course Mth 151 I didn't do QA 20 because I couldn't find it. ???~??????????Student Name: assignment #019
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16:41:24 `q001. There are 5 questions in this set. The preceding calculations have been done in our standard base-10 place value system. We can do similar calculations with bases other than 10. For example, a base-4 calculation might involve the number 3 * 4^2 + 2 * 4^1 + 1 * 4^0. This number will be expressed as 321{base 4}. What would this number be in base 10?
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RESPONSE --> 3*10^2+2*10^1+1*10^0
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16:42:45 `q002. What would the number 213{base 4} be in base 10 notation?
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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. I am not sure how to do this problem
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16:44:43 213{base 4} means 2 * 4^2 + 1 * 4^1 + 3 * 4^0 = 2 * 16 + 1 * 4 + 3 * 1 = 32 + 4 + 3 = 39.
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RESPONSE --> I am not really sure how you are doing this problem. I understand it in the book, but I am confused on here. I think I am confused by all the symbols.
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16:47:59 `q003. Suppose we had a number expressed in the form 6 * 4^2 + 7 * 4^1 + 3 * 4^0. This number isn't quite in the form needs to be if it is to be expressed in base 4. This is because we have the numbers 6 and 5, which exceed 4. How would this number be expressed without using any numbers 4 or greater?
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RESPONSE --> I think the problem 6 * 4^2 + 7 * 4^1 + 3 * 4^0 expressed without using numbers 4 or greater would be 2 * 3^2 + 3 * 3^1 + 1 *3^0
.................................................??f?p???????Student Name:
assignment #018
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16:25:24 `q001. There are 5 questions in this set. From lectures and textbook you will learn about some of the counting systems used by past cultures. Various systems enabled people to count objects and to do basic arithmetic, but the base-10 place value system almost universally used today has significant advantages over all these systems. The key to the base-10 place value system is that each digit in a number tells us how many times a corresponding power of 10 is to be counted. For example the number 347 tells us that we have seven 1's, 4 ten's and 3 one-hundred's, so 347 means 3 * 100 + 4 * 10 + 7 * 1. Since 10^2 = 100, 10^1 = 10 and 10^0 = 1, this is also written as 3 * 10^2 + 4 * 10^1 + 7 * 10^0. How would we write 836 in terms of powers of 10?
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RESPONSE --> The number 836 in terms of powers of ten means you have six 1's, three 10's and eight 100's. So 836 means 8*100+3*10+6*1.
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16:29:11 `q002. How would we write 34,907 in terms of powers of 10?
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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. 34,907 would be 3*10,000 + 4*1,000 +9*100 + 0*10 + 7*1
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16:31:39 `q003. How would we write .00326 in terms of powers of 10?
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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. I think .00326 in terms of 10 would be= 3*100 + 2*10 + 6*1
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16:33:39 First we note that .1 = 1/10 = 1/10^1 = 10^-1, .01 = 1/100 = 1/10^2 = 10^-2, .001 = 1/1000 = 1/10^3 = 10^-3, etc.. Thus .00326 means 0 * .1 + 0 * .01 + 3 * .001 + 2 * .0001 + 6 * .00001 = 0 * 10^-1 + 0 * 10^-2 + 3 * 10^-3 + 2 * 10^-4 + 6 * 10^-5 .
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RESPONSE --> ok
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16:34:55 `q004. How would we add 3 * 10^2 + 5 * 10^1 + 7 * 10^0 to 5 * 10^2 + 4 * 10^1 + 2 * 10^0?
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RESPONSE --> I am not sure
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16:37:05 We would write the sum as (3 * 10^2 + 5 * 10^1 + 7 * 10^0) + (5 * 10^2 + 4 * 10^1 + 2 * 10^0) , which we would then rearrange as (3 * 10^2 + 5 * 10^2) + ( 5 * 10^1 + 4 * 10^1) + ( 7 * 10^0 + 2 * 10^0), which gives us 8 * 10^2 + 9 * 10^1 + 9 * 10^0. This result would then be written as 899.
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RESPONSE --> ok
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?????e?????? Student Name: assignment #020
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???????b????? Student Name: assignment #021
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17:09:12 `q001. If we define the operation @ on two numbers x and y by x @ y = remainder when the product x * y is multiplied by 2 then divided by 3, then find the following: 2 @ 5, 3 @ 8, 7 @ 13.
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RESPONSE --> I am not really sure how to do this problem
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17:10:42 By the definition, 2 @ 5 is the remainder when the product 2 * 5 is doubled then divided by 3. We start with 2 * 5 = 10, then double that to get 20, then divide by three. 20 / 3 = 6 with remainder 2. So 2 @ 5 = 2. We follow the same procedure to find 3 @ 8. We get 3 * 8 = 24, then double that to get 48, then divide by three. 48 / 3 = 12 with remainder 0. So 3 @ 8 = 0. Following the same procedure to find 7 @ `2, we get 7 * 13 = 91, then double that to get 182, then divide by three. 182 / 3 = 60 with remainder 2. So 7 @ 13 = 2.
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RESPONSE --> Ok That is how I thought, i guess I should have put it down.
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17:14:13 `q002. If we define the @ operation from the previous exercise just on the set {5, 6, 7} , we can use the same process as in the preceding solution to get 5 @ 5 = 2, 5 @ 6 = 0, 5 @ 7 = 1, 6 @ 5 = 0, 6 @ 6 = 0, 6 @ 7 = 0, 7 @ 5 = 1, 7 @ 6 = 0 and 7 @ 7 = 2. We can put these results in a table as follows: @ 5 6 7 5 2 0 1 6 0 0 0 7 1 0 2. Make a table for the @ operation restricting x and y to the set {2, 3, 4}.
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RESPONSE --> Table for {2,3,4} @ 2 3 4 2 2 0 1 3 0 0 0 4 1 0 2
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17:15:32 `q003. All the x and y values for the table in the preceding problem came from the set {2, 3, 4}. From what set are the results x @ y taken?
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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. multiply by 2, then double, then divide by 3
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17:16:23 `q004. Are the results of the operation x @ y on the set {2, 3, 4} all members of the set {2, 3, 4}?
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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. Yes
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17:16:36 The possible results of the operation, whose table is @ 2 3 4 2 1 0 2 3 0 0 0 4 2 0 1 , are seen from the table to be 0, 1 and 2. Of these possible results, only 2 is a member of the set {2,3,4}. So it is not the case that all the results come from the set {2, 3, 4}.
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RESPONSE --> Ok
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17:17:31 `q005. Since the operation x @ y on the set {2, 3, 4} can result in at least some numbers which are not members of the set, we say that the @operation is not closed on the set {2, 3, 4}. Is the @ operation closed on the set S = {0, 1, 2}? Is the @ operation closed on the set T = {0, 2}? Is the @ operation closed on the set R = {1, 2}?
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RESPONSE --> Yes all these sets are closed because the nmbers 0,1,2 all exist in the set.
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17:19:08 `q006. How can we tell by looking at the table whether the operation is closed?
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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. I don't know how to tell if the operation is closed.
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17:19:41 If all the numbers in the table come from the far left-hand column of the table--e.g., the column underneath the @ in the tables given above, which lists all the members of the set being operated on --then all the results of the operation are in that set and the operation is therefore closed.
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RESPONSE --> ok
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17:20:09 `q007. When calculating x @ y for two numbers x and y, does it make a difference whether we calculate x @ y or y @ x?
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RESPONSE --> No, you can use a property
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17:22:50 `q008. Does the operation of subtraction of whole numbers have the commutative property?
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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. No you can not subtract whole numbers in the communitive property. To be communitive you have to be able to arrange the numbers so it can still be the same no matter what way you put them.
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17:23:16 `q009. Is the operation of subtraction closed on the set of whole numbers?
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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. NO
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17:23:44 `q010. Is the operation of addition closed and commutative on the set of whole numbers?
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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. Yes
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17:24:24 `q011. When we multiply a number by 1, what must be our result?
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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. When you multiply a number by one, the result must be the number which you were multiplying by.
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17:25:11 `q012. A number which does not change any number with which it is combined using a certain operation is called the identity for the operation. As we saw in the preceding exercise, the number 1 is the identity for the operation of multiplication on real numbers. Does the operation @ (which was defined in preceding exercises by x @ y = remainder when x * y is doubled and divided by 3) have an identity on the set {0, 1, 2}? Does @ have an identity on the set {0, 1}?
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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. No
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17:25:51 `q013. Does the set of whole numbers on the operation of addition have an identity?
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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. Yes
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?{?????????????Student Name: assignment #022
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17:28:01 `q001. There are nine questions in this assignment. A group is a set and an operation on that set which has the properties of closure, associativity, identity and inverse. The set {1, 2} on the operation @ of Assignment 21, defined by x @ y = remainder when the product x * y is doubled and divided by 3, does have the associative property. Is the set {1, 2} a group on @?
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RESPONSE --> Yes.
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17:31:53 `q002. Which of the properties closure, identity, commutativity, inverse, does the standard addition operation + have on the set {-1, 0, 1}?
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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. The set {-1,0,1} would fall under the inverse property due to the negatives
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17:33:03 `q003. Does the operation * of standard multiplication on the set {-1, 0, 1} have the properties of closure, identity and inverse?
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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. yes
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17:33:23 `q004. Does the operation * of standard multiplication on the set {-1, 1} have the properties of closure, identity and inverse?
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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. yes
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17:34:21 `q005. Is the operation * of standard multiplication on the set {-1, 1} a group. Note that the operation does have the property of associativity.
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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. yes it is a group
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17:35:44 `q006. We've referred to the property of associativity, but we haven't yet defined it. Associativity essentially means that when an operation (technically a binary operation, but don't worry about that a terminology at this point) is performed on three elements of a set, for example a + b + c, it doesn't matter whether we first perform a + b then add c, calculating (a + b) + c, or group the b and c so we calculate a + (b + c). If + means addition on real numbers, show that (3 + 4) + 5 = 3 + ( 4 + 5).
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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. (3+4) +5 = 7+5=12 3+(4+5)= 3+9=12
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17:36:12 `q008. Does the result of the preceding exercise prove that the @ operation is associative on the set {0, 1, 2}?
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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. yes
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17:38:04 `q009. Earlier we verified the properties of closure, identity and inverse for the multiplication operation * on the set {-1, 1}. We asserted that this operation was associative, so that this set with this operation forms a group. It would still be too time-consuming to prove that * is associative on {-1, 1}, but list the possible combinations of a, b, c from the set and verify associativity for any three of them.
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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. a, b, c a, c,b b, a, c c, a b b,c,a c, b, a
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