course Mth 151 bếxʹ˝assignment #002
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13:35:01 `q001Note that there are 2 questions in this assignment. `q001. We can represent the collection consisting of the letters a, b, c, d, e, f by a circle in which we write these letters. If we have another collection consisting of the letters a, c, f, g, k, we could represent it also by a circle containing these letters. If both collections are represented in the same diagram, then since the two collections have certain elements in common the two circles should overlap. Sketch a diagram with two overlapping circles. The two circles will create four regions (click below on 'Next Picture'). The first region is the region where the circles overlap. The second region is the one outside of both circles. The third region is the part of the first circle that doesn't include the overlap. The fourth region is the part of the second circle that doesn't include the overlap. Number these regions with the Roman numerals I (the overlap), II (first circle outside overlap), III (second circle outside overlap) and IV (outside both circles). Let the first circle contain the letters in the first collection and let the second circle contain the letters in the second collection, with the letters common to both circles represented in the overlapping region. Which letters, if any, go in region I, which in region II, which in region III and which in region IV?
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RESPONSE --> The letters that belong in region 1 are a,c,f. Because they are in both circles. And the letters in the region II are a,b,c,d,e,f. since those come from the first collection, and that the letters in region III are a,c,f,g,k. So using what we've been given, we know how to classify region IV: b,d,e,g,k. I am confident these are the correct classifications, especially with the help of the circle diagram. Originally, I almost classified the first collection with the first circle on the paper, but managed to find the mistake immediately. confidence assessment: 3
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13:36:30 The letters a, c and f go in the overlapping region, which we called Region I. The remaining letters in the first collection are b, d, and e, and they go in the part of the first circle that does not include the overlapping region, which we called Region II. The letters g and k go in the part of the second circle that does not include the overlapping region (Region III). There are no letters in Region IV. Click below on 'Next Picture' for a picture.
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RESPONSE --> I didn't compress the problem enough, I counted the overlaps in the circles as letters in the whole circle. I will delve into these type problems more carefully and critically in the future. self critique assessment: 2
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13:45:20 `q002. Suppose that we have a total of 35 people in a room. Of these, 20 have dark hair and 15 have bright eyes. There are 8 people with dark hair and bright eyes. Draw two circles, one representing the dark-haired people and the other representing the bright-eyed people. Represent the dark-haired people without bright eyes by writing this number in the part of the first circle that doesn't include the overlap (region II). Represent the number of bright-eyed people without dark hair by writing this number in the part of the second circle that doesn't include the overlap (region III). Write the appropriate number in the overlap (region I). How many people are included in the first circle, and how many in the second? How many people are included in both circles? How many of the 35 people are not included in either circle?
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RESPONSE --> After some heavy thought, I realized if there are 8 people with dark AND bright, then there can't be 20 people with just dark, or bright with 15. So I subtracted the 8 from the dark haired and the bright eyes total, which gave me the appropriate numbers for the regions. Region I: 8 Region II: 12 Region III: 7 That was the most certain solution I could come up with after drawing the circles and juggling with the numbers. But in basic terms, the overlap shares with both of the circles. So 8 has to be part of both circles, then it came to basic addition. 12+8=20 8+7=20 confidence assessment: 3
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13:46:11 Of the 20 dark-haired people in the preceding example, 8 also have bright eyes. This leaves 12 dark-haired people for that part of the circle that doesn't include the overlap (region I). The 8 having both dark hair and bright eyes will occupy the overlap (region I). Of the 15 people with bright eyes, 8 also have dark hair so the other 7 do not have dark hair, and this number will be represented by the part of the second circle that doesn't include the overlap (region III). We have accounted for 12 + 8 + 7 = 27 people. This leaves 35-27 = 8 people who are not included in either of the circles. The number 8 can be written outside the two circles (region IV) to indicate the 8 people who have neither dark hair nor bright eyes (click below on 'Next Picture').
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RESPONSE --> OK self critique assessment: 3
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