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course Mth 277
June 7 around 5
Question: `q001. If you are earning money at the rate of 8 dollars / hour and work for 4 hours, how much money do you make during this time? Answer in such a way as to explain your reasoning as fully as possible. A solution to this problem appears several lines below, but enter your own solution before you look at the given solution. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: (type in your solution starting in the next line)
8 dollars/hour * 4 hours worked = $32 earned: 3: ok
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Question: `q002. If you work 12 hours and earn $168, then at what rate, in dollars / hour, were you making money?
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Your solution: (type in your solution starting in the next line)
Earned $168 / 12 hours of work = $14 dollars per hour: 3: 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.
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Your solution: (type in your solution starting in the next line)
$72 / 8 dollars per hour = 9 hours: 3: 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: (type in your solution starting in the next line)
(8 + 3) * 5
you have to do whats in the parentheses first so (8 + 3) = 11; than you have to multiply by 5, so 11 * 5 = 55
8 + 3 * 5
you have to use the order of operations and multiplication comes first, so 5 * 3 = 15; than you have to add 8, so 15 + 8 = 23: 3: 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:
(2^4) * 3
you have to do whats in the parenthese first so (2*2*2*2) = 16, than you have to multiply by 3 which = 48
2^(4 * 3)
have to do whats in the parenthese first so (4 * 3) = 12, than you have to take 2^(12) which = 4,096
3 (confidence in my answer): 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:
calculate: 3 * 5 - 4 * 3 ^ 2
step 1: 3^2 = 9
step 2: 3 * 5 - 4 * 9 = .....
step 3: 3 * 5 = 15
step 4: 4 * 9 = 36
final step: 15 - 36 = -21
calculate: 3 * 5 - (4 * 3)^2
step 1: (4 * 3) = 12
step 2: 12^2= 144
step 3: 3 * 5 - 144 = ....
step 4: 3 * 5 = 15
final step: 15 - 144 = -129
3(confidence in my answer): 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.
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.
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Your solution:
when x= -2; y = 2(-2) + 3 = -1
when x= -1; y = 2(-1) + 3 = 1
when x= 0; y = 2(0) + 3 = 3
when x= 1; y = 2(1) + 3= 5
when x=2; y = 2(2) + 3 = 7
when we graph it the line is a straight line.
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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.
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Your solution:
when x= -2; y= (-2)^2 + 3 = 7
when x= -1; y= (-1)^2 + 3 = 4
when x= 0; y= (0)^2 + 3 = 3
when x= 1; y= (1)^2 + 3 = 4
when x= 2; y= (2)^2 + 3 = 7
its a parabolic graph
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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.
x y
1
2
3
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.
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Your solution:
when x= 1; y= 2^(1) + 3= 5
when x= 2; y= 2^(2) + 3= 7
when x= 3; y= 2^(3) + 3= 11
when x= 4; y= 2^(4) + 3= 19
the graph is exponential
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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:
if you divide any # by 1 the result will be the same as the original #
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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:
The bigger the # is the smaller the result will be. For example:
24/2 = 12
24/3 = 8
24/4 = 6
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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 any # by a positive # less than 1 you will get more of a result; as long as the number is positive.
For example:
24/.5 = 48
24/.3 = 80
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