course Mth 152 U J ^xassignment #001
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14:31:49 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 --> To solve this problem, I put each male (Andy, Bill, and David) in the President's spot. I then chose a female secretary (Kathy or Evelyn). The treasurer must also be a male, but cannot be the same male as the president. After systematically going through the possibilities, there are 12 possible ways that this scenario would work.
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14:32:24 ** 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 --> Correct answer.
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14:34:08 query 11.1.12,18 In how many ways can the total of two dice equal 5?
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RESPONSE --> The total of two dice can equal 5 in the following ways: (1,4), (2,3), (3,2), (4,1). There are four possibilities.
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14:34:20 ** 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 --> Correct answer.
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14:35:07 In how many ways can the total of two dice equal 11?
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RESPONSE --> There are only two ways that the two dice can equal 11. (5,6) and (6,5).
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14:35:37 ** 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 --> Correct answer.
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14:37:33 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 8 complete triangles. I first counted the 5 triangles that make up the points of the star. There are 3 larger triangles from the middle portion and the two points across from each other for a total of 8 triangles.
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14:38:49 ** 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 believe my answer of 8 triangles is correct.
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14:41:33 query 11.1.40 4 x 4 grid of squares, how many squares in the figure?
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RESPONSE --> I count 26 squares. There are 16 small squares in the grid. The entire grid counts as 1 square. The four squares on each corner make up another 4 squares. The four small squares in the middle make up another square. The four squares on each side in the middle make up another four squares. 16 + 1 + 4 + 1 + 4 = 26 squares.
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14:42:39 ** 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 --> Yes, I agree. I missed the four 3 x 3 squares.
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14:43:24 query 11.1.50 In how many ways can 30 be written as sum of two primes?
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RESPONSE --> 30 can be written as the sum of two primes: 2 * 15
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14:45:18 **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 did not read the problem carefully. I did the product rather than the sum. I understand the correct answer as given and understand that 1 is not a prime number so there are 3 ways that 30 can be written as the sum of two numbers.
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15:20:21 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 --> If no two adjacent switches can be off or on, then there are only two settings. If the first switch is off, then the second switch must be on, etc. If the first switch is on, then the second switch must be off, etc.
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15:20:37 ** 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 --> Correct answer.
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15:24:28 Query Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> I gained insight concerning question number 40 about the number of squares in the square. I also learned that I need to carefully read the question such as in question number 50 about the number of different ways the number 30 can be written as the sum of two primes.
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15:26:14 ** STUDENT COMMENT: No suprises and it's early so i'm reaching for insight as a child reaches for a warm bottle of milk I would like the answers to all the problems I worked in Assignment 11.1. I was surprised that you only ask for a few. I could not answer 11.1. 63 - What is a Cartesain plane? I could not find it in the text. INSTRUCTOR RESPONSE: I ask for selected answers so you can submit work quickly and efficiently. I don't provide answers to all questions, since the text provides answers to most of the odd-numbered questions. Between those answers and and comments provided here, most people get enough feedback to be confident in the rest of their work. Also I don't want people to get in the habit of 'working backward' from the answer to the solution. If you want to send in your work on other problems, including a full descripton of your reasoning, I'm always glad to look at them. You would have to make those problems self-contained (tell me enough about the problem so I know what the problem is), since I don't always respond from the place where I have my copy of the text. The Cartesian Plane is a plane defined by an x axis and a y axis, on which you can specify points by their coordinates. **
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RESPONSE --> No response.
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