course mth 151
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11:06:38 `questionNumber 10000 Note that there are 4 questions in this assignment. `q001. Let A stand for the collection of all whole numbers which have at least one even digit (e.g., 237, 864, 6, 3972 are in the collection, while 397, 135, 1, 9937 are not). Let A ' stand for the collection of all whole numbers which are not in the collection A. Let B stand for the collection { 3, 8, 35, 89, 104, 357, 4321 }. What numbers do B and A have in common? What numbers do B and A' have in common?
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RESPONSE --> The collections B and A have the numbers 8, 89, 104, 4321 in common. The collection B and A' have the numbers 3, 35, 357 in common.
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11:07:24 `questionNumber 10000 Of the numbers in B, 8, 89, 104, 4321 each have at least one even digit and so are common to both sets. 3 is odd, both of the digits in the number 35 are odd, as are all three digits in the number 357. Both of these numbers are therefore in A ' .
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RESPONSE --> ok
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11:12:15 `questionNumber 10002 `q002. I have in a room 8 people with dark hair brown, 2 people with bright red hair, and 9 people with light brown or blonde hair. Nobody has more than one hair color. Is it possible that there are exactly 17 people in the room?
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RESPONSE --> Yes, there is 17 people in this room. But the total amount of people exactly is 19. But in all reality, there is 17 people in this room.
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11:13:16 `questionNumber 10002 If we assume that dark brown, light brown or blonde, and bright red hair are mutually exclusive (i.e., someone can't be both one category and another, much less all three), then we have at least 8 + 2 + 9 = 19 people in the room, and it is not possible that we have exactly 17.
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RESPONSE --> Yes, but if you think about it then there is 17 people in that room, but the total is 19.
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11:16:28 `questionNumber 10003 `q003. I have in a room 6 people with dark hair and 10 people with blue eyes. There are only 14 people in the room. But 10 + 6 = 16, which is more than 14. How can this be?
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RESPONSE --> There must be at least 2 people that have dark hair AND blue eyes.
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11:16:51 `questionNumber 10003 The key here is that there is nothing mutully exclusive about these categories-a person can have blue eyes as well as dark hair. So if there are 2 people in the room who have dark hair and blue eyes, which is certainly possible, then when we add 10 + 6 = 16 those two people would be counted twice, once among the 6 blue-eyed people and once among the 10 dark-haired people. So the 16 we get would be 2 too high. To get the correct number we would have to subtract the 2 people who were counted twice to get 16 - 2 = 14 people.
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RESPONSE --> ok
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11:27:13 `questionNumber 10004 `q004. In a set of 100 child's blocks 60 blocks are cubical and 40 blocks are cylindrical. 30 of the blocks are red and 20 of the red blocks are cubical. How many of the cylindrical blocks are red?
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RESPONSE --> Enter, as appropriate, an answer to the question, a critique of your answer in response to a given answer, your insights regarding the situation at this point, notes to yourself, or just an OK. Always critique your solutions by describing any insights you had or errors you makde, and by explaining how you can make use of the insight or how you now know how to avoid certain errors. Also pose for the instructor any question or questions that you have related to the problem or series of problems. 10 Blocks of the cylindrical blocks are red. There are 40 cylindrical blocks. Therefore, 25% or 1/4 of your cylindrical blocks are red. If you have 100 blocks and 60 of them are cubical, then there are 40 that are cylindrical. But out of that 100 blocks then 30 of the blocks are red. Telling you that 20 of the blocks that are red are cubical lets you know that 10 of them are cylindrical and red. Therefore, 10 of them are cylindrical and red, out of the 40 Blocks that are cylindrical.
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11:28:52 `questionNumber 10004 Of the 30 red blocks 20 are cubical, so the rest must be cylindrical. This leaves 10 red cylindrical blocks.
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RESPONSE --> OK, but the way the question was worded, it made it seem like you wanted more. I got that there were 10 cylindrical blocks if 20 of them were cubes.
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