. 4.1 - College Enrollment The following table shows the...Ch. 4.1 - Medical Care A hospital district consists of six...Ch. 4.1 - What is the Alabama paradox?Ch. 4.1 - What is the population paradox?Ch. 4.1 - What is the new states paradox?Ch. 4.1 - 15. What is the Balinski-Young Impossibility...Ch. 4.1 - Apportionment of Projectors Consider the...Ch. 4.1 - Hotel Management A company operates four resorts....Ch. 4.1 - Prob. 18ES Ch. 4.1 - Management Scientific Research Corporation has...Ch. 4.1 - Prob. 20ES Ch. 4.1 - Elementary School Teachers The following table...Ch. 4.1 - Social Workers The following table shows the...Ch. 4.1 - Computer Usage The table below shows the number of...Ch. 4.1 - The population of Illinois increased by over...Ch. 4.1 - Prob. 25ES Ch. 4.1 - Prob. 26ES Ch. 4.1 - Computer Usage Use the Webster method to apportion...Ch. 4.1 - Demographics The table below shows the populations...Ch. 4.1 - Which of she following apportionment methods can...Ch. 4.1 - According to Michael Balinski and H. Peyton Young,...Ch. 4.1 - 31. What method is presently used to apportion the...Ch. 4.1 - Prob. 32ES Ch. 4.1 - John Quincy Adams, the sixth president of the...Ch. 4.1 - In the Huntington-Hill method of apportionment,...Ch. 4.1 - Prob. 35ES Ch. 4.2 - Using the Borda method of voting, which flavor of...Ch. 4.2 - Instead of using the normal Borda method, suppose...Ch. 4.2 - Prob. 3EE Ch. 4.2 - Suppose the Borda method used in Exercise I of...Ch. 4.2 - Prob. 5EE Ch. 4.2 - Can the assignment of points for first. Second,...Ch. 4.2 - Prob. 7EE Ch. 4.2 - Prob. 1ES Ch. 4.2 - Explain why the plurality voting system may not be...Ch. 4.2 - Prob. 3ES Ch. 4.2 - Explain how the plurality with elimination voting...Ch. 4.2 - Prob. 5ES Ch. 4.2 - Prob. 6ES Ch. 4.2 - Is there a best voting method? Is one method more...Ch. 4.2 - Explain why. if only two candidates are running,...Ch. 4.2 - Presidential Election The table below shows the...Ch. 4.2 - Breakfast Cereal Sixteen people were asked to rank...Ch. 4.2 - Cartoon Characters A kindergarten class was...Ch. 4.2 - Catering A 15-person committee is having lunch...Ch. 4.2 - Movies Fifty consumers were surveyed about their...Ch. 4.2 - Breakfast Cereal Use the Borda count method of...Ch. 4.2 - Prob. 15ES Ch. 4.2 - Catering Use the Borda count method of voting to...Ch. 4.2 - Class Election A senior high school class held an...Ch. 4.2 - Cell Phone Usage A journalist reviewing various...Ch. 4.2 - Baseball Uniforms A Little League baseball team...Ch. 4.2 - Radio Stations A number of college students were...Ch. 4.2 - Class Election Use plurality with elimination to...Ch. 4.2 - Prob. 22ES Ch. 4.2 - Campus Club A campus club has money left over in...Ch. 4.2 - Recreation A company is planning its annual summer...Ch. 4.2 - X-Men Movies Fans of the X-Men movies have been...Ch. 4.2 - Prob. 26ES Ch. 4.2 - School Mascot A new college needs to pick a moscot...Ch. 4.2 - Election Five candidates are running for president...Ch. 4.2 - Prob. 29ES Ch. 4.2 - Radio Stations Use the pairwise comparison method...Ch. 4.2 - Does the winner in Exercise tic satisfy the...Ch. 4.2 - 32. Does the winner in Exercise 12 satisfy the...Ch. 4.2 - Prob. 33ES Ch. 4.2 - Prob. 34ES Ch. 4.2 - Prob. 35ES Ch. 4.2 - Prob. 36ES Ch. 4.2 - Election Three candidates are running for mayor. A...Ch. 4.2 - Film Competition Three films have been selected as...Ch. 4.2 - 39. Election A campus club needs to elect four...Ch. 4.2 - Scholarship Awards The members of a scholarship...Ch. 4.2 - Another method of voting is to assign a weight. or...Ch. 4.2 - Prob. 42ES Ch. 4.2 - Prob. 43ES Ch. 4.3 - Using the data in Example 1 on page 211, list all...Ch. 4.3 - For the data in Example I on page 211, calculate...Ch. 4.3 - Prob. 3EE Ch. 4.3 - Prob. 4EE Ch. 4.3 - Create a voting system with three members that is...Ch. 4.3 - Prob. 6EE Ch. 4.3 - Prob. 7EE Ch. 4.3 - In the following exercises that involve weighted...Ch. 4.3 - In the following exercises that involve weighted...Ch. 4.3 - Prob. 3ES Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Prob. 8ES Ch. 4.3 - Prob. 9ES Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Prob. 13ES Ch. 4.3 - Prob. 14ES Ch. 4.3 - Music Education A music department Consists of a...Ch. 4.3 - Prob. 16ES Ch. 4.3 - Criminal Justice In a criminal trial, each of the...Ch. 4.3 - Criminal Justice In California civil court cases,...Ch. 4.3 - Identify any dictator and all dummies for each...Ch. 4.3 - Identify any dictator and all dummies for each...Ch. 4.3 - Prob. 21ES Ch. 4.3 - Prob. 22ES Ch. 4.3 - Football At the beginning of each football season,...Ch. 4.3 - Prob. 24ES Ch. 4.3 - Prob. 25ES Ch. 4.3 - Prob. 26ES Ch. 4.3 - Consider the weighted voting system { q:8,3,3,2 },...Ch. 4.3 - Prob. 28ES Ch. 4.3 - Prob. 29ES Ch. 4.3 - UN Security Council The United Nations C Security...Ch. 4 - Education The following table shows the...Ch. 4 - Airline Industry The following table shows the...Ch. 4 - Airline Industry The table below shows how the...Ch. 4 - 4. Education The following table shows the number...Ch. 4 - Technology A company has four offices. The...Ch. 4 - Automobile Sales Consider the apportionment of 27...Ch. 4 - Music Company MusicGalore.biz has offices in Los...Ch. 4 - Building Inspectors A city apportions 34 building...Ch. 4 - Prob. 9RE Ch. 4 - Prob. 10RE Ch. 4 - Corporate Security The Huntington-Hill...Ch. 4 - Essay Contest Four finalists are competing in an...Ch. 4 - Ski Club A campus ski club is trying o decide...Ch. 4 - Prob. 14RE Ch. 4 - Consumer Preferences A group of consumers were...Ch. 4 - Prob. 16RE Ch. 4 - Prob. 17RE Ch. 4 - Homecoming Queen Three high school students are...Ch. 4 - Prob. 19RE Ch. 4 - Prob. 20RE Ch. 4 - Prob. 21RE Ch. 4 - A weighted voting system for voters A. B. C. D....Ch. 4 - Prob. 23RE Ch. 4 - Prob. 24RE Ch. 4 - 25. Calculate the Banzhaf power indices for voters...Ch. 4 - Calculate the Banzhaf power indices for voters A,...Ch. 4 - Prob. 27RE Ch. 4 - Identify any dictator and all dummies for each...Ch. 4 - Four voters. A. B. C. and D. make decisions by...Ch. 4 - Postal Service The table below shows the number of...Ch. 4 - Computer Allocation The following table shows the...Ch. 4 - High School Counselors The following table shows...Ch. 4 - Prob. 4T Ch. 4 - Consumer Preference One hundred consumers ranked...Ch. 4 - Prob. 6T Ch. 4 - Exam Review A professor is preparing an extra...Ch. 4 - Prob. 8T Ch. 4 - Drama Department The four staff members. A, B,C,...Ch. 4 - Three voters. A. B. and C, make decisions by using...

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