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mathematics
contemporary mathematics

Contemporary Mathematics 1st Edition OpenStax - Solutions

Does the ranked-choice election violate the Condorcet criterion? Justify your answer.Use the table below. Number of Ballots 10 7 5 5 4 Candidate A 1 3 3 3 4 Candidate B 3 2 1 4 1 Candidate C 2 42 1 2 Candidate D 4 1 4 2 3
Can an election that fails the Condorcet criterion satisfy the majority criterion? Why or why not?Use the table below. Number of Ballots 10 7 5 5 4 Candidate A 1 3 3 3 4 Candidate B 3 2 1 4 1 Candidate C 2 42 1 2 Candidate D 4 1 4 2 3
Determine the winner of the election using the plurality method.Use the table below for the following exercise. Number of Ballots 49 48 3 Candidate A 1 3 3 Candidate B 2 1 2 Candidate C 3 2 1
Determine the winner by pairwise comparison.Use the table below for the following exercise. Number of Ballots 49 48 3 Candidate A 1 3 3 Candidate B 2 1 2 Candidate C 3 2 1
Is there a Condorcet candidate?Use the table below for the following exercise. Number of Ballots 49 48 3 Candidate A 1 3 3 Candidate B 2 1 2 Candidate C 3 2 1
Does this plurality election violate the Condorcet criterion? Justify your answer.Use the table below for the following exercise. Number of Ballots 49 48 3 Candidate A 1 3 3 Candidate B 2 1 2 Candidate C 3 2 1
If Candidate \(\mathrm{C}\) is removed from the ballot, which candidate wins by plurality?Use the table below for the following exercise. Number of Ballots 49 48 3 Candidate A 1 3 3 Candidate B 2 1 2 Candidate C 3 2 1
Does this plurality violate the IIA? Explain your reasoning.Use the table below for the following exercise. Number of Ballots 49 48 3 Candidate A 1 3 3 Candidate B 2 1 2 Candidate C 3 2 1
Determine the winner of the election using the ranked-choice method.Use the sample ballot summary below for the following exercise. Number of Ballots 16 20 24 8 Candidate A 1 3 2 1 Candidate B 3 1 4 4 Candidate C 4 2 1 2 Candidate D 2 4 3 3
Determine the winner by pairwise comparison.Use the sample ballot summary below for the following exercise Number of Ballots 16 20 24 8 Candidate A 1 3 2 1 Candidate B 3 1 4 4 Candidate C 4 2 1 2 Candidate D 2 4 3 3
Is there a Condorcet candidate?Use the sample ballot summary below for the following exercise Number of Ballots 16 20 24 8 Candidate A 1 3 2 1 Candidate B 3 1 4 4 Candidate C 4 2 1 2 Candidate D 2 4 3 3
Does this ranked-choice election violate the Condorcet criterion? Justify your answer.Use the sample ballot summary below for the following exercise Number of Ballots 16 20 24 8 Candidate A 1 3 2 1 Candidate B 3 1 4 4 Candidate C 4 2 1 2 Candidate D 2 4 3 3
If the four voters in the last column rank Candidate \(C\) ahead of \(A\), which candidate wins by the ranked-choice method?Use the sample ballot summary below for the following exercise Number of Ballots 16 20 24 8 Candidate A 1 3 2 1 Candidate B 3 1 4 4 Candidate C 4 2 1 2 Candidate D 2 4 3 3
Does this ranked-choice election violate the monotonicity criterion? Explain your reasoning.Use the sample ballot summary below for the following exercise Number of Ballots 16 20 24 8 Candidate A 1 3 2 1 Candidate B 3 1 4 4 Candidate C 4 2 1 2 Candidate D 2 4 3 3
Determine the winner of the election using the ranked-choice method.Use the sample ballot summary below for the following exercise. Number of Ballots 15 12 9 3 Candidate A 1 3 3 2 Candidate B 2 2 1 1 Candidate C 3 1 2 3
How could it be demonstrated that this ranked-choice election violates IIA?Use the sample ballot summary below for the following exercise Number of Ballots 15 12 9 3 Candidate A 1 3 3 2 Candidate B 2 2 1 1 Candidate C 3 1 2 3
Determine the winner of the election by the Borda method.Use the sample ballot summary below for the following exercise Number of Ballots 15 12 9 3 Candidate A 1 3 3 2 Candidate B 2 2 1 1 Candidate C 3 1 2 3
Does this Borda method election violate the IIA? Why or why not?Use the sample ballot summary below for the following exercise Number of Ballots 15 12 9 3 Candidate A 1 3 3 2 Candidate B 2 2 1 1 Candidate C 3 1 2 3
Does this Borda method election violate the monotonicity criterion? Why or why not?Use the sample ballot summary below for the following exercise Number of Ballots 15 12 9 3 Candidate A 1 3 3 2 Candidate B 2 2 1 1 Candidate C 3 1 2 3
Which candidate wins the pairwise election?Use the pairwise comparison matrix in the given figure for the following exercise. Opponent L M N Points Runner L wins ML 1 M wins LM 3 LN 2 NL 2 NM 1 N wins -2 MN 3 1 -|2
Determine the winner by pairwise comparison if \(\mathrm{N}\) were removed from the ballot.Use the pairwise comparison matrix in the given figure for the following exercise. Opponent L M N Points Runner L wins ML 1 M wins LM 3 LN 2 NL 2 NM 1 N wins -2 MN 3 1 -|2
Determine the winner by pairwise comparison if \(\mathrm{M}\) were removed from the ballot.Use the pairwise comparison matrix in the given figure for the following exercise. Opponent L M N Points Runner L wins ML 1 M wins LM 3 LN 2 NL 2 NM 1 N wins -2 MN 3 1 -|2
Does this pairwise election satisfy the IIA?Use the pairwise comparison matrix in the given figure for the following exercise. Opponent L M N Points Runner L wins ML 1 M wins LM 3 LN 2 NL 2 NM 1 N wins -2 MN 3 1 -|2
A parent has 25 pieces of candy to split among their four children. They will earn the candy based on how many minutes of chores they children did this week.Identify the states, the seats, and the state population (the basis for the apportionment) in the given scenarios.
The board of trustees of a college has recently approved the installation of 70 new emergency blue lights in five parking lots. The number of lights in each lot will be proportionate to the size of the parking lot, which is to be measured in acres.Identify the states, the seats, and the state
The reading coach at an elementary school has 52 prizes to distribute to students as a reward for time spent reading.Identify the states, the seats, and the state population (the basis for the apportionment) in the given scenarios.
"Top officials from Operation Warp Speed, the [U.S.] government's program to fast-track the development and delivery of COVID-19 vaccines, announced they've allocated 6.4 million doses of COVID-19 vaccines to states based on their total populations." (The Coronavirus Crisis, by Pien Huang, Shots
Refer to question 4, except suppose that the COVID-19 vaccine allocations were based on the most vulnerable population, residents aged 65 and over.Identify the states, the seats, and the state population (the basis for the apportionment) in the given scenarios.
The total population is 2,235 automobiles, and the number of seats is 14 warehouses.Use the given information to find the standard divisor to the nearest hundredth. Include the units.
The total population is 135 hospitals, and the number of seats is 200 respirators.Use the given information to find the standard divisor to the nearest hundredth. Include the units.
The state population is eight residents in a unit, and the standard divisor is 1.75 residents per parking space.Use the given information to find the standard quota. Include the units.
The state population is 52 ICU patients each week, and the number of seats is 6.5 patients per respirator.Use the given information to find the standard quota. Include the units.
The total population is 145 basketball players, the number of seats is 62 trophies, and the state population is 14 basketball players on Team Tigers.Use the given information to find the standard quota. Include the units.
The total population is 12 giraffes, the number of seats is nine water troughs, and the state population is three giraffes in Enclosure C.Use the given information to find the standard quota. Include the units.
Determine the \(F\) to \(T\) ratios for each department rounded to four decimal places as needed. What are the units?Use the table below, which shows student head count, class section, and total faculty in each of four college departments. Department (T) Student Head Count (M) Math (E) English (H)
Determine the \(C\) to \(F\) ratios for each department rounded to four decimal places as needed. What are the units?Use the table below, which shows student head count, class section, and total faculty in each of four college departments. Department (T) Student Head Count (M) Math (E) English (H)
What is the \(F\) to \(T\) ratio for the college overall? Include units. How does it compare to the \(F\) to \(T\) ratios for individual departments?Use the table below, which shows student head count, class section, and total faculty in each of four college departments. Department (T) Student Head
What is the overall \(C\) to \(F\) ratio? Include units. How does it compare to the \(C\) to \(F\) ratios for individual departments?Use the table below, which shows student head count, class section, and total faculty in each of four college departments. Department (T) Student Head Count (M) Math
Does there appear to be a constant \(F\) to \(T\) ratio? If so, what is the ratio? If not, what implications does this have about the different departments?Use the table below, which shows student head count, class section, and total faculty in each of four college departments. Department (T)
Does there appear to be a constant \(C\) to \(F\) ratio? If so, what is the ratio? If not, what implications does this have about the different departments?Use the table below, which shows student head count, class section, and total faculty in each of four college departments. Department (T)
If the departments are the states, the students are the population, and the faculty members are the seats, use the College Overall column to determine the standard divisor for the apportionment of the faculty rounded to two decimal places as needed. Include the units.Use the table below, which
If the departments are the states, the classes are the population, and the faculty members are the seats, use the Overall College column to determine the standard divisor rounded to two decimal places as needed. Include the units.Use the table below, which shows student head count, class section,
Use the standard divisor from question 18 to find the standard quota for each department rounded to two decimal places as needed. What are the units?Use the table below, which shows student head count, class section, and total faculty in each of four college departments. Department (T) Student Head
Use the standard divisor from question 19 to find the standard quota for each department rounded to two decimal places as needed.Use the table below, which shows student head count, class section, and total faculty in each of four college departments. Department (T) Student Head Count (M) Math (E)
Identify the states, the seats, and the state population (the basis for the apportionment) in this scenario.Wakanda, the domain of the Black Panther, King T'Challa has six fortress cities. In Wakandan, the word "birnin" means "fortress city." King T'Challa has found 111 Vibranium artifacts that
Find the standard divisor for the apportionment of the Vibranium artifacts. Round to the nearest tenth as needed. Include the units.Wakanda, the domain of the Black Panther, King T'Challa has six fortress cities. In Wakandan, the word "birnin" means "fortress city." King T'Challa has found 111
Find each birnin's standard quota for the apportionment of the Vibranium artifacts. Round to the nearest hundredth as needed. What are the units?Wakanda, the domain of the Black Panther, King T'Challa has six fortress cities. In Wakandan, the word "birnin" means "fortress city." King T'Challa has
Find the sum of the standard quotas. Is it reasonably close to the number of artifacts available for distribution?Wakanda, the domain of the Black Panther, King T'Challa has six fortress cities. In Wakandan, the word "birnin" means "fortress city." King T'Challa has found 111 Vibranium artifacts
Find the standard divisor for the apportionment of the vaccine doses by population using the estimate for the total U.S. population. Round to the nearest tenth as needed. Include the units.Suppose that 6.4 million doses of COVID-19 vaccine are to be distributed among U.S. states. The vaccines will
Find each state's standard quota for the apportionment of the vaccine doses. Round to the nearest tenth as needed. What are the units?Suppose that 6.4 million doses of COVID-19 vaccine are to be distributed among U.S. states. The vaccines will either be distributed based on the total state
Find the standard divisor for the apportionment of the vaccine doses by population age 65 and older using the estimate for the total U.S. population of people aged 65 and older. Round to the nearest tenth as needed. Include the units.Suppose that 6.4 million doses of COVID-19 vaccine are to be
Find each state's standard quota for the apportionment of the vaccine doses by total state population. Round to the nearest tenth as needed. What are the units?Suppose that 6.4 million doses of COVID-19 vaccine are to be distributed among U.S. states. The vaccines will either be distributed based
Compare the standard quota for each state based on the entire state population to the standard quota for each state based on the portion of the population age 65 and older. Which states would receive more doses of vaccine if the apportionment were based on the population of people age 65 and
Approximately 15.8 percent of U.S. residents are age 65 and older.a. Which of the five states listed have a percentage of residents age 65 and older greater than 15.8 percent?b. Which of the five states listed have a percentage of residents age 65 and older less than 15.8 percent?c. Explain the
Identify the states, the seats, and the state population (the basis for the apportionment) in this scenario.Children from five families-the Chorro family, the Eswaran family, the Javernick family, the Lahde family, and the Stolly family-joined a town-wide Easter egg hunt. When they returned with
Find the standard divisor for the apportionment of the Easter eggs. Round to five decimal places as needed. Include the units.Children from five families-the Chorro family, the Eswaran family, the Javernick family, the Lahde family, and the Stolly family-joined a town-wide Easter egg hunt. When
Find each family's standard quota for the apportionment of the Easter eggs. Round to the nearest hundredth as needed. What are the units?Children from five families-the Chorro family, the Eswaran family, the Javernick family, the Lahde family, and the Stolly family-joined a town-wide Easter egg
Find the sum of the standard quotas from exercise 34. Is the sum reasonably close to the number of Easter eggs available for distribution?Children from five families-the Chorro family, the Eswaran family, the Javernick family, the Lahde family, and the Stolly family-joined a town-wide Easter egg
Round the standard quota for each state in Scenario \(X\) using traditional rounding. Find the sum of the modified quotas. What is the difference between the sum and the house size?Use the standard quotas given in the table below. State A State B State C State D State E State F Total Seats Scenario
Round the standard quota for each state in Scenario \(Y\) using traditional rounding. Find the sum of the modified quotas. What is the difference between the sum and the house size?Use the standard quotas given in the table below. State A State B State C State D State E State F Total Seats Scenario
Round the standard quota for each state in Scenario \(Z\) using traditional rounding. Find the sum of the modified quotas. What is the difference between the sum and the house size?Use the standard quotas given in the table below. State A State B State C State D State E State F Total Seats Scenario
Find the lower quota for each state in Scenario Y. If each state is allocated its lower quota, how many seats remain to be allocated?Use the standard quotas given in the table below. State A State B State C State D State E State F Total Seats Scenario X 17.63 26.62 10.81 16.01 13.69 15.24 100
Find the lower quota for each state in Scenario \(X\). If each state is allocated its lower quota, how many seats remain to be allocated?Use the standard quotas given in the table below. State A State B State C State D State E State F Total Seats Scenario X 17.63 26.62 10.81 16.01 13.69 15.24 100
Find the lower quota for each state in Scenario Z. If each state is allocated its lower quota, how many seats remain to be allocated?Use the standard quotas given in the table below. State A State B State C State D State E State F Total Seats Scenario X 17.63 26.62 10.81 16.01 13.69 15.24 100
Find the upper quota for each state in Scenario \(X\) and determine how much the sum of the upper quotas exceeds the house size.Use the standard quotas given in the table below. State A State B State C State D State E State F Total Seats Scenario X 17.63 26.62 10.81 16.01 13.69 15.24 100 Scenario Y
Find the upper quota for each state in Scenario \(\mathrm{Y}\) and determine how much the sum of the upper quotas exceeds the house size.Use the standard quotas given in the table below. State A State B State C State D State E State F Total Seats Scenario X 17.63 26.62 10.81 16.01 13.69 15.24 100
Find the upper quota for each state in Scenario \(Z\) and determine how much the sum of the upper quotas exceeds the house size.Use the standard quotas given in the table below. State A State B State C State D State E State F Total Seats Scenario X 17.63 26.62 10.81 16.01 13.69 15.24 100 Scenario Y
Determine the Hamilton apportionment for Scenario \(\mathrm{Y}\).
Determine the Hamilton apportionment for Scenario \(X\).
Determine the Hamilton apportionment for Scenario \(Z\).
Does the apportionment resulting from method \(X\) satisfy the quota rule? Why or why not?Use the information in the table below, which gives standard and final quotas for Methods \(X, Y\), and \(Z\). State A State B State C State D State E Standard Quota 1.67 3.33 5.00 6.67 8.33 Method X 2 2 5 7 9
Does the apportionment resulting from method \(Z\) satisfy the quota rule? Why or why not?Use the information in the table below, which gives standard and final quotas for Methods \(X, Y\), and \(Z\). State A State B State C State D State E Standard Quota 1.67 3.33 5.00 6.67 8.33 Method X 2 2 5 7 9
Does the apportionment resulting from method \(Y\) satisfy the quota rule? Why or why not?Use the information in the table below, which gives standard and final quotas for Methods \(X, Y\), and \(Z\). State A State B State C State D State E Standard Quota 1.67 3.33 5.00 6.67 8.33 Method X 2 2 5 7 9
Modify the standard quota for each state using traditional rounding. Find the sum of the modified quotas. What is the difference between the sum and the house size?In the movie Black Panther, the hero lives in the fictional country of Wakanda. Imagine that 111 Vibranium artifacts must be
Find the standard lower quota for each state. If each state is allocated its lower quota, how many seats remain to be allocated?In the movie Black Panther, the hero lives in the fictional country of Wakanda. Imagine that 111 Vibranium artifacts must be distributed among the fortress cities, or
Find the standard upper quota for each state and determine how much the sum of the upper quotas exceeds the house size.In the movie Black Panther, the hero lives in the fictional country of Wakanda. Imagine that 111 Vibranium artifacts must be distributed among the fortress cities, or birnin, of
Use the Hamilton method to apportion the artifacts.In the movie Black Panther, the hero lives in the fictional country of Wakanda. Imagine that 111 Vibranium artifacts must be distributed among the fortress cities, or birnin, of Wakanda based on the population of each birnin. Use the population and
Find the modified lower quota for each state using a modified divisor of 2,000 . Is the sum of the modified quotas too high, too low, or equal to the house size?In the movie Black Panther, the hero lives in the fictional country of Wakanda. Imagine that 111 Vibranium artifacts must be distributed
Find the modified lower quota for each state using a modified divisor of 2,100 . Is the sum of the modified quotas too high, too low, or equal to the house size?In the movie Black Panther, the hero lives in the fictional country of Wakanda. Imagine that 111 Vibranium artifacts must be distributed
Use the Jefferson method to apportion the artifacts. Determine whether it is necessary to modify the divisor. If so, indicate the value of the modified divisor.In the movie Black Panther, the hero lives in the fictional country of Wakanda. Imagine that 111 Vibranium artifacts must be distributed
Does the Jefferson method result in an apportionment that satisfies or violates the quota rule in this scenario?In the movie Black Panther, the hero lives in the fictional country of Wakanda. Imagine that 111 Vibranium artifacts must be distributed among the fortress cities, or birnin, of Wakanda
Find the modified upper quota for each state using a modified divisor of 2,250. Is the sum of the modified quotas too high, too low, or equal to the house size?In the movie Black Panther, the hero lives in the fictional country of Wakanda. Imagine that 111 Vibranium artifacts must be distributed
Find the modified upper quota for each state using a modified divisor of 2,150. Is the sum of the modified quotas too high, too low, or equal to the house size?In the movie Black Panther, the hero lives in the fictional country of Wakanda. Imagine that 111 Vibranium artifacts must be distributed
Use the Adams method to apportion the artifacts. Determine whether it is necessary to modify the divisor. If so, indicate the value of the modified divisor.In the movie Black Panther, the hero lives in the fictional country of Wakanda. Imagine that 111 Vibranium artifacts must be distributed among
Does the Adams method result in an apportionment that satisfies or violates the quota rule in this scenario?In the movie Black Panther, the hero lives in the fictional country of Wakanda. Imagine that 111 Vibranium artifacts must be distributed among the fortress cities, or birnin, of Wakanda based
Which method of apportionment, Jefferson or Adams, is a resident of Birnin T'Chaka likely to prefer? Justify your answer.In the movie Black Panther, the hero lives in the fictional country of Wakanda. Imagine that 111 Vibranium artifacts must be distributed among the fortress cities, or birnin, of
Use the Webster method to apportion the artifacts. Determine whether it is necessary to modify the divisor. If so,indicate the value of the modified divisor.In the movie Black Panther, the hero lives in the fictional country of Wakanda. Imagine that 111 Vibranium artifacts must be distributed among
Does the Webster method result in an apportionment that satisfies or violates the quota rule in this scenario?In the movie Black Panther, the hero lives in the fictional country of Wakanda. Imagine that 111 Vibranium artifacts must be distributed among the fortress cities, or birnin, of Wakanda
Which of the four methods of apportionment from this section (Hamilton, Jefferson, Adams, or Webster) are the residents of Birnin S'Yan likely to prefer? Justify your answer.In the movie Black Panther, the hero lives in the fictional country of Wakanda. Imagine that 111 Vibranium artifacts must be
Modify the standard quota for each state using traditional rounding. Find the sum of the modified quotas. What is the difference between the sum and the house size?Children from five families-the Chorro family, the Eswaran family, the Javernick family, the Lahde family, and the Stolly family-joined
Find the standard lower quota for each state. If each state is allocated its lower quota, how many seats remain to be allocated?Children from five families-the Chorro family, the Eswaran family, the Javernick family, the Lahde family, and the Stolly family-joined a town Easter egg hunt. When they
Find the standard upper quota for each state, and determine how much the sum of the upper quotas exceeds the house size.Children from five families-the Chorro family, the Eswaran family, the Javernick family, the Lahde family, and the Stolly family-joined a town Easter egg hunt. When they returned
Use the Hamilton method to apportion the Easter eggs.Children from five families-the Chorro family, the Eswaran family, the Javernick family, the Lahde family, and the Stolly family-joined a town Easter egg hunt. When they returned with their baskets, they had 827 eggs! They decided to share their
Find the modified lower quota for each state using a modified divisor of 0.01800 . Is the sum of the modified quotas too high, too low, or equal to the house size?Children from five families-the Chorro family, the Eswaran family, the Javernick family, the Lahde family, and the Stolly family-joined
Find the modified lower quota for each state using a modified divisor of 0.01810 . Is the sum of the modified quotas too high, too low, or equal to the house size?Children from five families-the Chorro family, the Eswaran family, the Javernick family, the Lahde family, and the Stolly family-joined
Use the Jefferson method to apportion the Easter eggs. Determine whether it is necessary to modify the divisor. If so, indicate the value of the modified divisor.Children from five families-the Chorro family, the Eswaran family, the Javernick family, the Lahde family, and the Stolly family-joined a
Does the Jefferson method result in an apportionment that satisfies or violates the quota rule in this scenario?Children from five families-the Chorro family, the Eswaran family, the Javernick family, the Lahde family, and the Stolly family-joined a town Easter egg hunt. When they returned with
Find the modified upper quota for each state using a modified divisor of 0.0182 . Is the sum of the modified quotas too high, too low, or equal to the house size?Children from five families-the Chorro family, the Eswaran family, the Javernick family, the Lahde family, and the Stolly family-joined a
Find the modified upper quota for each state using a modified divisor of 0.01816 . Is the sum of the modified quotas too high, too low, or equal to the house size?Children from five families-the Chorro family, the Eswaran family, the Javernick family, the Lahde family, and the Stolly family-joined
Use the Adams method to apportion the Easter eggs. Determine whether it is necessary to modify the divisor. If so, indicate the value of the modified divisor.Children from five families-the Chorro family, the Eswaran family, the Javernick family, the Lahde family, and the Stolly family-joined a

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