course Mth 152 Ȗf}ǁ_assignment #001
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00:10:10 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 --> A,B,K,D,E There would be 12 different possibilities. eab,eda,ead,eba,edb,ebd kad,kda,kab,kba,kdb,kbd
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00:10:17 ** 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 --> o.k.
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00:12:50 query 11.1.12,18 In how many ways can the total of two dice equal 5?
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RESPONSE --> die 1 1,2,3,4,5,6 die 2 1,2,3,4,5,6 (2,3) (3,2) (1,4) (4,1) 4 ways
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00:12:56 ** 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 --> o.k.
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00:14:58 In how many ways can the total of two dice equal 11?
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RESPONSE --> 1,2,3,4,5,6 1,2,3,4,5,6 ( 5,6) or (6,5) two ways
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00:15:07 ** 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 --> o.k.
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00:19:42 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 --> i am not susre about this one but I think that there are 10. if there are 5 points and you were to fold each one of those points backward you will still have a five pointed figure so if each point represents a triangle then you have 5+5 = 10
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00:20:55 ** 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 --> o.k I lucked up on that one but I was looking at the figure as each point being a triangle. If you deleted the larger five points then you still have a five pointed figure.
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00:23:48 query 11.1.40 4 x 4 grid of squares, how many squares in the figure?
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RESPONSE --> I think that there would be twenty one 26 small squares then 4 2x2 squares and 1 large 4x4 26+4+1
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00:24:05 ** 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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00:25:00 query 11.1.50 In how many ways can 30 be written as sum of two primes?
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RESPONSE --> 19+11 23 + 7 17+3 theree ways
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00:25:05 **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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00:27:10 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 --> off on off on or we could have on off on off two ways
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00:27:13 ** 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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00:27:43 Query Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> No comments but i was plenty surprised at somw of the text material
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00:27:46 ** 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 -->
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course Mth 152 Ȗf}ǁ_assignment #001
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00:10:10 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 --> A,B,K,D,E There would be 12 different possibilities. eab,eda,ead,eba,edb,ebd kad,kda,kab,kba,kdb,kbd
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00:10:17 ** 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 --> o.k.
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00:12:50 query 11.1.12,18 In how many ways can the total of two dice equal 5?
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RESPONSE --> die 1 1,2,3,4,5,6 die 2 1,2,3,4,5,6 (2,3) (3,2) (1,4) (4,1) 4 ways
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00:12:56 ** 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 --> o.k.
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00:14:58 In how many ways can the total of two dice equal 11?
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RESPONSE --> 1,2,3,4,5,6 1,2,3,4,5,6 ( 5,6) or (6,5) two ways
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00:15:07 ** 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 --> o.k.
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00:19:42 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 --> i am not susre about this one but I think that there are 10. if there are 5 points and you were to fold each one of those points backward you will still have a five pointed figure so if each point represents a triangle then you have 5+5 = 10
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00:20:55 ** 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 --> o.k I lucked up on that one but I was looking at the figure as each point being a triangle. If you deleted the larger five points then you still have a five pointed figure.
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00:23:48 query 11.1.40 4 x 4 grid of squares, how many squares in the figure?
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RESPONSE --> I think that there would be twenty one 26 small squares then 4 2x2 squares and 1 large 4x4 26+4+1
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00:24:05 ** 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 -->
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00:25:00 query 11.1.50 In how many ways can 30 be written as sum of two primes?
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RESPONSE --> 19+11 23 + 7 17+3 theree ways
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00:25:05 **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 -->
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00:27:10 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 --> off on off on or we could have on off on off two ways
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00:27:13 ** 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 -->
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00:27:43 Query Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> No comments but i was plenty surprised at somw of the text material
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00:27:46 ** 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 -->
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