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course Mth164
6/5 2
Question: `q003. If you are earning 8 dollars / hour, how long will it take you to earn $72? The answer may well be obvious, but explain as best you can how you reasoned out your result.YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
You take the total you were trying to earn, and divide that by the amount per hour you are earning. $72 / 8 = 9 hours
confidence rating #$&*:
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Self-critique: OK
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Question: `q004. Calculate (8 + 3) * 5 and 8 + 3 * 5, indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results.
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Your solution:
To calculate (8+3) * 5, you would first add the numbers inside of the parenthesis. You take the sum of the numbers and then multiply it by 5. (11) * 5= 55
To calculate 8 + 3 * 5, you would first multiply. Once you have multiplied 3 * 5 and got 15, you would then add the 8 to reach a sum of 23.
confidence rating #$&*:
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Self-critique: OK
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Question: `q005. Calculate (2^4) * 3 and 2^(4 * 3), indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results. Note that the symbol '^' indicates raising to a power. For example, 4^3 means 4 raised to the third power, which is the same as 4 * 4 * 4 = 64.
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Your solution:
To calculate (2^4) * 3, you would first take 2 and raise it to the fourth power. 2*2*2*2 would equal 16. Then you would take 16 and multiply it by 3. (16) * 3 = 48
To calculate 2^(4*3), you would first simplify what is in parenthesis. Multiply 4*3 to get 12. You would then take 2 to the 12th power. To do this you would simply multiply 2 by itself 12 times. 2*2*2*2*2*2*2*2*2*2*2*2= 4096
confidence rating #$&*:
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Self-critique: OK
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Question: `q006. Calculate 3 * 5 - 4 * 3 ^ 2 and 3 * 5 - (4 * 3)^2 according to the standard order of operations, indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results.
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Your solution:
To calculate 3 * 5 - 4 * 3^2, you would first take 3 to the second power. You would get 9. The simplified equation would be 3*5-4*9. Multiplication would come next. Although there are two, there is no order in which you have to multiply them. Multiply 3*5 to get 15 and then multiply 4*9 to get 36. You now have a simple subtracting math problem in 15-36 = -21
To calculate 3*5 - (4*3)^2, you would first take what is in parenthesis and simplify it. Multiply 4*3 to get 12. You now have an equation that reads 3*5 - (12)^2. Your next step is to take 12 to the 2nd power. 12^2 = 144. Your equation has been simplified to 3*5 -144. Multiplication comes before subtraction, so you would multiply 3*5 to get 15. After this you would simply subtract 15-144. 15 - 144 = -129
The reason there are different answers is because they are different formulas. Although the same numbers, the way they are computed is determined by things such as parenthesis. You use the same order for every equation involving simple reductions such as this.
confidence rating #$&*:
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Self-critique: OK
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Question: `q007. Let y = 2 x + 3. (Note: Liberal Arts Mathematics students are encouraged to do this problem, but are not required to do it).
• Evaluate y for x = -2. What is your result? In your solution explain the steps you took to get this result.
• Evaluate y for x values -1, 0, 1 and 2. Write out a copy of the table below. In your solution give the y values you obtained in your table.
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Your Solution:
• If x = -2 then y = 2(-2)+3 = -4+3 = -1
• If x = -1 then y = 2(-1)+3 = -2+3 = 1
• If x = 0 then y = 2(0)+3 = 0+3 = 3
• If x = 1 then y = 2(1)+3 = 2+3 = 5
• If x = 2 then y = 2(2)+3 = 4+3 = 7
The table would look as follows:
X Y
-2 -1
-1 1
0 3
1 5
2 7
The table would be a straight line, linear function. It would look like the linear function given in the examples.
confidence rating #$&*:
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Self-critique: OK
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Question: `q009. Let y = 2 ^ x + 3.
• Evaluate y for x = 1. What is your result? In your solution explain the steps you took to get this result.
• Evaluate y for x values 2, 3 and 4. Write out a copy of the table below. In your solution give the y values you obtained in your table.
• If x = 1 then y = 2^1 + 3 = 2 + 3 = 5
• If x = 2 then y = 2^2 + 3 = 4 + 3 = 7
• If x = 3 then y = 2^3 + 3 = 8 + 3 = 11
• If x = 4 then y = 2^4 + 3 = 16 + 3 = 19
Just as the mathematical equations previously, you would take the number to its given power prior to any addition within the problem.
X Y
1 5
2 7
3 11
4 19
After graphing these points, the line shows that it rises from left to right. This shows the characteristics of an exponential graph, which is shown in the examples.
confidence rating #$&*:
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Self-critique: OK
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Question: `q010. If you divide a certain positive number by 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
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Your solution:
It does not matter what type of number you are using, if you divide something by 1, the number remains the same as it was.
confidence rating #$&*:
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Self-critique: OK
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Question: `q011. If you divide a certain positive number by a number greater than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
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Your solution:
If you divide any positive number by a number that is greater than 1, you will get a smaller number than you started with. If you take 100 and divide it by any positive number greater than 1, you will come out with a number that will be smaller than 100. It does not matter what positive number you may choose.
confidence rating #$&*:
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Self-critique: 2, I do not know how to explain it other than that. It may not fully give some the information they were looking for.
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Question: `q012. If you divide a certain positive number by a positive number less than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
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Your solution:
If you divide a positive number by a positive number that is less than 1, you will get a larger number than you originally started with. If you look at the positive number 1 as an equal sign, you can understand that dividing any number by a positive number above that equal sign will give you a smaller number, and any positive number below that equal sign will give you a larger number than you started with.
confidence rating #$&*:
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Self-critique: OK
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