course Mth 152 §ë~h½¾…Ñ×Dߟšè×püш¶×ìÆ¿¾assignment #001
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16:57:49 query 11.1.6 {Andy, Bill, Kathy, David, Evelyn}. In how many ways can a secretary, president and treasuer be selected if the secretary must be female and the others male?
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RESPONSE --> 2 out of 5 are women 3 out of 5 are men 5*4*3 = 60 ways
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16:57:54 query 11.1.6 {Andy, Bill, Kathy, David, Evelyn}. In how many ways can a secretary, president and treasuer be selected if the secretary must be female and the others male?
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RESPONSE -->
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16:59:31 ** Using letters for the names, there are 12 possibilities: kab, kba, kdb, kbd, kda, kad, edb, ebd, eba, eab, eda, ead. There are two women, so two possibilities for the first person selected. The other two will be selected from among the three men, so there are 3 possibilities for the second person chosen, leaving 2 possibilities for the third. The number of possiblities is therefore 2 * 3 * 2 = 12. **
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RESPONSE --> I see what I did wrong. First you figure out how many positions are for the men and then for the women and the multiply the 2 women who could hold position and the multiply the 3*2 for the men.
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16:59:34 ** Using letters for the names, there are 12 possibilities: kab, kba, kdb, kbd, kda, kad, edb, ebd, eba, eab, eda, ead. There are two women, so two possibilities for the first person selected. The other two will be selected from among the three men, so there are 3 possibilities for the second person chosen, leaving 2 possibilities for the third. The number of possiblities is therefore 2 * 3 * 2 = 12. **
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RESPONSE -->
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17:02:31 query 11.1.12,18 In how many ways can the total of two dice equal 5?
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RESPONSE --> 1+ 4 = 5 2+ 3 = 5 2 ways
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17:03:51 ** Listing possibilities on first then second die you can get 1,4, or 2,3 or 3,2 or 4,1. There are Four ways. **
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RESPONSE --> I only did the 1+4 and 2+3 I didn't do the 3+2 or 4+1, I forgot the order didn't matter because it was dice and both dice and be rolled to equal 5.
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17:05:19 In how many ways can the total of two dice equal 11?
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RESPONSE --> 5 + 6 and 6 + 5 The dice only go up to 6 so you would have to get the 5 or 6 on each dice
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17:06:09 ** STUDENT SOLUTION AND INSTRUCTOR RESPONSE: There is only 1 way the two dice can equal 11 and that is if one lands on 5 and the other on 6 INSTRUCTOR RESPONSE: There's a first die and a second. You could imagine that they are painted different colors to distinguish them. You can get 5 on the first and 6 on the second, or vice versa. So there are two ways. **
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RESPONSE --> The book showed a red dice and a green dice so that helped me see them as different dice.
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17:14:34 query 11.1.36 5-pointed star, number of complete triangles How many complete triangles are there in the star and how did you arrive at this number?
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RESPONSE --> There are 10 triangles becuase there are five big triangles and 5 small triangles
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17:16:14 ** If you look at the figure you see that it forms a pentagon in the middle (if you are standing at the very center you would be within this pentagon). Each side of the pentagon is the side of a unique triangle; the five triangles formed in this way are the 'spikes' of the star. Each side of the pentagon is also part of a longer segment running from one point of the start to another. This longer segment is part of a larger triangle whose vertices are the two points of the star and the vertex of the pentagon which lies opposite this side of the pentagon. There are no other triangles, so we have 5 + 5 = 10 triangles. *&*&, BDE and CDE. Each of these is a possible triangle, but not all of these necessarily form triangles, and even if they all do not all the triangles will be part of the star. You count the number which do form triangles and for which the triangles are in fact part of the star. **
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RESPONSE --> I drew a star and labeled the points A - J and followed the lines to get the small ones and the the larger ones.
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17:20:33 query 11.1.40 4 x 4 grid of squares, how many squares in the figure?
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RESPONSE --> 22 squares - 16 single blocks. 5 four blocks, 1 the whole block
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17:24:09 ** I think there would be 16 small 1 x 1 squares, then 9 larger 2 x 2 squares (each would be made up of four of the small squares), 4 even larger 3 x 3 squares (each made up of nin small squares) and one 4 x 4 square (comprising the whole grid), for a total of 30 squares. Do you agree? **
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RESPONSE --> I came up with 22. I didn't do the 3X3 squares and I only did 4 2X2 squares.
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17:28:31 query 11.1.50 In how many ways can 30 be written as sum of two primes?
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RESPONSE --> three ways, 7 and 23; 11 and 19; 13 and 17
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17:29:14 **STUDENT SOLTION AND INSTRUCTOR COMMENT: There are 4 ways 30 can be written as the sum of two prime numbers: 29 + 1 19 + 11 23 + 7 17 + 13 INSTRUCTOR COMMENT: Good, but 1 isn't a prime number. It only has one divisor. **
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RESPONSE --> I only got three because I didn't put 1 as a prime.
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17:35:04 query 11.1.60 four adjacent switches; how many settings if no two adj can be off and no two adj can be on
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RESPONSE --> 8 times 4 switches at 2 settings
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17:35:59 ** There are a total of 16 settings but only two have the given property of alternating off and on. If the first switch is off then the second is on so the third is off so the fourth is on. If the first is off then then the second is on and the third is off so the fourth is on. So the two possibilies are off-on-off-on and on-off-on-off. If we use 0's and 1's to represent these possibilities they are written 0101 and 1010. **
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RESPONSE --> I got 8. I looked at Example 8 in the book and substituted the on and offs.
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17:36:47 Query Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> These assignments are hard. You really have to read them close and think them out.
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17:37:37
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