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nature of mathematics

Questions and Answers of Nature Of Mathematics

The seniors at Weseltown High School are voting for where to go for their senior trip. They are deciding on Angel Falls (A), Bend Canyon (B), Cedar Lake (C), or Danger Gap (D). The results of the
Use this information to answer the questions in Problems 18-23.a. What does the notation (ADBC) mean?b. What does the " 8 " under (ADBC) mean? In voting among four candidates, the outcomes are
Find the standard divisor (to two decimal places) for the given populations and number of representative seats in Problems 15-22. Population 23,000,000 # Seats 125
In Problems 19-22, apportion the indicated number of representatives to three states, A, B, and C, using Hamilton's plan. Next, use the revised populations to reapportion the representatives. Decide
The seniors at Weseltown High School are voting for where to go for their senior trip. They are deciding on Angel Falls (A), Bend Canyon (B), Cedar Lake (C), or Danger Gap (D). The results of the
Use this information to answer the questions in Problems 18-23.a. If a person ranks \(B\) as his first choice, \(C\) as his second choice, \(\mathrm{D}\) as his third choice, and A last, how would
Find the standard divisor (to two decimal places) for the given populations and number of representative seats in Problems 15-22. Population 62,300,000 # Seats 225
In Problems 19-22, apportion the indicated number of representatives to three states, A, B, and C, using Hamilton's plan. Next, use the revised populations to reapportion the representatives. Decide
The seniors at Weseltown High School are voting for where to go for their senior trip. They are deciding on Angel Falls (A), Bend Canyon (B), Cedar Lake (C), or Danger Gap (D). The results of the
Use this information to answer the questions in Problems 18-23.a. How many possibilities are there for voter preferences with four candidates?b. Name those possibilities that have 0 voter
For the given year, find the standard quotas for the New York City boroughs given in Table 17.5 in Problems 23-28. Assume there are eight council seats.Table 17.51800 Year Total 1790 49 1800 81 1840
In Problems 23-26, apportion the indicated number of representatives to two states, A, and B, using Hamilton's plan. Next, recalculate the apportionment using Hamilton's plan for the three states,
The seniors at Weseltown High School are voting for where to go for their senior trip. They are deciding on Angel Falls (A), Bend Canyon (B), Cedar Lake (C), or Danger Gap (D). The results of the
Which of the following are examples of a dictatorship?a. Dad comes home with a surprise for the family—he just bought tickets for the family to vacation in Hawaii.b. The choice of selecting the
For the given year, find the standard quotas for the New York City boroughs given in Table 17.5 in Problems 23-28. Assume there are eight council seats.Table 17.51840 Year Total 1790 49 1800 81 1840
In Problems 23-26, apportion the indicated number of representatives to two states, A, and B, using Hamilton's plan. Next, recalculate the apportionment using Hamilton's plan for the three states,
The seniors at Weseltown High School are voting for where to go for their senior trip. They are deciding on Angel Falls (A), Bend Canyon (B), Cedar Lake (C), or Danger Gap (D). The results of the
For the given year, find the standard quotas for the New York City boroughs given in Table 17.5 in Problems 23-28. Assume there are eight council seats.Table 17.51900 Year Total 1790 49 1800 81 1840
a. How many different ways can a voter rank 3 candidates (no ties are allowed)?b. How many different ways can a voter rank 4 candidates (no ties are allowed)?c. How many different ways can a voter
In Problems 23-26, apportion the indicated number of representatives to two states, A, and B, using Hamilton's plan. Next, recalculate the apportionment using Hamilton's plan for the three states,
The seniors at Weseltown High School are voting for where to go for their senior trip. They are deciding on Angel Falls (A), Bend Canyon (B), Cedar Lake (C), or Danger Gap (D). The results of the
For the given year, find the standard quotas for the New York City boroughs given in Table17.5 in Problems 23-28. Assume there are eight council seats.Table 17.51940 Year Total 1790 49 1800 81 1840
a. If there are 10 voters and 5 candidates, how many total points would there be in a Borda count?b. If there are 20 voters and 4 candidates, how many total points would there be in a Borda count?c.
In Problems 23-26, apportion the indicated number of representatives to two states, A, and B, using Hamilton's plan. Next, recalculate the apportionment using Hamilton's plan for the three states,
The seniors at Weseltown High School are voting for where to go for their senior trip. They are deciding on Angel Falls (A), Bend Canyon (B), Cedar Lake (C), or Danger Gap (D). The results of the
How many different ways can a voter rank \(n\) candidates (no ties are allowed)?
For the given year, find the standard quotas for the New York City boroughs given in Table 17.5 in Problems 23-28. Assume there are eight council seats.Table 17.51990 Year Total 1790 49 1800 81 1840
The city district attorney has 30 litigators to be divided among three courts. The following table shows the schedule of the number of pending cases for each court.Apportion the 30 litigators using
The seniors at Weseltown High School are voting for where to go for their senior trip. They are deciding on Angel Falls (A), Bend Canyon (B), Cedar Lake (C), or Danger Gap (D). The results of the
It can be shown that\[1+2+3+\cdots+m=\frac{m(m+1)}{2}\]Use this formula to determine how many total points there would be in a Borda count with \(n\) voters and \(m\) candidates.
For the given year, find the standard quotas for the New York City boroughs given in Table 17.5 in Problems 23-28. Assume there are eight council seats.Table 17.52000 Year Total 1790 49 1800 81 1840
A city has 57 delegates to a Green World conference, and these delegates are to be apportioned according to the borough that they represent.Apportion the delegates to each borough using Hamilton's
The seniors at Weseltown High School are voting for where to go for their senior trip. They are deciding on Angel Falls (A), Bend Canyon (B), Cedar Lake (C), or Danger Gap (D). The results of the
Determine the winner, if any, using the voting methods in Problems 29-34.Majority rule In voting among three candidates, the outcomes are reported as: (CBA) (ACB) (BAC) (BCA) (CAB) 3 0 4 2 5 (ABC) 8
Consider the populations given in Problems 29-32.a. Find the standard divisor.b. Find the standard quota for each precinct.c. Total, rounding the standard quotas down.d. Find a modified divisor that
The city district attorney has 60 litigators to be divided among three courts. The following table shows the schedule of the number of pending cases for each court.Apportion the 60 litigators using
The seniors at Weseltown High School are voting for where to go for their senior trip. They are deciding on Angel Falls (A), Bend Canyon (B), Cedar Lake (C), or Danger Gap (D). The results of the
Determine the winner, if any, using the voting methods in Problems 29-34.Plurality method In voting among three candidates, the outcomes are reported as: (CBA) (ACB) (BAC) (BCA) (CAB) 3 0 4 2 5 (ABC)
Consider the populations given in Problems 29-32.a. Find the standard divisor.b. Find the standard quota for each precinct.c. Total, rounding the standard quotas down.d. Find a modified divisor that
The city district attorney has 60 litigators to be divided among three courts. The following table shows the schedule of the number of pending cases for each court.Decide if the Alabama paradox
A focus group of 33 people for \(A B C T V\) were asked to rank the government spending priorities of education \((\mathrm{E})\), military spending \((\mathrm{M})\), health care \((\mathrm{H})\),
Determine the winner, if any, using the voting methods in Problems 29-34.Borda count method In voting among three candidates, the outcomes are reported as: (CBA) (ACB) (BAC) (BCA) (CAB) 3 0 4 2 5
Consider the populations given in Problems 29-32.a. Find the standard divisor.b. Find the standard quota for each precinct.c. Total, rounding the standard quotas down.d. Find a modified divisor that
The city district attorney has 60 litigators to be divided among three courts. The following table shows the schedule of the number of pending cases for each court.Suppose that a fourth court is
A focus group of 33 people for \(A B C T V\) were asked to rank the government spending priorities of education \((\mathrm{E})\), military spending \((\mathrm{M})\), health care \((\mathrm{H})\),
Determine the winner, if any, using the voting methods in Problems 29-34.Hare method In voting among three candidates, the outcomes are reported as: (CBA) (ACB) (BAC) (BCA) (CAB) 3 0 4 2 5 (ABC) 8
Consider the populations given in Problems 29-32.a. Find the standard divisor.b. Find the standard quota for each precinct.c. Total, rounding the standard quotas down.d. Find a modified divisor that
The city district attorney has 60 litigators to be divided among three courts. The following table shows the schedule of the number of pending cases for each court. Court: Pending cases: A 209 B 769
A focus group of 33 people for \(A B C T V\) were asked to rank the government spending priorities of education \((\mathrm{E})\), military spending \((\mathrm{M})\), health care \((\mathrm{H})\),
Determine the winner, if any, using the voting methods in Problems 29-34.Pairwise comparison method In voting among three candidates, the outcomes are reported as: (CBA) (ACB) (BAC) (BCA) (CAB) 3 0 4
Consider the populations given in Problems 33-36.a. Find the standard divisor.b. Find the standard quota for each precinct.c. Total, rounding the standard quotas up.d. Find a modified divisor that
A focus group of 33 people for \(A B C T V\) were asked to rank the government spending priorities of education \((\mathrm{E})\), military spending \((\mathrm{M})\), health care \((\mathrm{H})\),
Determine the winner, if any, using the voting methods in Problems 29-34.Tournament method In voting among three candidates, the outcomes are reported as: (CBA) (ACB) (BAC) (BCA) (CAB) 3 0 4 2 5
Consider the populations given in Problems 33-36.a. Find the standard divisor.b. Find the standard quota for each precinct.c. Total, rounding the standard quotas up.d. Find a modified divisor that
A focus group of 33 people for \(A B C T V\) were asked to rank the government spending priorities of education \((\mathrm{E})\), military spending \((\mathrm{M})\), health care \((\mathrm{H})\),
Twelve board members are voting on after-meeting activities, and they are asked to check any that they might like. The outcome of their choices is shown here:What is the outcome using approval
Consider the populations given in Problems 33-36.a. Find the standard divisor.b. Find the standard quota for each precinct.c. Total, rounding the standard quotas up.d. Find a modified divisor that
A focus group of 33 people for \(A B C T V\) were asked to rank the government spending priorities of education \((\mathrm{E})\), military spending \((\mathrm{M})\), health care \((\mathrm{H})\),
Twelve board members are voting on admitting two new board members. They interview 5 candidates and vote " \(x\) " for an acceptable candidate and no vote for an unacceptable candidate. The outcome
Consider the populations given in Problems 33-36.a. Find the standard divisor.b. Find the standard quota for each precinct.c. Total, rounding the standard quotas up.d. Find a modified divisor that
In 1988 the 94th International Olympic Committee (IOC) met in Seoul to select the 1994 Winter Olympics site. The cities in the running were Anchorage (A), Lillehammer (L), Ostersund (T), and Sofia
In the 2014 race for the governor of Illinois, the state vote was as follows:Was there a majority winner in this election, and if so, who was it? B. Rauner P. Quinn C. Grimm TOTAL: 1,781,052
In the apportionment of the House of Representatives based on the 1790 census , there are 15 states. At that time, Maine was still considered part of Massachusetts. If Maine had been a separate
Packard-Hue manufactures testing equipment at four locations, and has just hired 300 new employees. Those employees are to be apportioned using production levels at the four locations according to
In 1988 the 94th International Olympic Committee (IOC) met in Seoul to select the 1994 Winter Olympics site. The cities in the running were Anchorage (A), Lillehammer (L), Ostersund (T), and Sofia
In the 2014 race for governor of Alaska, the vote was as follows:Was there a majority winner in this election, and if so, who was it? B. Walker S. Parnell C. Clift J. Myers TOTAL: 117,130 113,126
In the apportionment of the House of Representatives based on the 1790 census , there are 15 states. At that time, Maine was still considered part of Massachusetts. If Maine had been a separate
Packard-Hue manufactures testing equipment at four locations, and has just hired 300 new employees. Those employees are to be apportioned using production levels at the four locations according to
In 1993 the 101st International Olympic Committee met in Monaco to select the 2000 Winter Olympics site. The cities in the running were Beijing (B), Berlin (L), Istanbul (I), Manchester (M), and
Twelve people serve on a board and are considering three alternatives: A, B, and C. Here are the choices followed by vote:Determine the winner, if any, using the voting methods in Problems
In the apportionment of the House of Representatives based on the 1790 census , there are 15 states. At that time, Maine was still considered part of Massachusetts. If Maine had been a separate
Packard-Hue manufactures testing equipment at four locations, and has just hired 300 new employees. Those employees are to be apportioned using production levels at the four locations according to
In 1993 the 101st International Olympic Committee met in Monaco to select the 2000 Winter Olympics site. The cities in the running were Beijing (B), Berlin (L), Istanbul (I), Manchester (M), and
Twelve people serve on a board and are considering three alternatives: A, B, and C. Here are the choices followed by vote:Determine the winner, if any, using the voting methods in Problems
In the apportionment of the House of Representatives based on the 1790 census , there are 15 states. At that time, Maine was still considered part of Massachusetts. If Maine had been a separate
Packard-Hue manufactures testing equipment at four locations, and has just hired 300 new employees. Those employees are to be apportioned using production levels at the four locations according to
The U.S. president is elected with a vote of the Electoral College. However, if the vote were conducted using the Hare method, what would be the outcome? Use the data in Table 17.3, and assume that
Twelve people serve on a board and are considering three alternatives: A, B, and C. Here are the choices followed by vote:Determine the winner, if any, using the voting methods in Problems
Consider the following apportionment problem for College Town:Suppose each council member is to represent approximately 2,500 citizens. Use the apportionment plan requested in Problems 41-45 assuming
The English enrollments at five high schools in the Santa Rosa Unified School District are as follows:In Problems 42-47, suppose that 45 copies of an important instructional video are to be allocated
Article 7 of the French constitution states, "The President of the Republic is elected by an absolute majority of votes cast. If this is not obtained on the first ballot, a second round of voting
Twelve people serve on a board and are considering three alternatives: A, B, and C. Here are the choices followed by vote:Determine the winner, if any, using the voting methods in Problems 39-44.Hare
Consider the following apportionment problem for College Town:Suppose each council member is to represent approximately 2,500 citizens. Use the apportionment plan requested in Problems 41-45 assuming
The English enrollments at five high schools in the Santa Rosa Unified School District are as follows:In Problems 42-47, suppose that 45 copies of an important instructional video are to be allocated
A group of fun-loving people have decided to play a practical joke on one of their friends, but they can't decide which friend, Alice (A), Betty (B), or Connie (C). Their preferences are:Use this
Twelve people serve on a board and are considering three alternatives: A, B, and C. Here are the choices followed by vote:Determine the winner, if any, using the voting methods in Problems
Consider the following apportionment problem for College Town:Suppose each council member is to represent approximately 2,500 citizens. Use the apportionment plan requested in Problems 41-45 assuming
The English enrollments at five high schools in the Santa Rosa Unified School District are as follows:In Problems 42-47, suppose that 45 copies of an important instructional video are to be allocated
A group of fun-loving people have decided to play a practical joke on one of their friends, but they can't decide which friend, Alice (A), Betty (B), or Connie (C). Their preferences are:Use this
Twelve people serve on a board and are considering three alternatives: A, B, and C. Here are the choices followed by vote:Determine the winner, if any, using the voting methods in Problems
Consider the following apportionment problem for College Town:Suppose each council member is to represent approximately 2,500 citizens. Use the apportionment plan requested in Problems 41-45 assuming
The English enrollments at five high schools in the Santa Rosa Unified School District are as follows:In Problems 42-47, suppose that 45 copies of an important instructional video are to be allocated
A group of fun-loving people have decided to play a practical joke on one of their friends, but they can't decide which friend, Alice (A), Betty (B), or Connie (C). Their preferences are:Use this
A group of fun-loving people have decided to play a practical joke on one of their friends, but they can't decide which friend, Alice (A), Betty (B), or Connie (C). Their preferences are:Use this
Determine the winner, if any, using the voting methods in Problems \(45-50\).Seventeen people serve on a board and are considering three alternatives: A, B, and C. Here are the choices followed by
Consider the following apportionment problem for College Town:Suppose each council member is to represent approximately 2,500 citizens. Use the apportionment plan requested in Problems 41-45 assuming
The English enrollments at five high schools in the Santa Rosa Unified School District are as follows:In Problems 42-47, suppose that 45 copies of an important instructional video are to be allocated
The township of Bella Rosa is divided into two districts, uptown (pop. 16,980) and downtown (pop. 3,350) and is governed by 100 council members. Use this information in Problems 48-53.What is the
The fraternity \(\Sigma \Delta \Gamma\) is electing a national president, and there are four candidates: Alberto (A), Bate (B), Carl (C), and Dave (D). The voter preferences are:a. How many votes
Determine the winner, if any, using the voting methods in Problems \(45-50\).Seventeen people serve on a board and are considering three alternatives: A, B, and C. Here are the choices followed by

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