course Mth 151
HELLO
Answer: If you work for 4 hours at 8 dollars an hour than you multiply 4 times 8 and that will give you how much money you would earn in the four hours worked. 8*4= 32 dollars.
“Ok”
`q002. If you work 12 hours and earn $168, then at what rate, in dollars / hour, were you making money?
Answer: To find how much money you are making per hour, if you know the total amount of money made, you divide the amount of money, in this case is $168 and divide that by the number of hours worked and you come up with $14 an hour
“Ok”
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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.
Answer: If you are earning 8 dollars an hour and you make a total of $72 then you would divide $72 by 8 to see how many hours you worked to earn the $72, which would be 9 hours.
“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.
Answer: If you put something in () then you are telling the calculator that you want it to solve that and then do the next step which would be to multiply by 5. If you do it all at once then you are telling the calculator to do the steps in order which would be multiply then add so it does 3*5 which gives you 15 and then it adds 8 to that.
“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.
Answer: In the first you would raise 2 to the fourth power and then times by 3. In the second you would do 4 times 3 which is 12 and then raise 2 to the 12th power
“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.
Answer: When you set something in () then the calculator solves that first and then does the order of operations.
“Ok”
`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.
x y
-2 -1
-1 1
0 3
1 5
2 7
• Sketch a graph of y vs. x on a set of coordinate axes resembling the one shown below. You may of course adjust the scale of the x or the y axis to best depict the shape of your graph.
Answer: Substitute the x values for the x place in y=2x+3 and you will then get the y values
“Ok”
• In your solution, describe your graph in words, and indicate which of the graphs depicted previously your graph most resembles. Explain why you chose the graph you did.
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Question: `q008. Let y = x^2 + 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.
x y
-2
-1
0
1
2
• Sketch a graph of y vs. x on a set of coordinate axes resembling the one shown below. You may of course adjust the scale of the x or the y axis to best depict the shape of your graph.
• In your solution, describe your graph in words, and indicate which of the graphs depicted previously your graph most resembles. Explain why you chose the graph you did.
Answer: Linear
“Ok”
Question: `q009. 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 = 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.
Answer: Same as question 8
Recall that the exponentiation in the expression 2^x + 1 must be done before, not after the addition.
When x = 1 we obtain y = 2^1 + 3 = 2 + 3 = 5.
When x = 2 we obtain y = 2^2 + 3 = 4 + 3 = 7.
When x = 3 we obtain y = 2^3 + 3 = 8 + 3 = 11.
When x = 4 we obtain y = 2^4 + 3 = 16 + 3 = 19####
x y
1 7
2 4
3 3
4 4
• Sketch a graph of y vs. x on a set of coordinate axes resembling the one shown below. You may of course adjust the scale of the x or the y axis to best depict the shape of your graph.
• In your solution, describe your graph in words, and indicate which of the graphs depicted previously your graph most resembles. Explain why you chose the graph you did.
Answer: Exponental
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?
Equal
“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?
Less than original number
“Ok”
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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?
Larger number
“Ok”
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Question: `q013. Students often get the basic answers to nearly all, or even all these questions, correct. Your instructor has however never seen anyone who addressed all the subtleties in the given solutions in their self-critiques, and it is very common for a student to have given no self-critiques. It is very likely that there is something in the given solutions that is not expressed in your solution.
Answer: Recall that the exponentiation in the expression 2^x + 1 must be done before, not after the addition.
When x = 1 we obtain y = 2^1 + 3 = 2 + 3 = 5.
When x = 2 we obtain y = 2^2 + 3 = 4 + 3 = 7.
When x = 3 we obtain y = 2^3 + 3 = 8 + 3 = 11.
When x = 4 we obtain y = 2^4 + 3 = 16 + 3 = 19####
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