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nature of mathematics

Questions and Answers of Nature Of Mathematics

Discuss the ideas of arithmetic mean and geometric mean.
What is the population paradox?
A taste test is conducted on the Atlantic City Boardwalk. People are given samples of Coke, Pepsi, and Safeway brands of cola in unmarked cups, and are then asked to rank them in order of preference.
What is the Condorcet criterion?
Describe and discuss the Hare voting method.
Which apportionment schemes for the U.S. Congress favor the smaller states? Which ones favor the larger states? Are any neutral as far as state size is concerned?
A taste test is conducted on the Atlantic City Boardwalk. People are given samples of Coke, Pepsi, and Safeway brands of cola in unmarked cups, and are then asked to rank them in order of preference.
What is the new states paradox?
What is the monotonicity criterion?
Describe and discuss the pairwise comparison method.
What is the quota rule? Does this rule make sense to you? Discuss.
What does Balinski and Young's impossibility theorem say?
What is the irrelevant alternatives criterion?
A taste test is conducted on the Atlantic City Boardwalk. People are given samples of Coke, Pepsi, and Safeway brands of cola in unmarked cups, and are then asked to rank them in order of preference.
Describe and discuss the tournament method.
If you round the standard quotas down, how do you need to change the standard divisor to find the modified quotas?
In an election with three candidates, \(\mathrm{A}, \mathrm{B}\), and \(\mathrm{C}\), we find the following results of the voting:Use this information in Problems 6-7.Is there a Condorcet winner?
A college hired seven new counselors to apportion among its three divisions. Although one department has the same proportion of the college's enrollments as it did before the counselors were hired,
In an election with three candidates, \(\mathrm{A}, \mathrm{B}\), and \(\mathrm{C}\), we find the following results of the voting:Use this information in Problems 6-7.Does anyone receive a plurality?
What are the fairness criteria?
Use Adams' plan in Problems 8-10. Show that it violates the quota rule. State: A Population: 68,500 Number of seats: 100 B 34,700 C 16,000 D 9,500
Describe and discuss the approval voting method.
If you round the standard quotas up, how do you need to change the standard divisor to find the modified quotas?
The population of Windsor grew at a faster rate than that of Rhonert Park, but Windsor lost an apportioned seat on the county board to Rhonert Park. Does this make any sense?
If you could have only one of the fairness criteria, which one would you choose and why?
Give one example in which you have participated in voting where the count was tabulated by the plurality voting method. Your example can be made up or factual, but you should be specific.
Modified quotas are given in Problems 7-14. Round your answers to two decimal places.a. Find the lower and upper quotas.b. Find the arithmetic mean of the lower and upper quotas.c. Find the geometric
If you could have only two of the fairness criteria, which ones would you choose and why?
Give one example in which you have participated in voting where the count was tabulated by the Borda count method. Your example can be made up or factual, but you should be specific.
In 2011 the voting for the Heisman Trophy involved 927 ballots voting for three college football players. The results (in alphabetical order) were as follows: Borda count:Montee Ball (Wisconsin): 22,
The population in California was 33,871,648 in January 2000, and 37,253,956 in January 2010. Predict California's population in the year 2020.
What is a linear inequality in two variables?
Graph the lines, curves, or half-planes in Problems 1-12.\(5 x-y=15\)
What is a conic section?
Graph \(3 x-y \geq 5\).
If the path of a baseball is parabolic and is \(200 \mathrm{ft}\) wide at the base and \(50 \mathrm{ft}\) high at the vertex, write an equation that specifies the path of the baseball if the origin
Explain the notation \(f(x)\).
Before GPS, ships at sea located their positions using the LOng-RAnge Navigation system known as LORAN. In this system, which ceased operation in 2010, a master station sent signals that could be
The population in Sebastopol, California, was 7,774 in January 2000, and 7,598 in January 2013. Predict Sebastopol's population in the year 2020.
Outline a procedure for graphing first-degree inequalities in two variables.
What does the symbol \(e\) represent?
Graph the lines, curves, or half-planes in Problems 1-12.\(y=-\frac{4}{5} x-3\)
Define a parabola.
Which of the sets in Problems 3-14 are functions?\(\{(1,4),(2,5),(4,7),(9,12)\}\)
Predict the population of your city or state for the year 2020.
State whether each statement in Problems 3-12 is true or false. If it is false, explain why you think that is the case.The linear inequality \(2 x+5 y
Sketch the graph of each equation in Problems 3-30.\(y=3 x^{2}\)
Graph the lines, curves, or half-planes in Problems 1-12.\(2 x+3 y=15\)
Define an ellipse.
Investigate the topic of conic sections. Build models and/or find three-dimensional models for the conic sections. What did the Greeks know of the conic sections? How do the conic sections relate to
Which of the sets in Problems 3-14 are functions?\(\{(4,1),(5,2),(7,4),(12,9)\}\)
State whether each statement in Problems 3-12 is true or false. If it is false, explain why you think that is the case.The linear inequality \(x \geq y\) has the boundary line \(y-x=0\).
Sketch the graph of each equation in Problems 3-30.\(y=2 x^{2}\)
Graph the lines, curves, or half-planes in Problems 1-12.\(x=-\frac{2}{3} y+1\)
Define a hyperbola.
Which of the sets in Problems 3-14 are functions?\(\{(1,1),(2,1),(3,4),(4,4),(5,9),(6,9)\}\)
Write a short paper exploring the concept of the eccentricity of an ellipse.
State whether each statement in Problems 3-12 is true or false. If it is false, explain why you think that is the case.A good test point for the linear inequality \(y>x\) is \((0,0)\).
Sketch the graph of each equation in Problems 3-30.\(y=10 x^{2}\)
Graph the lines, curves, or half-planes in Problems 1-12.\(x=150\)
Give a procedure for sketching an ellipse using its equation.
Which of the sets in Problems 3-14 are functions?\(\{(1,1),(1,2),(4,3),(4,4),(9,5),(9,6)\}\)
State whether each statement in Problems 3-12 is true or false. If it is false, explain why you think that is the case.The test point \((0,0)\) does not work for \(y>x\) because 0 is not greater than
Sketch the graph of each equation in Problems 3-30.\(y=-x^{2}\)
Graph the lines, curves, or half-planes in Problems 1-12.\(x
Give a procedure for sketching a hyperbola using its equation.
Which of the sets in Problems 3-14 are functions?\(\{(4,3),(17,29),(18,52),(4,19)\}\)
State whether each statement in Problems 3-12 is true or false. If it is false, explain why you think that is the case.The test point \((0,0)\) satisfies the inequality \(2 y-3 x
Sketch the graph of each equation in Problems 3-30.\(y=-2 x^{2}\)
Graph the lines, curves, or half-planes in Problems 1-12.\(y=1-x^{2}\)
Explain how you recognize each of the following conics by inspecting the equation.a. lineb. parabolac. ellipsed. hyperbola
Which of the sets in Problems 3-14 are functions?\(\{(13,4),(29,4),(5,4),(9,4)\} \quad\)
State whether each statement in Problems 3-12 is true or false. If it is false, explain why you think that is the case.The test point \((0,0)\) satisfies the inequality \(3 x-2 y \geq-1\).
Sketch the graph of each equation in Problems 3-30.\(y=-3 x^{2}\)
Graph the lines, curves, or half-planes in Problems 1-12.\(y=-2^{x}\)
What is the eccentricity for each of the given conics? Also, explain how changes in the eccentricity affect the curve.a. parabolab. ellipsec. hyperbola
Which of the sets in Problems 3-14 are functions?\(\{(19,4),(52,18),(29,17),(3,4)\}\)
State whether each statement in Problems 3-12 is true or false. If it is false, explain why you think that is the case.The test point \((0,0)\) satisfies the inequality \(3 x>2 y\).
Sketch the graph of each equation in Problems 3-30.\(y=-5 x^{2}\)
Graph the lines, curves, or half-planes in Problems 1-12.\(\frac{x^{2}}{16}-\frac{y^{2}}{9}=1\)
If \(A x^{2}+C y^{2}+D x+E y+F=0\), for Problems 9-13, then list conditions on the constants to assure that the indicated graph results.a hyperbola \(A\) and Chave opposite signs
Which of the sets in Problems 3-14 are functions?\(\{(4,9),(4,4),(4,29),(4,19)\}\)
State whether each statement in Problems 3-12 is true or false. If it is false, explain why you think that is the case.The test point \((-2,4)\) satisfies the inequality \(y>2 x-1\).
Sketch the graph of each equation in Problems 3-30.\(y=5 x^{2}\)
Sketch the graph of each equation in Problems 3-30.\(y=\frac{1}{2} x^{2}\)
Graph the lines, curves, or half-planes in Problems 1-12.\(\frac{x^{2}}{20}+\frac{y^{2}}{10}=1\)
Which of the sets in Problems 3-14 are functions?\(\{(5,0)\}\)
State whether each statement in Problems 3-12 is true or false. If it is false, explain why you think that is the case.The test point \((-2,4)\) satisfies the inequality \(5 x+2 y \leq 9\).
Graph the lines, curves, or half-planes in Problems 1-12.\(x^{2}+y^{2}=1\)
If \(A x^{2}+C y^{2}+D x+E y+F=0\), for Problems 9-13, then list conditions on the constants to assure that the indicated graph results.a circle \(A=C eq 0\)
If \(A x^{2}+C y^{2}+D x+E y+F=0\), for Problems 9-13, then list conditions on the constants to assure that the indicated graph results.a parabola \(A=O\) and \(C eq O\) or \(A eq O\) and \(C=O\)
Which of the sets in Problems 3-14 are functions?\(\{(0,0)\}\)
State whether each statement in Problems 3-12 is true or false. If it is false, explain why you think that is the case.The test point \((-2,4)\) satisfies the inequality \(4 x
Sketch the graph of each equation in Problems 3-30.\(x=2 y^{2}\)
Graph the lines, curves, or half-planes in Problems 1-12.\(x^{2}-y^{2}=1\)
If \(A x^{2}+C y^{2}+D x+E y+F=0\), for Problems 9-13, then list conditions on the constants to assure that the indicated graph results.an ellipse \(A\) and Chave the same signs
Which of the sets in Problems 3-14 are functions?\(\{1,2,3,4,5\}\)
Graph the first-degree inequalities in two unknowns in Problems 13-48.\(y \leq 2 x+1\)
Sketch the graph of each equation in Problems 3-30.\(x=-3 y^{2}\)
Is \(\{(4,3),(5,-2),(6,3)\}\) a function? Tell why or why not.

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