course Mth 152 Mr. Smith I finished this last night but in the middle of getting my access code to paste I got a phone call and forgot about it until this morning. I'm sorry I'm turning it in late. The time stamps on it should tell you I'm being honest.
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21:40:53 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 --> There are six different ways.
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21:42:29 ** 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 --> Oh I only did it for the president and the secretary.
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21:49:06 query 11.1.12,18 In how many ways can the total of two dice equal 5?
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RESPONSE --> There are four ways.
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21:49:13 ** 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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21:52:27 In how many ways can the total of two dice equal 11?
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RESPONSE --> There are only two ways 5.6 and 6.5
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21:52:45 ** 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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21:55:01 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 triangles. I looked not only at the points but also inside.
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22:09:53 ** 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 can't see the other triangles I really cant.
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22:12:02 query 11.1.40 4 x 4 grid of squares, how many squares in the figure?
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RESPONSE --> The is one big square and 16 tiny squares and 6 medium sized squares
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22:14:17 ** 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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22:20:33 query 11.1.50 In how many ways can 30 be written as sum of two primes?
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RESPONSE --> There are four ways. 1+29, 7+23, 11+19, 13+17
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22:20:57 **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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22:24:24 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 --> There are only two options On, off, on, off or off, on, off, on.
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22:24:37 ** 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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22:25:34 Query Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> I was suprised a lot with the exercises about determining how many triangles or squares there were in the pictures. I just looked at the obvious instead of going into detail.
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22:26:09 ** 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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???????€???D??assignment #002 002. `query 2 Liberal Arts Mathematics II 01-25-2009
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22:37:08 query 11.2.12 find 10! / [ 4! (10-4)! ] without calculator
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RESPONSE --> 10![4!(10-4)!] 3,628,800 [ 4! (10 - 4) !] 3,628,800 [24 (6) !] 3,628,800 [24 (720)] 3,628,800 [17,280] 62,705,664,000
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22:41:13 ** 10! / [ 4! * (10-4) ! ] can be simplified to get 10! / ( 4! * 6! ). This gives you 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 / [ ( 4 * 3 * 2 * 1) * ( 6 * 5 * 4 * 3 * 2 * 1) ] . The numerator and denominator could be multiplied out but it's easier and more instructive to divide out like terms. Dividing ( 6 * 5 * 4 * 3 * 2 * 1) in the numerator by ( 6 * 5 * 4 * 3 * 2 * 1) in the denominator leaves 10 * 9 * 8 * 7 / (4 * 3 * 2 * 1). Every factor of the denominator divides into the numerator without remainder: Divide 4 into 8, divide 3 into 9 and 2 into 10 and you get 5 * 3 * 2 * 7 = 210. NOTE ON WHAT NOT TO DO: You could figure out that 10! = 3628800, and that 4! * 6! = 24 * 720 = 16480, then finally divided 3628800 by 16480. But that would process would lose accuracy and be ridiculously long for something like 100 ! / ( 30! * 70!). Much better to simply divide out like factors until the denominator goes away. **
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RESPONSE --> Ok I didn't understand this in the book at all even with the examples but I think I am begining to understand it with this example.
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22:45:10 query 11.2.25 3 switches in a row; fund count prin to find # of possible settings
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RESPONSE --> This question doesn't match up with the book so I'm not certain how to answer it.
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22:45:50 ** There are two possible settings for the first switch, two for the second, two for the third. The setting of one switch in independent of the setting of any other switch so the fundamental counting principle holds. There are therefore 2 * 2 * 2 = 8 possible setting for the three switches. COMMON ERROR: There are six possible settings and I used fundamental counting principle : first choice 3 ways, second choice 2 ways and third choice 1 way or 3 times 2 times 1 equals 6 ways. INSTRUCTOR CRITIQUE: You're choosing states of the switches and there are only two states on each. **
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22:47:21 query 11.2.27 If no two adjacent switches are off why does the fundamental counting principle not apply?
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RESPONSE --> Because there is only one option.
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22:47:36 ** The reason is that the Fund. Counting Principle requires that the events be independent. Here we have the state of one switch influencing the state of its neighbors (neither neighbor can be the same as that switch). The Fund. Counting Principle requires that the events be independent. **
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22:50:22 query 11.2.36 How many odd 3-digit #'s from the set {3, 4, 5}?
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RESPONSE --> 17 odd 3 digit numbers
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22:50:37 ** Using the box method: 1st can be any of the three so the first number of possibilities is 3 2nd number can also be any of the three so the second number of possibilities is 3 The last digit must be odd, so there are only 2 choices for it. We therefore have 3*3*2=18 possible combinations.
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22:55:36 query 11.2.50 10 guitars, 4 cases, 6 amps, 3 processors; # possible setups
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RESPONSE --> 10*4*6*3= 720
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22:55:46 ** A setup consists of a guitar, a case, an amp and a processor. There are 10 choices for the guitar, 4 for the case, 6 for the amp and 3 for the processor. So there are 10 * 4 * 6 * 3 = 720 possible setups. **
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22:55:55 Add comments on any surprises or insights you experienced as a result of this assignment.
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