Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
6th Edition
ISBN: 9780321914620
Author: Jeffrey O. Bennett, William L. Briggs
Publisher: PEARSON
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Chapter 12.D, Problem 20E
To determine
a. What would be the most likely distribution of House seats if districts were drawn randomly
b. What would be the maximum and minimum number of Republican representatives who could be sent to Congress if the districts could be drawn without restriction (unlimited gerrymandering).
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Assume {u1, U2, 13, 14} spans R³.
Select the best statement.
A. {U1, U2, u3} never spans R³ since it is a proper subset of a spanning set.
B. {U1, U2, u3} spans R³ unless one of the vectors is the zero vector.
C. {u1, U2, us} spans R³ unless one of the vectors is a scalar multiple of another vector in the set.
D. {U1, U2, us} always spans R³.
E. {U1, U2, u3} may, but does not have to, span R³.
F. none of the above
Refer to page 14 for calculating eigenvalues and eigenvectors of a matrix.
Instructions:
•
Compute the characteristic polynomial by finding the determinant of A - XI.
• Solve for eigenvalues and substitute them into (A - I) x = 0 to find the eigenvectors.
• Normalize the eigenvectors if required and verify your results.
Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440 AZF/view?usp=sharing]
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Chapter 12 Solutions
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
Ch. 12.A - Prob. 1QQCh. 12.A - Prob. 2QQCh. 12.A - Prob. 3QQCh. 12.A - Prob. 4QQCh. 12.A - Prob. 5QQCh. 12.A - Prob. 6QQCh. 12.A - Prob. 7QQCh. 12.A - Prob. 8QQCh. 12.A - 9. Study Table 12.5. Which candidate received the...Ch. 12.A - 10. What is the primary lesson of the preference...
Ch. 12.A - 1. What is majority rule? When can it definitively...Ch. 12.A - Prob. 2ECh. 12.A - What is a filibuster? What percentage of the vote...Ch. 12.A - Prob. 4ECh. 12.A - Prob. 5ECh. 12.A - Prob. 6ECh. 12.A - Prob. 7ECh. 12.A - Prob. 8ECh. 12.A - Prob. 9ECh. 12.A - Prob. 10ECh. 12.A - 11. Herman won a plurality of the vote, but Hanna...Ch. 12.A - Fred beat Fran using the point system (Borda...Ch. 12.A - 13. Candidate Reagan won the popular vote for the...Ch. 12.A - Prob. 14ECh. 12.A - Prob. 15ECh. 12.A - Prob. 16ECh. 12.A - Prob. 17ECh. 12.A - Prob. 18ECh. 12.A - Prob. 19ECh. 12.A - Presidential Elections. The following tables give...Ch. 12.A - Prob. 21ECh. 12.A - Presidential Elections. The following tables give...Ch. 12.A - 23. Super Majorities.
a. Of the 100 senators in...Ch. 12.A - 24. Super Majorities.
a. According to the bylaws...Ch. 12.A - Prob. 25ECh. 12.A - Prob. 26ECh. 12.A - Prob. 27ECh. 12.A - Prob. 28ECh. 12.A - Prob. 29ECh. 12.A - Prob. 30ECh. 12.A - 31—34. Interpreting Preference Schedules. Answer...Ch. 12.A - 31—34. Interpreting Preference Schedules. Answer...Ch. 12.A - 31—34. Interpreting Preference Schedules. Answer...Ch. 12.A - Prob. 34ECh. 12.A - Prob. 35ECh. 12.A - Prob. 36ECh. 12.A - Prob. 37ECh. 12.A - Prob. 38ECh. 12.A - Prob. 39ECh. 12.A - Prob. 40ECh. 12.A - Prob. 41ECh. 12.A - Prob. 42ECh. 12.A - Prob. 43ECh. 12.A - Condorcet Winner. If a candidate wins all...Ch. 12.A - 45. Condorcet Paradox. Consider the following...Ch. 12.A - 46. Pairwise Comparisons Question.
a. How many...Ch. 12.A - Prob. 47ECh. 12.A - Prob. 48ECh. 12.A - Prob. 49ECh. 12.A - Better Voting. Look for recent news about changes...Ch. 12.A - Prob. 51ECh. 12.A - Academy Awards. The election process for the...Ch. 12.A - Sports Polls. Most men’s and women’s major college...Ch. 12.A - Elections Around the World. Many countries have...Ch. 12.B - l. How many of the four fairness criteria (see p....Ch. 12.B - Prob. 2QQCh. 12.B - Prob. 3QQCh. 12.B - Prob. 4QQCh. 12.B -
5. Suppose that Berman is declared the winner of...Ch. 12.B - 6. Suppose that Freedman is declared the winner of...Ch. 12.B - 7. Notice that if Goldsmith dropped out, Freedman...Ch. 12.B - Prob. 8QQCh. 12.B - Which of the following is not an advantage of...Ch. 12.B - Prob. 10QQCh. 12.B - Briefly summarize each of the four fairness...Ch. 12.B - Prob. 2ECh. 12.B - What is approval voting? How is it different from...Ch. 12.B - Prob. 4ECh. 12.B - Prob. 5ECh. 12.B - Prob. 6ECh. 12.B - Prob. 7ECh. 12.B - Prob. 8ECh. 12.B - Plurality and Criterion 1. Explain in words why...Ch. 12.B - 10. Plurality and Criterion 2. Consider the...Ch. 12.B - 11. Plurality and Criterion 2. Devise a preference...Ch. 12.B - Prob. 12ECh. 12.B - Plurality and Criterion 4. Suppose the plurality...Ch. 12.B - Prob. 14ECh. 12.B - Runoff Methods and Criterion 1. Explain in words...Ch. 12.B - Prob. 16ECh. 12.B - Prob. 17ECh. 12.B - Sequential Runoff and Criterion 2. Devise a...Ch. 12.B - Prob. 19ECh. 12.B - Prob. 20ECh. 12.B - Prob. 21ECh. 12.B - Prob. 22ECh. 12.B - Point System and Criterion 1. Devise your own...Ch. 12.B - 24. Point System and Criterion 2. Suppose the...Ch. 12.B - 25. Point System and Criterion 2. Devise a...Ch. 12.B - Prob. 26ECh. 12.B - Prob. 27ECh. 12.B - Prob. 28ECh. 12.B - Prob. 29ECh. 12.B - Prob. 30ECh. 12.B - Prob. 31ECh. 12.B - Pairwise Comparisons and Criterion 4. Suppose the...Ch. 12.B - Prob. 33ECh. 12.B - Approval Voting. Suppose that Candidates A and B...Ch. 12.B - Prob. 35ECh. 12.B - Power Voting. Imagine that a small company has...Ch. 12.B - Prob. 37ECh. 12.B - Prob. 38ECh. 12.B - Prob. 39ECh. 12.B - Prob. 40ECh. 12.B - Prob. 41ECh. 12.B - Prob. 42ECh. 12.B - Prob. 43ECh. 12.B - Prob. 44ECh. 12.B - Prob. 45ECh. 12.B - Prob. 46ECh. 12.B - Prob. 47ECh. 12.B - Prob. 48ECh. 12.B - Prob. 49ECh. 12.B - Prob. 50ECh. 12.B - Prob. 51ECh. 12.B - 52. Swing Votes. Suppose that the following...Ch. 12.B - Prob. 53ECh. 12.B - Other Fairness Criteria. The fairness criteria...Ch. 12.B - Prob. 55ECh. 12.B - Power Voting and Coalitions. Use the Web...Ch. 12.B - General Voting Power. Find the news report about...Ch. 12.C - Prob. 1QQCh. 12.C - Prob. 2QQCh. 12.C - Prob. 3QQCh. 12.C - 4. Suppose that, in 2030, the census shows that...Ch. 12.C - 5. Consider a school district with 50 schools,...Ch. 12.C - 6. Consider the school district described in...Ch. 12.C - Prob. 7QQCh. 12.C - Prob. 8QQCh. 12.C - Prob. 9QQCh. 12.C - Prob. 10QQCh. 12.C - Prob. 1ECh. 12.C - Prob. 2ECh. 12.C - Prob. 3ECh. 12.C - What is the Alabama paradox? What other paradoxes...Ch. 12.C - Prob. 5ECh. 12.C - What is the quota criterion? Why are violations of...Ch. 12.C - 7. Briefly describe how Webster’s method and the...Ch. 12.C - 8. Explain why Webster’s method and the...Ch. 12.C - is the president of a large company with 12...Ch. 12.C - 10. Charlene is the head judge in a figure skating...Ch. 12.C - Prob. 11ECh. 12.C - Prob. 12ECh. 12.C - Prob. 13ECh. 12.C - Prob. 14ECh. 12.C - Prob. 15ECh. 12.C - Prob. 16ECh. 12.C - Prob. 17ECh. 12.C - 15-18: State Representation. The following table...Ch. 12.C - 19. Standard Quotas in Business. A large company...Ch. 12.C - 20. Standard Quota in Education. Capital...Ch. 12.C - Prob. 21ECh. 12.C - Prob. 22ECh. 12.C - Prob. 23ECh. 12.C - Prob. 24ECh. 12.C - Prob. 25ECh. 12.C - Prob. 26ECh. 12.C - Prob. 27ECh. 12.C - Prob. 28ECh. 12.C - Prob. 29ECh. 12.C - Prob. 30ECh. 12.C - 29-32: Jefferson's Method. Apply Jefferson's...Ch. 12.C - Jefferson's Method. Apply Jefferson's method to...Ch. 12.C - 33. Webster’s Method. Use Webster’s method to...Ch. 12.C - 34. Webster’s Method. Use Webster’s method to...Ch. 12.C - Prob. 35ECh. 12.C - Prob. 36ECh. 12.C - Prob. 37ECh. 12.C - Prob. 38ECh. 12.C - Comparing Methods. Assume 100 delegates are to be...Ch. 12.C - Prob. 40ECh. 12.C - Prob. 41ECh. 12.C - 39-42: Comparing Methods. Assume 100 delegates are...Ch. 12.C - 43-46: Non-House Apportionments. The following...Ch. 12.C - 43-46: Non-House Apportionments. The following...Ch. 12.C - 43-46: Non-House Apportionments. The following...Ch. 12.C - Prob. 46ECh. 12.C - Prob. 47ECh. 12.C - Prob. 48ECh. 12.C - Prob. 49ECh. 12.D - Prob. 1QQCh. 12.D - Prob. 2QQCh. 12.D - 3. If we compare results in presidential elections...Ch. 12.D - 4. In 2010, Republicans in North Carolina received...Ch. 12.D - Prob. 5QQCh. 12.D - Prob. 6QQCh. 12.D - Prob. 7QQCh. 12.D - Prob. 8QQCh. 12.D - Prob. 9QQCh. 12.D - Prob. 10QQCh. 12.D - What is redistricting, and when must it be done?Ch. 12.D - 2. How has the competitiveness of elections for...Ch. 12.D - 3. What is gerrymandering? Where does this term...Ch. 12.D - 4. Briefly describe how the drawing of boundaries...Ch. 12.D - What requirements must be met in drawing district...Ch. 12.D - Briefly describe two ideas for reforming the...Ch. 12.D - In the last election in my home state, 48% of the...Ch. 12.D - Prob. 8ECh. 12.D - Polls show that half voters in our state plan to...Ch. 12.D - Prob. 10ECh. 12.D - Prob. 11ECh. 12.D - Prob. 12ECh. 12.D - Redistricting and House Elections. The 2010 census...Ch. 12.D - Prob. 14ECh. 12.D - Redistricting and House Elections. The 2010 census...Ch. 12.D - Redistricting and House Elections. The 2010 census...Ch. 12.D - Redistricting and House Elections. The 2010 census...Ch. 12.D -
18-23: Average and Extreme Districts. Consider...Ch. 12.D - Prob. 19ECh. 12.D - Prob. 20ECh. 12.D - 18—23: Average and Extreme Districts. Consider the...Ch. 12.D - Average and Extreme Districts. Consider the...Ch. 12.D - Prob. 23ECh. 12.D - Prob. 24ECh. 12.D - Prob. 25ECh. 12.D - Prob. 26ECh. 12.D - Prob. 27ECh. 12.D - Prob. 28ECh. 12.D - 28—29: Drawing Districts Set III. Refer to Figure...Ch. 12.D - 30—32: Drawing Districts Set IV. Refer to Figure...Ch. 12.D - 30—32: Drawing Districts Set IV. Refer to Figure...Ch. 12.D - Prob. 32ECh. 12.D - Prob. 33ECh. 12.D - Prob. 34ECh. 12.D - Prob. 35ECh. 12.D - Prob. 36ECh. 12.D - Prob. 37ECh. 12.D - Prob. 38ECh. 12.D - Prob. 39ECh. 12.D - Prob. 40ECh. 12.D - Prob. 41ECh. 12.D - 42. Redistricting Procedures. Choose a state that...Ch. 12.D - 43. Reform Efforts. Investigate the current status...Ch. 12.D - 44. Mathematical Algorithms for Reform. Search for...
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