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mathematics
contemporary mathematics

Questions and Answers of Contemporary Mathematics

Suppose the constant ratio of \(A\) to \(B\) is 0.75 . Student 1 says the ratio of \(A\) to \(B\) is \(\frac{4}{3}\) Student 2 says the ratio of \(B\) to \(\mathrm{A}\) is \(\frac{3}{4}\).
Student 1 says that Standard Divisor \(=\frac{\text { House Size }}{\text { Total Population }}\). Student 2 says that Standard Divisor \(=\frac{\text { Sum of the State Populations }}{\text { Total
Student 1 says that State's Standard Divisor \(=\frac{\text { Total Population }}{\text { State's Standard Quota }}\).Student 2 says that State's Standard Quota \(=\frac{\text { State Population
Student 1 says that State's Standard Quota \(=\) State Population \(\div \frac{\text { Total Population }}{\text { House Size }}\). Student 2 says that State's Standard Quota \(=\frac{\text { State
Which of the four apportionment methods discussed in this section does not use a modified divisor?
Which of the four apportionment methods discussed in this section satisfies the quota rule?
Which of the four apportionment methods discussed in this section is biased toward states with larger populations?
Which of the four apportionment methods discussed in this section is biased toward states with smaller populations?
Which of the four apportionment methods discussed in this section begin the apportionment with a state's upper quota and adjust down?
Which of the four apportionment methods discussed in this section begin the apportionment with a state's lower quota and adjust up?
Which of the four apportionment methods discussed in this section use traditional rounding?
Does the change from a standard divisor to a modified divisor tend to change the number of seats for larger or smaller states more?
A city purchased five new firetrucks and apportioned them among the existing fire stations. Although your neighborhood fire station has the same proportion of the city's firetrucks as before the new
The school resources officers in a county were reapportioned based on the most recent census. The number of students at Chapel Run Elementary went up while the number of students at Panther Trail
The standard quota for States A, B, and C are 1.19, 2.73, and 5.71 respectively. State A received 1 seat, State B received 3 seats, and State \(C\) received 4 seats.A scenario is given. Determine
A corporation that owns several hospitals purchased an additional hospital, causing the doctor to patient ratio to decrease.A scenario is given. Determine whether the scenario is an example of a
When the city of Cocoa annexed an adjacent unincorporated community, the number of seats on the city council was increased to maintain the standard ratio of citizens to seats, but one existing
A reapportionment occurs because the populations of the states change, and the house size remains the same.A type of scenario is described. Indicate which paradox could arise in a scenario of this
A reapportionment occurs because the house size increases, and the populations of the states remain the same.A type of scenario is described. Indicate which paradox could arise in a scenario of this
A reapportionment occurs because an additional state is added to the union, the populations of the original states remain the same, and the house size is increased to correspond to the population of
Refer back to Table 11.1. Did any single candidate secure the majority of popular votes? Candidate (Party Label) Popular Vote Total Al Gore (Democrat) 50,999,897 George W. Bush (Republican)
Refer again to Table 11.1. In the 2000 U.S. presidential election, which candidate had a plurality of popular votes? Candidate (Party Label) Popular Vote Total 50,999,897 Al Gore (Democrat) George W.
A condominium association elects a new president every two years by a two-round system of voting. If none of the candidates receive a majority, the association charter states that the top two
The five members of the Chionilis family-Annette, Rene, Seema, Titus, and Galen-have decided to get takeout for dinner. They are trying to decide on a restaurant. The options are Rainbow China, Dough
Refer to the table below containing voters' preference rankings to answer the following questions.1. How many voters ranked the options in the following order: Option A in fourth place, Option B in
Let's review the kindergarten class color preferences again, and this time determine which color would be selected based on these results using the ranked-choice method. Number of Ballots 46 Red 4 7
Let's review the ballots from the kindergarten class again, as shown in the table below. This time, let's determine the Borda score received by the color purple. Number of Ballots 4 6 4 7 Red 26 25
Use the table below, which displays a sample preference summary, to answer the questions that follow.1. Use the ranked-choice voting method to determine the winner of the election.2. Use the Borda
Consider the summary of ranked ballots shown in the table below. Determine the winner of an election using the pairwise comparison method.1. Construct a pairwise comparison matrix for the sample
Suppose that three people are playing the game Rock, Paper, Scissors. On the count of three, each person shows a hand signal for rock, paper, or scissors. Each hand signal beats another hand signal.
1. Suppose there is an election with five candidates-A, B, C, D, and E-and that Candidate \(C\) is a Condorcet candidate. How many points did Candidate \(\mathrm{C}\) win?2. What is the greatest
Suppose that Person A/B/C were just about to give up on their game of Rock, Paper, Scissors when they were joined by Person D who reminded them that their updated version, Rock, Paper, Scissors,
The eight members of the Chionilis family-Annette, Rene, Seema, Titus, Galen, Elena, Max and Demitri-have another decision to make. Approval voting worked out nicely the last time. They are going to
Because the vote counts for George W. Bush and Al Gore differed by only 537 votes, many Democrats blamed Ralph Nader and the Green Party for their loss. Let's consider how the election results might
In the future, humans have explored distant solar systems and found three habitable planets which could be colonized. Since it will take all available resources to colonize one planet, humans must
It's final exams week and seven college students are hungry. They must get food, but from which drive thru? Their preferences are listed in the table below. The majority have listed McDonald's as
Those seven college students are hungry again! Their preferences haven't changed, as shown below. Let's calculate if the results change when we use different voting methods.1. Which restaurant is the
A survey asked a random sample of 100 people in the United States to rank their priorities for spending their tax refund. The options were (V) go on vacation, (S) put into savings, (D) pay off debt,
Let's return to the survey about tax refund spending from Example 11.18. We know that the Condorcet criterion applies because Option D, "Pay off debt," is a Condorcet candidate, which wins every
The local animal shelter is having a vote-by-donation charity event. For a \(\$ 10\) donation, an individual can complete a ranked ballot indicating their favorite large dog breed: standard poodle,
Earlier, we discovered that the summary of ranked ballots shown in the table below results in the pairwise comparison matrix in Figure 11.12. Use this information to answer the questions.1. Determine
Suppose that 30 students in a class are going to vote on whether to have apple, blueberry, or cherry pie. Use the summary of ranked ballots in below to answer each question.1. Determine the winner of
The NBC sitcom The Office ran for nine years and has been one of the most popular streamed television shows of all time. One of the trademarks of the show was that characters would often break the
The following table provides a comparison of the number of faculty members in each department at a particular college to the student head count in that department and the number of class sections in
Refer to the information given in Example 11.24 .1. If there are 32 class sections each semester in the Fine Art department, and the same ratio is used to determine the number of faculty members, how
Table 11.4 contains a list of the five U.S. states with the greatest number of representatives in the U.S. House of Representatives, along with the population of that state in 2021. Use the
As of this writing, the Census.gov website U.S. Population clock showed a population of 332,693,997. There are 435 seats in the U.S. House of Representatives. Find the standard divisor rounded to the
The public schools in a certain county have been allotted 349 school resource officers to be distributed among 327 public schools attended by approximately 271,500 students.1. Identify the states,
Example 27 outlined that the Census.gov website U.S. Population clock showed a population of \(330,147,881\), there are 435 seats in the U.S. House of Representatives, and the standard divisor was
The science department of a high school has received a grant for 34 laptops. They plan to apportion them among their six classrooms based on each classroom's student capacity. Use the values in the
The board of trustees of a college has recently approved the installation of 70 new emergency blue lights in three parking lots. The number of lights in each lot will be proportionate to the size of
In 2015, the U.S. Air Force had a fleet of approximately 281 A-10C Thunderbolt II aircraft. Suppose that the Air Force administration wanted to distribute 27 aircrafts across six bases based on the
The Air Force administration wants to distribute 27 aircrafts across six bases based on the number of qualified pilots stationed at those bases. The standard quotas for each base are listed in the
Suppose that the Hawaii State Department of Education has a budget for 616 schools and is doing a research study to determine the equitable number of schools to have in each of the five counties
Several apportionment methods have been used to allocate 125 seats to ten states and the results are shown in the table below. Determine which apportionments do not satisfy the quota rule and justify
Suppose the population of a state is 50 and the standard divisor is 12.5 .1. Find the state's standard quota.2. Increase the standard divisor by 2 units and use the modified divisor to determine the
Suppose that the Hawaii State Department of Education has a budget for 616 schools and is doing a research study to determine the equitable number of schools to have in each of five counties based on
As in earlier examples, suppose that the Hawaii State Department of Education has a budget for 616 schools and is doing a research study to determine the equitable number of schools to have in each
Use the data in the table below to apportion 616 schools to Hawaiian counties. This time, use Webster's method. Hawaii Honolulu Kalawao Kauai Maui Total Residents under Age 19 46,310 224,230 20
Let's use the results from Example 11.34, Example 11.37, Example 11.38, and Example 11.39 to compare the four apportionment methods we have discussed. The following table summarizes the results of
The following table displays the effect of reducing the size of the divisor. Observe the effect this has on the modified quotas of smaller states versus larger states and use the table answer each
The 1880 census recorded the population of Alabama as \(1,513,401\) and that of the U.S. as \(62,979,766\).1. Calculate the standard divisor and standard quota for the State of Alabama based on a
Suppose that States A and B each have a population of 6 , while State \(C\) has a population of 2.1. Use the Hamilton method to apportion 10 seats.2. Use the Hamilton method to apportion 11 seats.3.
Suppose that 18 respirators are to be apportioned to three hospitals based on their capacities. The Hamilton method is used to allocate the respirators in 2020, then to reallocate based on new
The country of Costaguana has three states: Azuera with a population of 894,000; Punta Mala with a population of 696,000; and Esmeralda with a population of 215,000. There are 38 seats in the
The country of San Lorenzo has grown from two states to three. The house size of the congress has been increased by eight and the seats have been reapportioned to accommodate the new state of
The country of Gulliversia has two states: Lilliput with a population of 700,000 and Brobdingnag with a population of 937,000. The constitution of Gulliversia requires that the 90 congressional seats
Oklahoma was admitted as the 46th state on November 16, 1907. Before Oklahoma joined the union, the U.S. population was approximately \(75,030,000\) and the House of Representatives had 386 seats.
The incorporated town of Orange Grove consists of two subdivisions: The Oaks with 1,254 residents and The Villages with 10,746 residents. A council with 100 members supervises the municipality's
A company with an office in each of four cities must distribute 145 new Chromebooks to the four offices. It is determined that Office \(A\) will receive 42 , Office \(B\) will receive 17 , Office
A county with three towns has 30 garbage trucks to apportion. Attenborough receives 6 trucks, Breckenridge receives 8 trucks, and Cabbotsville receives 16 trucks, in proportion to their populations.
A group of 60 dentists work for a company that runs five offices. The dentists have been apportioned to the offices by the number of patients. Office A receives 14 dentists, Office B receives 11,
A company with locations in three cities plans to give 200 achievement awards that shall be apportioned to the three cities by population. City A with 9,150 employees is allotted 61 awards, City B
A soccer club must apportion soccer balls to the teams among four age brackets based on the number of teams in each bracket. Bracket U8 receives 32 balls, U12 receives 46 balls, U15 receives 29
READ (Reading Education Assistance Dogs) trains and certifies therapy animals to serve in classrooms and help children develop a love of reading in a low-stress environment. Suppose that 20 therapy
A charity organization has 851 volunteers in Country A and 3449 volunteers in Country B. There are 43 lead organizers that must be apportioned to the two locations. Country A receives 9 while Country
A country has two states. There are 22 seats in the legislature. State A has 4 seats, and State B has 18 seats. When State \(\mathrm{C}\) joins the union, the number of representatives is increased
In the Garunga Solar System, there are four inhabited planets. Three of the planets are members of the United Association of Garungan Planets (UAGP). The UAGP has 67 seats. Planet Angluertka has 40
When the number of seats changed from 147 to 148 , the standard quotas changed from A 44.24, B 17.35 , C 37.12 , and D 48.29 to A 45.54, B 17.47, C 37.37, and D 48.62 .a. How did the increase in
When the number of seats changed from 126 to 127 , the standard quotas changed from \(A 9.57, B 29.49, C\) 33.89, D 28.43, and E 24.61 to A 9.65, B 29.72, C 34.16, D 38.66, and E 24.81.a. How did the
When the number of seats changed from 25 to 26 , the standard quotas changed from \(A 2.21, B 5.25, C\) 11.27, and D 6.27 to A \(2.30, B 5.46\), C 11.72 , and D 6.52 .a. How did the increase in seats
When the number of seats changed from 25 to 26 , the standard quotas changed from A 2.43, B 5.42, and C 8.15 to A 2.46, B 5.47 , and C 8.07 .a. How did the increase in seats impact the
The house size is 18 . When the population of State \(A\) increases by 11.76 percent, State \(B\) increases by 16.22 percent, and State C increases by 12.18 percent, the standard quotas change from A
The house size is 100 . When the population of State \(A\) increases by 20 percent, State \(B\) increases by 10 percent, State \(C\) increases by 30 percent, and the populations of States \(D, E\),
The house size is 17 . When the population of State \(A\) increases by 12.73 percent, State \(B\) increases by 15.63 percent, and State C increases by 12.90 percent, the standard quotas change from A
The house size is 38 seats. When the population of State A increases by 6.60 percent, State B increases by 1.44 percent, and State C increases by 1.40 percent, the standard quotas change from A
The house size is 24 seats. When the population of State A increases by 28 percent, State B increases by 26 percent, and State C increases by 15 percent, the standard quotas change from A 3.38, B
The house size was 60 . There were three states with standard quotas of A 4.18, B 15.38, and C 40.44. A fourth state was annexed, and the house size was increased to 65 . The new standard quotas are
The house size was 50.There were three states with standard quotas of A 9.41, B 24.42, and C 16.17. A fourth state was annexed, and the house size was increased to 66 . The new standard quotas are A
The house size was 27.There were three states with standard quotas of A 6.39, B 11.40, and C 9.21. A fourth state was annexed, and the house size was increased to 35 . The new standard quotas are A
The house size was 100 . There were three states with standard quotas of A 26.09, B 30.43 , and \(C 43.48\). A fourth state was annexed, and the house size was increased to 122.The new standard
Consider States A, B, and C.a. Determine the apportionment for States A, B, and C with the original house size using the Hamilton method.b. Determine the apportionment for States A, B, and C with the
Consider States \(D, E, F\), and G.a. Determine the apportionment for States D, E, F, and G with the original house size using the Hamilton method.b. Determine the apportionment for States D, E, F,
Consider States H, I, J, K, and L.a. Determine the apportionment for States \(\mathrm{H}, \mathrm{I}, \mathrm{J}, \mathrm{K}\), and \(\mathrm{L}\) with the original house size using the Hamilton
Consider States P, Q and R.a. Determine the apportionment for States \(P, Q\), and \(R\) with the original house size using the Hamilton method.b. Determine the apportionment for States P, Q, and R
Calculate the population growth rates \(d, e\), and \(f\) for States D, E, and F. Give answer as a percentage rounded to one decimal place.Use the information in the table below. State Original
Calculate the population growth rates \(p, q, r\), and \(s\) for States \(P, Q, R\), and \(S\). Give answer as a percentage rounded to one decimal place.Use the information in the table below. State
Calculate the population growth rates \(x, y\), and \(z\) for States \(X, Y\), and \(Z\). Give answer as a percentage rounded to one decimal place.Use the information in the table below. State
Consider States A, B, and C.a. Determine the Hamilton apportionment for States A, B, and C with the original population.b. Determine the Hamilton apportionment for States A, B, and C with the updated
Consider States \(D, E\), and \(F\).a. Determine the Hamilton apportionment for States \(\mathrm{D}, \mathrm{E}\), and \(\mathrm{F}\) with the original population.b. Determine the Hamilton

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