Rates QA

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course MTH 158

Question: If you make $50 in 5 hr, then at what rate are you earning money? Your solution: You would divide 50 by 5 giving you the answer and it would be 10$ an hour.

confidence rating #$&*: 3

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Question: `q003.If you make $60,000 per year then how much do you make per month?

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Your solution: You would make 5000$ a month you would take the 60,000 a year and divide it by the amount of months in a year which is 12. That would look like 60,000/12.

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Question: `q004. Suppose that the $60,000 is made in a year by a small business. Would be more appropriate to say that the business makes $5000 per month, or that the business makes an average of $5000 per month?

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Your solution: The business would make an average of 5000$ a month. Every month the business wouldn’t make that quota. Some months it could be lower some months could be higher it depends on the amount of business and as well as the type of business.

confidence rating #$&*: 3.

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Question: `q005. If you travel 300 miles in 6 hours, at what average rate are you covering distance, and why do we say average rate instead of just plain rate?

Your solution: You are traveling at 50 miles on average every hour. Some of the time you could be making great time and there could be no obstacles and during another hour there could be some type of traffic, weather, or delays.

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Question: `q006. If you use 60 gallons of gasoline on a 1200 mile trip, then at what average rate are you using gasoline, with respect to miles traveled?

Your solution: Your using .05 gallons of gasoline per mile. To get this you would have to divide 60 divided by 1200 (60/1200).

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Question: `q007. The word 'average' generally connotes something like adding two quantities and dividing by 2, or adding several quantities and dividing by the number of quantities we added. Why is it that we are calculating average rates but we aren't adding anything?

Your solution: The average normally is spoken when you talk about distances and lengths when you have several of them that needed to be summed or averaged. You are looking for the sum of the problem for example you add 1 + 2 +3 +4 +5= 15 then you would divide that by 5 which is the amount of numbers added up giving you 3.

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Question: `q008. In a study of how lifting strength is influenced by various ways of training, a study group was divided into 2 subgroups of equally matched individuals. The first group did 10 pushups per day for a year and the second group did 50 pushups per day for year. At the end of the year to lifting strength of the first group averaged 147 pounds, while that of the second group averaged 162 pounds. At what average rate did lifting strength increase per daily pushup?

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Your solution: The second group did 40 more pushups on average and gained also 15 more pounds on average then the first group. Next you would take those two and divide them together giving you .375 pounds per pushups.

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Question: `q009. In another part of the study, participants all did 30 pushups per day, but one group did pushups with a 10-pound weight on their shoulders while the other used a 30-pound weight. At the end of the study, the first group had an average lifting strength of 171 pounds, while the second had an average lifting strength of 188 pounds. At what average rate did lifting strength increase with respect to the added shoulder weight?

Your solution: Theres a difference in weight at 20 pounds in weight difference and a 17 pound diference in strength gained. Then you would divide those two together that would look like 17/20. That would give you .85. The average was .85 per pounds when it comes to the weight added.

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Question: `q010. During a race, a runner passes the 100-meter mark 12 seconds after the start and the 200-meter mark 22 seconds after the start. At what average rate was the runner covering distance between those two positions?

Your solution: First you minus the meters and the seconds together. 200-100=100 and 22-12. Then you divide those together which would be 100/10 which equals 10 meters per second. This would be on average because the runners start would be slower than the steady picked up speed.

Question: `q011. During a race, a runner passes the 100-meter mark moving at 10 meters / second, and the 200-meter mark moving at 9 meters / second. What is your best estimate of how long it takes the runner to cover the intervening 100 meter distance?

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Your solution: First you have to find the average time and to do that we take the 10mps and the 9mps and get the sum of that. Which would be 9+10= 19 then you have to divid that by 2. Which is 9.5. Then you take the meters that are being asked for which is 100 and divide the sum of the two mps and you get 100 meters / 9.5mps. That would equal 10.5.

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Question: `q012. We just averaged two quantities, adding them and dividing by 2, to find an average rate. We didn't do that before. Why we do it now?

Your solution: We do it now because we don’t have the average rate that we need to complete the problem the way we were doing it in the earlier problems. I am also given a different set of quantities that can be used to make the rates equation work.

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Question: `q013. The volume of water in a container increases from 1400 cm^3 to 1600 cm^3 as the depth of the water in the container changes from 10 cm to 14 cm. At what average rate was the volume changing with respect to depth?

Optional question: What does this rate tell us about the container?

Your solution: First you subtract the two cm^3 which gives you 200cm^3 and then you minus the container size which is 14cm minus 10cm which is 4cm then you divide the 200cm^3 minus 4cm which is 50.

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Question: `q014. An athlete's rate of doing work increases more or less steadily from 340 Joules / second to 420 Joules / second during a 6-minute event. How many Joules of work did she do during this time?

Your solution: First you add them up to find the sum and that would be 760 then you divide by 2. Then she would have done 380 joules in that time.

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