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Inductive Reasoning

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These are a total of 18 mixed problems all ranging from inductive reasoning to estimation. I need help coming to the conclusion. Please help me answer these study questions and show me step by step how to get the answer and how to check if the answer is correct.

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The solution does a great job of clearly listing out the steps that are needed to get to the answers. The student can then use these steps and concepts and apply them to similar problems in the future. The response is very detailed and the attachment is more than 5 pages long and covers everything in extensive detail. Overall, an excellent response to the questions asked. Solutions to each problem are given and explained in clear terms.

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These are a couple of questions in my study packet that I do not understand. Please help me answer the following problems. SHOW YOUR WORK step by step please.

1. Jane determines that her lawn contains an average of 3.8 grubs per square foot (ft2). If her rectangular lawn measures 60.4 ft by 80.2 ft, estimate the total number of grubs in her lawn.

Solution:

Estimated area of rectangular lawn = 60*80 = 4800 square feet

Estimated number of grubs = 4*4800 = 19200

2. Sandra drove for 148.2 miles and used 9.9 gallons of gas. Estimate the number of miles Sandra's car gets per gallon.

Estimated miles = 150
Estimated number of gallons of gas = 10

Estimated number of miles Sandra's car gets per gallon = 150/10 = 15 miles per gallon

3. Bob wants to have concrete driveway in front of his house. The driveway will measure 58 2/3 feet long and 18 1/2 feet wide; and will be 3/4 foot thick. How many cubic yards of cement will be needed for the driveway? Round your answer to the nearest cubic yard. [1 cubic yd = 27 cubic feet]

Volume of concrete needed = length*width*thickness
=
cubic feet
= cubic yd

4. Use inductive reasoning to determine the next three numbers in the pattern:
0, 1, 3, 6, 10, 15 .....

Look at the difference:
1 - 0 = 1
3 - 1 = 2
6 - 3 = 3
10 - 6 = 4
15 - 10 = 5

Thus, the difference between consecutive terms is increasing.

To get next term add 6 to 15

Next term : 15 + 6 = 21

Now add 7 to 21 to get next term
= 21 + 7 = 28

Now add 8 to 28 to get next term
= 28 + 8 = 36

Next three terms will be: 21, 28, 36

5. Find a counterexample to show that the following statement is incorrect:
"The sum of any two prime numbers is divisible by ...

Solution provided by:
Sandhya Sharma, MSc
Education
  • BSc, Meerut University
  • MSc, Meerut University
  • MPhil, Institute of Advanced Studies
  • MSc, AIT
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