course Mth 151 I hope this is the right material I am posting. ?|??]??o??????P??assignment #001001. Rates
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17:23:21
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RESPONSE --> E
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17:24:01
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RESPONSE --> B
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17:25:48
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RESPONSE --> E
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17:25:53
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RESPONSE --> E
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17:52:23 `q001. Note that there are 4 questions in this assignment. `q001. Let A stand for the collection of all whole numbers which have at least one even digit (e.g., 237, 864, 6, 3972 are in the collection, while 397, 135, 1, 9937 are not). Let A ' stand for the collection of all whole numbers which are not in the collection A. Let B stand for the collection { 3, 8, 35, 89, 104, 357, 4321 }. What numbers do B and A have in common? What numbers do B and A' have in common?
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RESPONSE --> B and A = {8, 89, 104, 4321} B and A' = {3, 35, 357} confidence assessment: 2
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18:47:38 Of the numbers in B, 8, 89, 104, 4321 each have at least one even digit and so are common to both sets. 3 is odd, both of the digits in the number 35 are odd, as are all three digits in the number 357. Both of these numbers are therefore in A ' .
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RESPONSE --> 18,10 self critique assessment: 2
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22:35:49 `q002. I have in a room 8 people with dark hair brown, 2 people with bright red hair, and 9 people with light brown or blonde hair. Nobody has more than one hair color. Is it possible that there are exactly 17 people in the room?
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RESPONSE --> No, 8+9+2= 19 confidence assessment: 3
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23:23:09 `q003. I have in a room 6 people with dark hair and 10 people with blue eyes. There are only 14 people in the room. But 10 + 6 = 16, which is more than 14. How can this be?
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RESPONSE --> I would assume that some of these 2 of these 14 people are being counted because they do in fact have both of these features. confidence assessment: 2
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23:24:35
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RESPONSE --> I was quite confused, when reading this question on why the blue eyes came into the picture, but then got back on track. self critique assessment: 3
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23:36:57 `q004. In a set of 100 child's blocks 60 blocks are cubical and 40 blocks are cylindrical. 30 of the blocks are red and 20 of the red blocks are cubical. How many of the cylindrical blocks are red?
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RESPONSE --> 10. There are 30 red blocks. 20 of those are cubes. That leaves 10 that must be cylindrical confidence assessment: 3
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23:37:22 Of the 30 red blocks 20 are cubical, so the rest must be cylindrical. This leaves 10 red cylindrical blocks.
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RESPONSE --> I got that one right! self critique assessment: 3
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?P???eP??E???€? assignment #001 001. `Query 1 College Algebra 07-02-2008 |??^?K?????S?}???assignment #001
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qa prelim
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09:47:38 `q001. Part 1 includes six activities. If you have completed an activity, just enter the answer 'completed'. This question is appearing in the Question box. The box to the right is the Answer box, where you will type in your answers to the questions posed here. To use this program you read a question, then enter your answer in the Answer box and click on Enter Answer. In your answers give what is requested, but don't go into excruciating detail. Try to give just enough that the instructor can tell that you understand an item. After entering an answer click on Next Question/Answer above the Question box. Do you understand these instructions?
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RESPONSE --> Yes
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09:49:44 This program has created the folder c:\vhmthphy on your hard drive. Browse to that folder and locate the file whose name begins with SEND. The name of this file will also include your name, as you gave it to the program, and the file will show as a Text file. Never tamper with a SEND file in any way. It contains internal codes as if these codes are tampered with you won't get credit for the assignment. However you are welcome to copy this file to another location and view it, make changes, etc. Just be sure that when requested to do so you send the instructor the original, tamper-free file. State in the Answer box whether or not you have been able to locate the SEND file. Don't send the SEND file yet. Note that more questions/instructions remain in the q_a_prelim.
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RESPONSE --> Yes, I understand
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09:50:33 `q002. Note that every time you click on Enter Answer the program writes your response to your SEND file. Even if the program disappears all the information you have entered with the Enter Answer button will remain in that file. This program never 'unwrites' anything. Even if this program crashes your information will still be there in the SEND file. Explain this in your own words.
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RESPONSE --> Every answer you submit saves to my SEND file.
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09:51:30 Any time the instructor does not post a response to your access site by the end of the following day, you should resubmit your work using the Submit Work form, and be sure at the beginning to indicate that you are resubmitting, and also indicate the date on which you originally submitted your work. If you don't know where your access site is or how to access it, go to http://www.vhcc.edu/dsmith/_vti_bin/shtml.dll/request_access_code.htm and request one now. You can submit the q_a_prelim without your access code, but other assignments should contain your code.
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RESPONSE --> I already have my access code.
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09:51:51 `q003. If you are working on a VHCC computer, it is probably set up in such a way as to return to its original configuration when it is rebooted. To avoid losing information it is suggested that you back up your work frequently, either by emailing yourself a copy or by using a key drive or other device. This is a good idea on any computer. Please indicate your understanding of this suggestion.
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RESPONSE --> Always back up your work.
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09:52:52 Once more, locate the SEND file in your c:\vhmthphy folder, and open the file. Copy its contents to the clipboard (this is a common operation, but in case you don't know how, just use CTRL-A to highlight the contents of the file and CTRL-C to copy the contents to the clipboard). Then return to the form that instructed you to run this program, and paste the contents into the indicated box (just right-click in the box and select Paste). You may now click on the Quit button, or simply close the program.
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RESPONSE --> ???~?????????assignment #001 001. Only assignment: prelim asst qa prelim
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10:06:32 `q001. Part 1 includes six activities. If you have completed an activity, just enter the answer 'completed'. This question is appearing in the Question box. The box to the right is the Answer box, where you will type in your answers to the questions posed here. To use this program you read a question, then enter your answer in the Answer box and click on Enter Answer. In your answers give what is requested, but don't go into excruciating detail. Try to give just enough that the instructor can tell that you understand an item. After entering an answer click on Next Question/Answer above the Question box. Do you understand these instructions?
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RESPONSE --> Okay
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10:08:00 This program has created the folder c:\vhmthphy on your hard drive. Browse to that folder and locate the file whose name begins with SEND. The name of this file will also include your name, as you gave it to the program, and the file will show as a Text file. Never tamper with a SEND file in any way. It contains internal codes as if these codes are tampered with you won't get credit for the assignment. However you are welcome to copy this file to another location and view it, make changes, etc. Just be sure that when requested to do so you send the instructor the original, tamper-free file. State in the Answer box whether or not you have been able to locate the SEND file. Don't send the SEND file yet. Note that more questions/instructions remain in the q_a_prelim.
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RESPONSE --> Yes, I have been able to locate the SEND file.
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10:09:11 `q002. Note that every time you click on Enter Answer the program writes your response to your SEND file. Even if the program disappears all the information you have entered with the Enter Answer button will remain in that file. This program never 'unwrites' anything. Even if this program crashes your information will still be there in the SEND file. Explain this in your own words.
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RESPONSE --> Everything you enter using the Enter response will be saved to the Send file no matter what!
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10:10:10 Any time the instructor does not post a response to your access site by the end of the following day, you should resubmit your work using the Submit Work form, and be sure at the beginning to indicate that you are resubmitting, and also indicate the date on which you originally submitted your work. If you don't know where your access site is or how to access it, go to http://www.vhcc.edu/dsmith/_vti_bin/shtml.dll/request_access_code.htm and request one now. You can submit the q_a_prelim without your access code, but other assignments should contain your code.
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RESPONSE --> I already have an access code.
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10:10:43 `q003. If you are working on a VHCC computer, it is probably set up in such a way as to return to its original configuration when it is rebooted. To avoid losing information it is suggested that you back up your work frequently, either by emailing yourself a copy or by using a key drive or other device. This is a good idea on any computer. Please indicate your understanding of this suggestion.
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RESPONSE --> I will back everything up with a jump drive.
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??????????assignment #001
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qa prelim
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09:53:30 `q001. Part 1 includes six activities. If you have completed an activity, just enter the answer 'completed'. This question is appearing in the Question box. The box to the right is the Answer box, where you will type in your answers to the questions posed here. To use this program you read a question, then enter your answer in the Answer box and click on Enter Answer. In your answers give what is requested, but don't go into excruciating detail. Try to give just enough that the instructor can tell that you understand an item. After entering an answer click on Next Question/Answer above the Question box. Do you understand these instructions?
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RESPONSE --> Yes
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09:54:05 This program has created the folder c:\vhmthphy on your hard drive. Browse to that folder and locate the file whose name begins with SEND. The name of this file will also include your name, as you gave it to the program, and the file will show as a Text file. Never tamper with a SEND file in any way. It contains internal codes as if these codes are tampered with you won't get credit for the assignment. However you are welcome to copy this file to another location and view it, make changes, etc. Just be sure that when requested to do so you send the instructor the original, tamper-free file. State in the Answer box whether or not you have been able to locate the SEND file. Don't send the SEND file yet. Note that more questions/instructions remain in the q_a_prelim.
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RESPONSE --> Yes, I have been able to locate my send file
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09:55:41 `q002. Note that every time you click on Enter Answer the program writes your response to your SEND file. Even if the program disappears all the information you have entered with the Enter Answer button will remain in that file. This program never 'unwrites' anything. Even if this program crashes your information will still be there in the SEND file. Explain this in your own words.
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RESPONSE --> This program saves every answer you submit, even if the program shuts down.
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09:55:55 Any time the instructor does not post a response to your access site by the end of the following day, you should resubmit your work using the Submit Work form, and be sure at the beginning to indicate that you are resubmitting, and also indicate the date on which you originally submitted your work. If you don't know where your access site is or how to access it, go to http://www.vhcc.edu/dsmith/_vti_bin/shtml.dll/request_access_code.htm and request one now. You can submit the q_a_prelim without your access code, but other assignments should contain your code.
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RESPONSE --> I already have my acess code.
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09:56:10 `q003. If you are working on a VHCC computer, it is probably set up in such a way as to return to its original configuration when it is rebooted. To avoid losing information it is suggested that you back up your work frequently, either by emailing yourself a copy or by using a key drive or other device. This is a good idea on any computer. Please indicate your understanding of this suggestion.
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RESPONSE --> Always back up your work.
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09:56:47 Once more, locate the SEND file in your c:\vhmthphy folder, and open the file. Copy its contents to the clipboard (this is a common operation, but in case you don't know how, just use CTRL-A to highlight the contents of the file and CTRL-C to copy the contents to the clipboard). Then return to the form that instructed you to run this program, and paste the contents into the indicated box (just right-click in the box and select Paste). You may now click on the Quit button, or simply close the program.
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RESPONSE --> ???~?????????assignment #001 001. Only assignment: prelim asst qa prelim
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10:06:32 `q001. Part 1 includes six activities. If you have completed an activity, just enter the answer 'completed'. This question is appearing in the Question box. The box to the right is the Answer box, where you will type in your answers to the questions posed here. To use this program you read a question, then enter your answer in the Answer box and click on Enter Answer. In your answers give what is requested, but don't go into excruciating detail. Try to give just enough that the instructor can tell that you understand an item. After entering an answer click on Next Question/Answer above the Question box. Do you understand these instructions?
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RESPONSE --> Okay
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10:08:00 This program has created the folder c:\vhmthphy on your hard drive. Browse to that folder and locate the file whose name begins with SEND. The name of this file will also include your name, as you gave it to the program, and the file will show as a Text file. Never tamper with a SEND file in any way. It contains internal codes as if these codes are tampered with you won't get credit for the assignment. However you are welcome to copy this file to another location and view it, make changes, etc. Just be sure that when requested to do so you send the instructor the original, tamper-free file. State in the Answer box whether or not you have been able to locate the SEND file. Don't send the SEND file yet. Note that more questions/instructions remain in the q_a_prelim.
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RESPONSE --> Yes, I have been able to locate the SEND file.
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10:09:11 `q002. Note that every time you click on Enter Answer the program writes your response to your SEND file. Even if the program disappears all the information you have entered with the Enter Answer button will remain in that file. This program never 'unwrites' anything. Even if this program crashes your information will still be there in the SEND file. Explain this in your own words.
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RESPONSE --> Everything you enter using the Enter response will be saved to the Send file no matter what!
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10:10:10 Any time the instructor does not post a response to your access site by the end of the following day, you should resubmit your work using the Submit Work form, and be sure at the beginning to indicate that you are resubmitting, and also indicate the date on which you originally submitted your work. If you don't know where your access site is or how to access it, go to http://www.vhcc.edu/dsmith/_vti_bin/shtml.dll/request_access_code.htm and request one now. You can submit the q_a_prelim without your access code, but other assignments should contain your code.
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RESPONSE --> I already have an access code.
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10:10:43 `q003. If you are working on a VHCC computer, it is probably set up in such a way as to return to its original configuration when it is rebooted. To avoid losing information it is suggested that you back up your work frequently, either by emailing yourself a copy or by using a key drive or other device. This is a good idea on any computer. Please indicate your understanding of this suggestion.
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RESPONSE --> I will back everything up with a jump drive.
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???????????y??assignment #001 001. typewriter notation qa initial problems 07-05-2008
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12:41:00 `q001. Explain the difference between x - 2 / x + 4 and (x - 2) / (x + 4). The evaluate each expression for x = 2.
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RESPONSE --> Because of order of operations, ""x - 2 / x + 4"" is equal to ""x - (2 / x) + 4"", which can be quite different than the other. x - 2 / x + 4 2 - 2 / 2 + 4 2 - 1 + 4 5 (x - 2) / (x + 4) (2 - 2) / (2 + 4) 0 / 6 0 confidence assessment: 3
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12:41:43 The order of operations dictates that grouped expressions must be evaluated first, that exponentiation must be done before multiplication or division, which must be done before addition or subtraction. It makes a big difference whether you subtract the 2 from the x or divide the -2 by 4 first. If there are no parentheses you have to divide before you subtract. Substituting 2 for x we get 2 - 2 / 2 + 4 = 2 - 1 + 4 (do multiplications and divisions before additions and subtractions) = 5 (add and subtract in indicated order) If there are parentheses you evaluate the grouped expressions first: (x - 2) / (x - 4) = (2 - 2) / ( 4 - 2) = 0 / 2 = 0.
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RESPONSE --> I understand this completely. self critique assessment: 3
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13:05:54 `q002. Explain the difference between 2 ^ x + 4 and 2 ^ (x + 4). Then evaluate each expression for x = 2. Note that a ^ b means to raise a to the b power. This process is called exponentiation, and the ^ symbol is used on most calculators, and in most computer algebra systems, to represent exponentiation.
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RESPONSE --> In the first one, only x is the exponent of 2 and then you add 4 to it afterwards. In the second one, x + 4 is the exponent of 2. 2^x + 4 2^2 + 4 4 + 4 8 2^(x + 4) 2^(2 + 4) 2^6 64 confidence assessment: 3
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13:06:18 2 ^ x + 4 indicates that you are to raise 2 to the x power before adding the 4. 2 ^ (x + 4) indicates that you are to first evaluate x + 4, then raise 2 to this power. If x = 2, then 2 ^ x + 4 = 2 ^ 2 + 4 = 2 * 2 + 4 = 4 + 4 = 8. and 2 ^ (x + 4) = 2 ^ (2 + 4) = 2 ^ 6 = 2*2*2*2*2*2 = 64.
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RESPONSE --> I understand completely :) self critique assessment: 3
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13:40:19 `q003. What is the numerator of the fraction in the expression x - 3 / [ (2x-5)^2 * 3x + 1 ] - 2 + 7x? What is the denominator? What do you get when you evaluate the expression for x = 2?
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RESPONSE --> The Numerator is 3 The Denominator is (2x-5)^2 2-[3/(2x-5)(2x-5) * 3x+1 +7x 2-[3/(2(2)-5)(2(2)-5)]* 3(2)+1 + 7(2) 2-[3]*7+14 =-21 confidence assessment: 2
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13:41:33 We get (4-5)^2 * 4 - 1 + 3 / 1 - 4 = (-1)^2 * 4 - 1 + 3 / 4 - 2 evaluating the term in parentheses = 1 * 4 - 1 + 3 / 4 - 2 exponentiating (2 is the exponent, which is applied to -1 rather than multiplying the 2 by 4 = 4 - 1 + 3/4 - 2 noting that 3/4 is a fraction and adding and subtracting in order we get = 1 3/4 = 7 /4 (Note that we could group the expression as 4 - 1 - 2 + 3/4 = 1 + 3/4 = 1 3/4 = 7/4). COMMON ERROR: (4 - 5) ^ 2*4 - 1 + 3 / 4 - 2 = -1 ^ 2*4 - 1 + 3 / 4-2 = -1 ^ 8 -1 + 3 / 4 - 2. INSTRUCTOR COMMENTS: There are two errors here. In the second step you can't multiply 2 * 4 because you have (-1)^2, which must be done first.?Exponentiation precedes multiplication. ? Also it isn't quite correct to write -1^2*4 at the beginning of the second step. If you were supposed to multiply 2 * 4 the expression would be (-1)^(2 * 4).? Note also that the -1 needs to be grouped because the entire expression (-1) is taken to the power.?-1^8 would be -1 because you would raise 1 to the power 8 before applying the - sign, which is effectively a multiplication by -1.?......!!!!!!!!................................... RESPONSE --> I think I got lost somewhere.
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13:42:32 *&*& Standard mathematics notation is easier to see. On the other hand it's very important to understand order of operations, and students do get used to this way of doing it. You should of course write everything out in standard notation when you work it on paper. It is likely that you will at some point use a computer algebra system, and when you do you will have to enter expressions through a typewriter, so it is well worth the trouble to get used to this notation. Indicate your understanding of the necessity to understand this notation.
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RESPONSE --> Get use to algebra notation. self critique assessment: 1
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13:47:42 `q005. At the link http://www.vhcc.edu/dsmith/genInfo/introductory problems/typewriter_notation_examples_with_links.htm (copy this path into the Address box of your Internet browser; alternatively use the path http://vhmthphy.vhcc.edu/ > General Information > Startup and Orientation (either scroll to bottom of page or click on Links to Supplemental Sites) > typewriter notation examples and you will find a page containing a number of additional exercises and/or examples of typewriter notation.Locate this site, click on a few of the links, and describe what you see there.
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RESPONSE --> The typewriter expression link shows many examples of typewriter notation. Standard form expression is the way I would normally write the problems and then I should go back and look at the Typewriter version before submitting my answers. The typewriter and Standard Form with explanations gives many examples of the problem typed in standard from, explained, and then the answer is in typewriter form. confidence assessment: 3
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13:48:02 You should see a brief set of instructions and over 30 numbered examples. If you click on the word Picture you will see the standard-notation format of the expression. The link entitled Examples and Pictures, located in the initial instructions, shows all the examples and pictures without requiring you to click on the links. There is also a file which includes explanations. The instructions include a note indicating that Liberal Arts Mathematics students don't need a deep understanding of the notation, Mth 173-4 and University Physics students need a very good understanding,
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RESPONSE --> I understood this part completely. self critique assessment: 2
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?????z?P????q??assignment #001 001. `Query 1 College Algebra 07-07-2008 _???\?????????assignment #001 001. Sets Liberal Arts Mathematics I 07-07-2008
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10:30:06 `q001. Note that there are 4 questions in this assignment. `q001. Let A stand for the collection of all whole numbers which have at least one even digit (e.g., 237, 864, 6, 3972 are in the collection, while 397, 135, 1, 9937 are not). Let A ' stand for the collection of all whole numbers which are not in the collection A. Let B stand for the collection { 3, 8, 35, 89, 104, 357, 4321 }. What numbers do B and A have in common? What numbers do B and A' have in common?
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RESPONSE --> B and A = {8, 89, 104, 4321} B and A' = {3, 35, 357} Basically group A contains one set of numbers, A' contains everything else. Since A contains all numbers with at least one even digit, then B and A have those numbers from set B that contain at least one even digit. Everything else is in B and A'. confidence assessment: 3
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10:32:05 Of the numbers in B, 8, 89, 104, 4321 each have at least one even digit and so are common to both sets. 3 is odd, both of the digits in the number 35 are odd, as are all three digits in the number 357. Both of these numbers are therefore in A ' .
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RESPONSE --> B and A = {8, 89, 104, 4321} B and A' = {3, 35, 357} I understand completely self critique assessment: 3
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13:33:19 The key here is that there is nothing mutully exclusive about these categories-a person can have blue eyes as well as dark hair. So if there are 2 people in the room who have dark hair and blue eyes, which is certainly possible, then when we add 10 + 6 = 16 those two people would be counted twice, once among the 6 blue-eyed people and once among the 10 dark-haired people. So the 16 we get would be 2 too high. To get the correct number we would have to subtract the 2 people who were counted twice to get 16 - 2 = 14 people.
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RESPONSE --> Adter reading the conclusion it gives me a better understanding. self critique assessment: 0
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13:34:38 `q004. In a set of 100 child's blocks 60 blocks are cubical and 40 blocks are cylindrical. 30 of the blocks are red and 20 of the red blocks are cubical. How many of the cylindrical blocks are red?
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RESPONSE -->
...........Red...Blue....Total
------------------------------------ Cubic.|....20...|.......|.60 blocks are cubical ----------------------------| Cylin...|.........|.......|.40 blocks are cylindrical ------------------------------------- Totals.|....30..|.......|.100 set of 100 blocks Fill in the blanks.
...........Red...Blue....Total
------------------------------------ Cubic.|....20...|.40...|.60 blocks are cubical ----------------------------| Cylin...|...10...|..30..|.40 blocks are cylindrical ------------------------------------- Totals.|....30..|..70..|.100 set of 100 blocks 10 of the cylindrical blocks are red.<==ANSWER confidence assessment: 3
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13:35:00 Of the 30 red blocks 20 are cubical, so the rest must be cylindrical. This leaves 10 red cylindrical blocks.
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RESPONSE --> I understand this completely. self critique assessment: 2
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???????|??????assignment #002 002. Representing Sets Liberal Arts Mathematics I 07-07-2008
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13:47:49 `q002. Suppose that we have a total of 35 people in a room. Of these, 20 have dark hair and 15 have bright eyes. There are 8 people with dark hair and bright eyes. Draw two circles, one representing the dark-haired people and the other representing the bright-eyed people. Represent the dark-haired people without bright eyes by writing this number in the part of the first circle that doesn't include the overlap (region II). Represent the number of bright-eyed people without dark hair by writing this number in the part of the second circle that doesn't include the overlap (region III). Write the appropriate number in the overlap (region I). How many people are included in the first circle, and how many in the second? How many people are included in both circles? How many of the 35 people are not included in either circle?
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RESPONSE --> In the first circle, (Dark Hair) there are 20 people that have Dark Hair. In the second circle, (Bright Eyes) there are 15 people. In both circles there are 8 people who have both dark hair, and bright eyes. confidence assessment: 3
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???????????\?assignment #003 003. Intersection, Union, Complement, de Morgans Laws Liberal Arts Mathematics I 07-07-2008
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17:08:40 `q001. Note that there are 5 questions in this assignment. Again we have a total of 35 people in a room. Of these, 20 have dark hair and 15 have bright eyes. There are 8 people with dark hair and bright eyes. Let A stand for the collection of people who have dark hair and B for the collection who have bright eyes. The Intersection of these two collections is denoted A ^ B, and stands for the collection of all people who have both dark hair and bright eyes. The Union of these two collections is denoted A U B, and stands for the collection of all people who have at least one of these characteristics. In terms of the diagram you made for the preceding problem, describe the collection A ^ B and the collection A U B. Give the number of people in each of these collections (these numbers are designated by the notation n ( A ^ B) and n(A U B) ). Refer to the diagrams you have made.
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RESPONSE --> A^B=8 ''the collection of all people who have both dark hair and bright eyes'' A U B=A+B-A^B=20+15-8=35-8=27 and stands for the collection of all people who have at least one of these characteristics. confidence assessment: 2
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17:09:11 The collection A ^ B consists of all the people with both dark hair and bright eyes, which corresponds to the overlap between the two circles (region I). There are 8 people in this overlap, so we say n(A ^ B) = 8. The collection A U B consists of all the people who have least one of the characteristics. This would include the 12 people with dark hair but not bright eyes, located in the first circle but outside the overlap (region II); plus the 7 people with bright eyes but not dark hair, located in the second circle but outside the overlap (region III); plus the 8 people with both characteristics, located in the overlap (region I). Thus we include the 12 + 8 + 7 = 27 people who might be located anywhere within the two circles.
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RESPONSE --> I got these both correct! self critique assessment: 3
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17:09:32 `q002. Continuing the preceding example, we let A' stand for the people who are not in the collection A, and we let B' stand for the people who are not in the collection B. What are the characteristics of the people in A', and what characterizes people in B' ? What are n(A ') and n(B '), the numbers of people in A' and B' ?
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RESPONSE --> ... confidence assessment:
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17:09:40 Of the 35 people, those in A' are those outside of A. Since A consists of all the dark-haired people, A' consists of all the people lacking dark hair. This includes the 8 people outside of both circles (people having neither dark hair nor bright eyes, region IV) and the 7 people in the second circle but outside the overlap (people having bright eyes but not dark hair, region III). n(A ' ) is therefore 8 + 7 = 15. Since B consists of all the bright-eyed people, B' consists of all the people lacking bright eyes. This would include the 8 people outside both circles (region IV), all of whom lack both dark hair and bright eyes, and the 12 people in the first circle but outside the overlap (region II), who have dark hair but not bright eyes. n ( B ' ) is therefore 12 + 8 = 20.
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RESPONSE --> self critique assessment: 0
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17:09:56 `q003. ( A U B ) ' stands for the everyone outside A U B, and ( A ^ B ) ' stands for everyone outside A ^ B. What characterizes the people in each of these collections, and how many people are there in each?
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RESPONSE --> confidence assessment:
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17:22:01 `q005. Succinctly describe the relationships between ( A U B ) ', A ' U B ', (A ^ B) ' and A ' ^ B '.
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RESPONSE --> (A U B)' = empty set A' U B' = A ^ B (A^B)' = A U B A' ^ B' = empty set confidence assessment: 0
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17:22:33 ( A U B ) ' = A ' ^ B ' and ( A ^ B ) ' = A ' U B '. The collection outside of the union A U B is the intersection A ' ^ B ', and the collection outside the intersection A ^ B is the union A ' U B '. The ' operation changes union to intersection and intersection to union.
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RESPONSE --> Okay, I now understand. self critique assessment: 0
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?????e?????? assignment #001 001. `Query 1 College Algebra 07-08-2008
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10:57:24 **A list of the elements would just be 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14. **
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RESPONSE --> {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}. self critique assessment: 3
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????????????????assignment #001 001. `Query 1 College Algebra 07-08-2008
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11:17:32 Query 2.1.12 counting #'s 4 to 14 List the elements of the set.
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RESPONSE --> 4,5,6,7,8,9,10,11,12,13,14 confidence assessment: 2
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11:17:51 **A list of the elements would just be 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14. **
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RESPONSE --> I got that answer correct. self critique assessment: 2
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11:19:03 query 2.1.24 set builder for set of presidents between LBJ and Clinton
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RESPONSE --> {Richard M. Nixon, Gerald R. Ford, James Carter} confidence assessment: 2
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11:22:33 ** Set-builder notation is {x|x is a president who served between Lyndon Johnson and William Clinton} x is a variable and the condition 'x is a president who served between Lyndon Johnson and William Clinton' tells you what possible things the variable can be. COMMON ERROR: It's incorrect to say {x | x is the set of presidents who served between Johnson and Clinton}. x is a president, not a set of presidents. Should be {x|x is a president who served between Lyndon Johnson and William Clinton} **
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RESPONSE --> After reading the answer I know exactly what I did wrong self critique assessment: 2
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11:23:32 2.1.40 finite or infinite: set of rat #'s 0 to 1
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RESPONSE --> Finite confidence assessment: 3
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11:23:48 ** Rational numbers have form p/q, where p and q are integers. Numbers like 5/8, 57/31, -3/5, -57843/7843, etc. The subset {1/2, 1/3, 1/4, 1/5, ... } is just by itself an infinite set of rational numbers between 0 and 1. Then you have things like 348/937, and 39827389871 / 4982743789, and a whole infinite bunch of others. There are thus infinitely many rational numbers in any interval of the real line. COMMON MISCONCEPTION: finite, because it doesn't go on forever Rational numbers have form p/q, where p and q are integers. Numbers like 5/8, 57/31, -3/5, -57843/7843, etc. Not all of these lie between 0 and 1, of course. **
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RESPONSE --> self critique assessment: 3
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12:06:17 2.1.48 n(A), A={x|x is a U.S. senator} What is n(A) and why?
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RESPONSE --> n(A) means the number of things or people in set A, when set A consists of all values of x, such that x is a US senator. Since there are 50 states with 2 senators from each state, there are 100 US senators. Therefore, n(A) = 100 confidence assessment: 3
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12:06:26 ** n(A) stands for the number of elements in the set--in this case for the number of senators. There are 100, 2 from each State. So n(A) = 100. **
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RESPONSE --> self critique assessment: 0
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12:22:31 query 2.1.54 {x|x is neagtive number}
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RESPONSE --> Well defined confidence assessment: 3
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12:22:52 ** This notation means all possible values of x such that x is a negative number. The question is whether the set is well-defined or not. It is in fact well-defined because there is a definite way to decide whether a given object is an element of the set, because there is a definite way to determine whether an object is a negative number or not. ALTERNATIVE ANSWER: The set is well-defined because you have a criterion by which you can definitely decide whether something is or is not in the set. **
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RESPONSE --> I got that answer correct self critique assessment: 3
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12:23:26 2.1.72 true or false 2 not subset of {7,6,5,4}
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RESPONSE --> True confidence assessment: 2
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12:23:43 ** The statement is that 2 is not a subset. The statement is true because 2 isn't even a set, it's just a number. {2} is a set and could be a subset of something. 2 is just a number; it isn't a set so it can't be a subset of anything. The usual answer is that 2 isn't a subset because 2 isn't in the set. However that's not the correct reason. The correct reason is that 2 isn't a set and a subset must be a set. COMMON MISCONCEPTION: the statement says that 2 is not a subset, not that it is not an element of the set. So the reason it's not a subset is that 2 isn't a set at all, so it can't be a subset of anything. **
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RESPONSE --> self critique assessment: 3
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12:24:17 2.1.84 C={4,10,12}, B={2,4,8,10} Is it true or false that every element of C is also an element of B?
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RESPONSE --> True confidence assessment: 2
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12:24:43 ** Specifically it's false because the element 12 is in C but not in B. **
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RESPONSE --> self critique assessment:
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z???}???Q??t??assignment #002 002. `Query 2 College Algebra 07-08-2008
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12:26:23 2.2.24 U={a,b,...,g}, A={a,e}, B={a,b,e,f,g}, C={b,f,g}, D={d,e} Is C ps U? Is the statement true or false and why?
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RESPONSE --> True confidence assessment: 2
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12:26:28 ** It's true because all elements of C are in the universal set, and because there are elements of U that aren't in C. You have to have both conditions, since a proper subset cannot be identical to other set. **
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RESPONSE --> self critique assessment:
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12:26:38 Query 2.2.30 phi s D
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RESPONSE --> False confidence assessment: 2
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12:27:25 ** Note that You should be responding to problem 2.2.30 from the homework you worked out on paper. The shorthand notation is for my reference and won't always make sense to you. For clarification, though, the symbol for the empty set is the Greek letter phi. One set is a subset of another if every element of that set is in the other. To show that a set isn't a subset of another you have to show something in that set that isn't in the other. There's nothing in the empty set so you can never do this--you can never show that it has something the other set doesn't. So you can never say that the empty set isn't a subset of another set. Thus the empty set is a subset of any given set, and in particular it's a subset of D. ALTERNATIVE ANSWER: As the text tells you, the empty set is a subset of every set. ANOTHER ALTERNATIVE Every element of the empty set is in D because there is no element in the empty set available to lie outside of D. ONE MORE ALTERNATIVE: The empty set is a subset of every set. Any element in an empty set is in any set, since there's nothing in the empty set to contradict that statement. **
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RESPONSE --> I think I got mixed up on the question, and answerd it w/ the wrong answer. self critique assessment: 2
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12:28:17 2.2.33 D not s B Is the statement true or false and why?
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RESPONSE --> True confidence assessment: 2
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12:28:29 ** D is a subset of B if every element of D is an element of B-i.e., if D doesn't contain anything that B doesn't also contain. The statement says that D is not a subset of B. This will be so if D contains at least one element that B doesn't. **
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RESPONSE --> self critique assessment: 2
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12:28:53 2.2.36 there are exactly 31 subsets of B
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RESPONSE --> False confidence assessment: 2
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12:28:58 ** If a set has n elements then is has 2^n subsets, all but one of which are proper subsets. B has 5 elements so it has 2^5 = 32 subsets. So the statement is false. There are exactly 31 proper subsets of B, but there are 32 subsets of B. **
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RESPONSE --> self critique assessment:
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12:29:09 Query 2.2.40 there are exactly 127 proper subsets of U Is the statement true or false and why?
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RESPONSE --> False confidence assessment: 2
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12:29:14 ** The set is not a proper subset of itself, and the set itself is contained in the 2^n = 2^7 = 128 subsets of this 7-element set. This leaves 128-1 = 127 proper subsets. **
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RESPONSE --> self critique assessment: 3
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12:56:24 Query 2.2.48 U={1,2,...,10}, complement of {2,5,7,9,10} What is the complement of the given set?
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RESPONSE --> let X = {2,5,7,9,10) then X' = U-X = {1,3,4,6,8} all those members of U that are not in X a set with n members has 2^n subsets including the empty set and the set itself. all but one of these (the set itself) are proper subsets so X and X' both have 32 subsets, of which 31 are proper subsets. U has 1024 subsets, of which 1023 are proper. confidence assessment: 2
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13:00:43 ** the complement is {1,3,4,6,8}, the set of all elements in U that aren't in the given set. **
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RESPONSE --> self critique assessment: 3
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13:24:26 query 2.2.63 in how many ways can 3 of the five people A, B, C, D, E gather in a suite?
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RESPONSE --> (5*4*3) / (3*2*1) 10 ways confidence assessment: 2
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13:24:31 ** The answer here would consist of a list of all 3-element subsets: {a,b,c}, {a,b,d}, {a,b,e}, {a,c,d} etc. There are ten such subsets. Using a,b,c,d,e to stand for the names, we can list them in alphabetical order: {a,b,c), {a,b,d}, {a,b,e}, {a,c,d}, {a,c,e}, {a,d,e|, {b,c,d}, {b,c,e}, {b,d,e}, {c, d, e}**
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RESPONSE --> self critique assessment: 3
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??K?v???dz??v???? assignment #003 003. `Query 3 College Algebra 07-08-2008
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14:23:30 Query 2.3.15 (Y ^ Z')U X, univ={a,..g}, X={a,c,e,g}, Y = {a,b,c}, Z = {b, ..., f} What is the set (Y ^ Z')U X?
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RESPONSE --> Y ^ Z means all elements that are both in Y and in Z thus : {b,c} {b,c} U X are all elements in {b,c} or in X ( or in both )b thus {b,c} U X = {b,c, a,e,g} confidence assessment: 2
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14:23:35 **Z' = {a,g}, the set of all elements of the universal set not in Z. Y ^ Z' = {a}, since a is the only element common to both Y and Z'. So (Y ^ Z') U X = {a, c, e, g}, the set of all elements which lie in at least one of the sets (Y ^ Z') U X. **
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RESPONSE --> self critique assessment: 3
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14:24:01 **Z' = {a,g}, the set of all elements of the universal set not in Z. Y ^ Z' = {a}, since a is the only element common to both Y and Z'.**
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RESPONSE --> Z' = {a,g}, the set of all elements of the universal set not in Z. Y ^ Z' = {a}, since a is the only element common to both Y and Z' self critique assessment: 3
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14:36:12 2.3.51 always or not always true: n(A U B) = n(A)+n(B)
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RESPONSE --> Not always true confidence assessment: 3
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14:36:21 ** This conclusion is contradicted by many examples, including the one of the dark-haired and bright-eyed people in the q_a_. Basically n(A U B) isn't equal to n(A) + n(B) if there are some elements which are in both sets--i.e., in the intersection. } MORE DETAIL: The statement can be either true or false, depending on the sets A and B; it is not always true. The statement n(A U B) = n(A)+n(B) means that the number of elements in A U B is equal to the sum of the number of elements in A and the number of elements in B. The statement would be true for A = { c, f } and B = { a, g, h} because A U B would be { a, c, f, g, h} so n(A U B) = 5, and n(A) + n(B) = 2 + 3 = 5. The statement would not be true for A = { c, f, g } and B = { a, g, h} because A U B would be the same as before so n(AUB) = 5, while n(A) + n(B) = 3 + 3 = 6. The precise condition for which the statement is true is that A and B have nothing in common. In that case n(A U B) = n(A) + n(B). A more precise mathematical way to state this is to say that n(A U B) = n(A) + n(B) if and only if the intersection A ^ B of the two sets is empty. **
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RESPONSE --> self critique assessment: 3
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15:02:28 Query 2.3.60 X = {1,3,5}, Y = {1,2,3}. Find (X ^ Y)' and X' U Y'.
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RESPONSE --> (XUY) = 1,2,3,5 this is X union Y which is both X and Y combined. You don't repeat the number if it is already there, so that's why 1 and 3 are only put down once. (X^Y) = 1,3 this is X intersection Y. These are the numbers that are repeated in X and Y. Only 1 and 3 are the same in both. confidence assessment: 3
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15:02:32 ** X ^ Y = {1,3} so (X ^ Y) ' = {1,3}' = {2, 4, 5}. (X ' U Y ' ) = {2, 4} U {4, 5} = {2, 4, 5} The two resulting sets are equal so a reasonable conjecture would be that (X ^ Y)' = X' U Y'. **
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RESPONSE --> self critique assessment: 3
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15:03:05 Query 2.3.100 Shade (A' ^ B) ^ C
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RESPONSE --> confidence assessment: 3
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15:03:08 ** you would have to shade every region that lies outside of A and also inside B and also inside C. This would be the single region in the overlap of B and C but not including any part of A. Another way to put it: the region common to B and C, but not including any of A **
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RESPONSE --> self critique assessment:
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15:03:13 Describe the shading of the set (A ^ B)' U C.
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RESPONSE --> confidence assessment:
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15:03:16 ** All of C would be shaded because we have a union with C, which will include all of C. Every region outside A ^ B would also be shaded. A ^ B is the 'overlap' region where A and B meet, and only this 'overlap' would not be part of (A ^ B) '. The 'large' parts of A and B, as well as everything outside of A and B, would therefore be shaded. Combining this with the shading of C the only the part of the diagram not shaded would be that part of the 'overlap' of A and B which is not part of C. **
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RESPONSE --> self critique assessment: 3
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15:03:20 2.3.114 Largest area of A shaded (sets A,B,C). Write a description using A, B, C, subset, union, intersection symbols, ', - for the shaded region.
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RESPONSE --> confidence assessment:
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15:03:36 ** Student Answer and Instructor Response: (B'^C')^A Instructor Response: Good. Another alternative would be A - (B U C ), and others are mentioned below. COMMON ERROR: A ^ (B' U C') INSTRUCTOR COMMENT: This is close but A ^ (B' U C') would contain all of B ^ C, including a part that's not shaded. A ^ (B U C)' would be one correct answer. **
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RESPONSE --> self critique assessment:
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n??????ì|???????? assignment #011 011. How many triangles? Liberal Arts Mathematics I 07-08-2008
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15:33:18 `q001. . There are five questions in this set. Draw four points in a square pattern (i.e., if the points were properly connected, they should form a square). From each of the points, draw a straight line to each of the other points. How many lines did you draw?
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RESPONSE --> 4 confidence assessment: 3
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15:35:08 Each corner of the square will connected to each of the other three corners, so from each corner you would have drawn three lines. Since there are four corners, had you followed the instructions precisely you would have drawn 4 * 3 = 12 lines. However each of these lines will be identical with another line you would have drawn, since for any two corners you would be drawing a line from the first to the second then another overlapping line from the second to the first. Therefore you might have said that there are 6 lines.
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RESPONSE --> I see where I went wrong self critique assessment: 0
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15:35:34 You should have a total of 8 triangles. The diagonals divide the square up into 4 small triangles. Each diagonal also divides the square into 2 larger triangles. Since there are 2 diagonals there are 4 larger triangles. The 4 small triangles and the 4 larger triangles total 8 triangles.
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RESPONSE --> 8 triangles self critique assessment:
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15:36:40 The easiest way to list these sequences is alphabetically: ABC, ABD, ABE all start with AB; then ACD and ACE start with AC and ADE starts with AD. This is a list of all possible combinations containing A. We next list all possible remaining combinations containing B: BCD, BCE and BDE. Then we write down CDE, the only remaining combination containing C. We thus have the 10 combinations ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, CDE.
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RESPONSE --> self critique assessment:
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?}???L????? assignment #011 011. How many triangles? Liberal Arts Mathematics I 07-08-2008
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15:37:42 `q001. . There are five questions in this set. Draw four points in a square pattern (i.e., if the points were properly connected, they should form a square). From each of the points, draw a straight line to each of the other points. How many lines did you draw?
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RESPONSE --> 12 confidence assessment: 3
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15:37:49 Each corner of the square will connected to each of the other three corners, so from each corner you would have drawn three lines. Since there are four corners, had you followed the instructions precisely you would have drawn 4 * 3 = 12 lines. However each of these lines will be identical with another line you would have drawn, since for any two corners you would be drawing a line from the first to the second then another overlapping line from the second to the first. Therefore you might have said that there are 6 lines.
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RESPONSE --> self critique assessment: 0
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15:38:21 `q002. How many triangles are there in the figure you drew?
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RESPONSE --> 6 confidence assessment: 2
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15:39:09 You should have a total of 8 triangles. The diagonals divide the square up into 4 small triangles. Each diagonal also divides the square into 2 larger triangles. Since there are 2 diagonals there are 4 larger triangles. The 4 small triangles and the 4 larger triangles total 8 triangles.
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RESPONSE --> I see where I went wrong self critique assessment: 2
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15:44:06 `q003. The lines you drew should form a square with its two diagonals. Label the corners of the square A, B, C and D, going in order around the square, and label the center where the diagonals cross E. Now list all possible combinations of 3 of the letters A, B, C, D, E (note: combinations don't care about order, so A D E is the same as D A E or E A D or any other combination of these same three letters, so list each possible combination only once. That is, if you list for example ADE you won't list DAE).
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RESPONSE --> ABC ADC CDA BAD BCD DAB DCB ACD BDC CBA CAD CDB =12 confidence assessment: 2
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15:44:21 The easiest way to list these sequences is alphabetically: ABC, ABD, ABE all start with AB; then ACD and ACE start with AC and ADE starts with AD. This is a list of all possible combinations containing A. We next list all possible remaining combinations containing B: BCD, BCE and BDE. Then we write down CDE, the only remaining combination containing C. We thus have the 10 combinations ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, CDE.
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RESPONSE --> self critique assessment:
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