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Solutions for Session 1 Homework
See solutions for Problems: H1 | H2 | H3 | H4 | H5 | H6 | H7 | H8 | H9
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Problem H1 | |
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According to Maria's criterion, here are the values:
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Name (Country/Continent) |
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Height (cm) + Weight (kg) |
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Water Buffalo (Asia) |
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1,165 |
African Buffalo |
695 |
Yak (Tibet) |
750 |
Guar (Asia) |
1,070 |
American Bison (North America) |
1,180 |
European Bison |
1,100 |
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The three largest animals by this criterion are the American bison, the water buffalo, and the European bison.
Note that this method is somewhat problematic since the answers could change drastically if we change the units of measurement. For example, the results would look quite different if we measured weight in tons (1 metric ton = 1,000 kg) instead of in kilograms. Clearly, this can lead to potential errors.
<< back to Problem H1
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Problem H2 | |
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Here are the ranks according to Jacob's criterion:
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Name (Country/Continent) |
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Height Rank |
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Weight Rank |
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Total |
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Water Buffalo (Asia) |
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2 |
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5.5 (tie) |
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7.5 |
African Buffalo |
1 |
2 |
3 |
Yak (Tibet) |
4.5 (tie) |
1 |
5.5 |
Guar (Asia) |
6 |
3 |
9 |
American Bison (North America) |
3 |
5.5 (tie) |
8.5 |
European Bison |
4.5 (tie) |
4 |
8.5 |
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The three largest animals by this criterion are the guar, the American bison, and the European bison.
<< back to Problem H2
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Problem H3 | |
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Here are the products for each animal:
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Name (Country/Continent) |
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Height (cm) • Weight (kg) |
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Water Buffalo (Asia) |
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165,000 |
African Buffalo |
75,600 |
Yak (Tibet) |
110,000 |
Guar (Asia) |
187,000 |
American Bison (North America) |
180,000 |
European Bison |
180,000 |
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The three largest animals by Quentin's criterion are the guar, the American bison, and the European bison.
<< back to Problem H3
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Problem H4 | |
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These two methods result in the same ordering of the animals, but some may argue that Quentin's method is more capricious than Jacob's, since there is no natural meaning to multiplying height and weight.
<< back to Problem H4
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Problem H5 | |
a. | 
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b. | Using the Pythagorean theorem, we can derive a formula for the distance between two points A (x1,y1) and B (x2,y2) as 
Next, we can calculate the distances. So for the Asian water buffalo
Here is the completed table:
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Name (Country/Continent) |
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Coordinates |
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Distance from (220,1000) |
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Water Buffalo (Asia) |
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(165,1000) |
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55 |
African Buffalo |
(135,560) |
448.13 |
Yak (Tibet) |
(200,550) |
450.44 |
Guar (Asia) |
(220,850) |
150 |
American Bison (North America) |
(180,1000) |
40 |
European Bison |
(200,900) |
101.98 |
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To learn more about the Pythagorean theorem and distance formula, go to Learning Math: Geometry, Session 6.
<< back to Problem H5
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Problem H6 | |
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The three species closest to (220,1000) are the American bison, the water buffalo, and the European bison.
<< back to Problem H6
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Problem H7 | |
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Here is the completed table:
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Name (Country/Continent) |
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Coordinates |
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Distance from (0,0) |
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Water Buffalo (Asia) |
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(165,1000) |
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1,013.52 |
African Buffalo |
(135,560) |
576.04 |
Yak (Tibet) |
(200,550) |
585.23 |
Guar (Asia) |
(220,850) |
878.01 |
American Bison (North America) |
(180,1000) |
1,016.07 |
European Bison |
(200,900) |
921.95 |
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According to Marcy's criterion, the three largest animals are the American bison, the water buffalo, and the European bison.
<< back to Problem H7
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Problem H8 | |
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Answers will vary. Another possible method is to use weight as the first determining factor and to use height only in case of a tie.
<< back to Problem H8
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Problem H9 | |
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Answers will vary, but the most likely answer is the African buffalo, which is the shortest and nearly the lightest. It wins easily on Jacob's criterion and is the smallest for many others.
<< back to Problem H9
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