MTH/215T: Quantitative Reasoning I – 7 problems
Question Description
1. In May you used 1500 kilowatt-hours of energy for electricity.
a. Calculate the total electrical energy use in joules.
b. Calculate your average power use in watts.
c. Assume that your power supplier generates electricity by burning oil. Note that 1 liter of oil releases 12 million joules of energy. How much oil is needed to generate the electricity you use? Give your answer in both liters and gallons.
a. calculate the total electrical energy use was __ joules.
b. The average power use is __ watts.
c. To generate the electricity you used, __ L is needed.
To generate the electricity you used, __ gal is needed.
2. Describe the four basic steps of problem solving.
1. What is the first basic step of problem solving? Choose the correct answer below.
Understand the problem.
Obtain extra information that is not provided in the problem statement, if necessary.
Keep an organized, neat, and written record of your work.
Be sure that your result makes sense.
2. What is the second basic step of problem solving? Choose the correct answer below.
Think about the context of the problem.
Double-check each step so that errors are not carried through to the solution.
Devise a strategy for solving the problem.
Find an independent way of checking the result.
3. What is the third basic step of problem solving? Choose the correct answer below.
Carry out your strategy, and revise it if necessary.
Restate the problem in different ways to clarify its question.
Consider and discuss any pertinent implications of the result.
Map out a strategy with a flow chart or diagram.
4. What is the fourth basic step of problem solving? Choose the correct answer below.
Constantly reevaluate your strategy and create a revised strategy as needed.
Make a mental or written model of the situation.
Look back to check, interpret, and explain your result.
Make a list of possible strategies.
3. Suppose a railroad rail is 6 kilometers and it expands on a hot day by 12 centimeters in length. Approximately how many meters would the center of the rail rise above the ground.
a. The center of the rail would rise approximately __ meters above the ground.
4. Compare the following pair of numbers A and B in three ways.
a. Find the ration of A to B.
b. Find the ratio of B to A.
c. Complete the sentence: A is __ percent of B.
A = 160 and B=420
a. The ratio of A to B is –
b. The ratio of B to A is –
c. A is __ percent of B
4. Express the first number as a percentage of the second number.
1142 people per square mile in new Jersey and a national average of 89.5 Americans per square mile in 2012.
a. 1142 people per square mile in New Jersey is __% of the national average of 89.5 Americans per square mile in 2012.
5. The annual interest rate for jacks savings account increased from 2.1% to 3.5%. Complete parts (a) and (b) below.
a. Describe the change an an absolute change in terms of percentage points.
The annual interest rate increased by __ percentage points.
b. Describe the change as a relative change in terms of a percentage.
The annual interest rate increased by __%
6. Answer the following question about the following quote from a news source.
“at $1.36 million, they closed last month for … 19 percent above what they paid in 2007. “how much did they pay in 2007?
They paid $__ million
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