For Exercises 25–34, use inductive reasoning to find a pattern for the answers. Then use the pattern to guess the result of the final calculation, and perform the operation to see if your answer is correct . 34. A Greek mathematician named Pythagoras is said to have discovered the following number pattern. Find the next three sums by using inductive reasoning. Don’t just add! 1 = 1 1 + 3 = 4 1 + 3 + 5 = 9 1 + 3 + 5 + 7 = 16 1 + 3 + 5 + 7 + 9 = ? 1 + 3 + 5 + 7 + 9 + 11 = ? 1 + 3 + 5 + 7 + 9 + 11 + 13 = ?
For Exercises 25–34, use inductive reasoning to find a pattern for the answers. Then use the pattern to guess the result of the final calculation, and perform the operation to see if your answer is correct . 34. A Greek mathematician named Pythagoras is said to have discovered the following number pattern. Find the next three sums by using inductive reasoning. Don’t just add! 1 = 1 1 + 3 = 4 1 + 3 + 5 = 9 1 + 3 + 5 + 7 = 16 1 + 3 + 5 + 7 + 9 = ? 1 + 3 + 5 + 7 + 9 + 11 = ? 1 + 3 + 5 + 7 + 9 + 11 + 13 = ?
Solution Summary: The author explains that inductive reasoning is the process of reasoning to a general conclusion through observations of specific cases.
For Exercises 25–34, use inductive reasoning to find a pattern for the answers. Then use the pattern to guess the result of the final calculation, and perform the operation to see if your answer is correct.
34. A Greek mathematician named Pythagoras is said to have discovered the following number pattern. Find the next three sums by using inductive reasoning. Don’t just add!
The
Student Store holds a contest to hand out souvenir shirts featuring four designs
from the Mathematics Hall of Fame. Each shirt is size XL.
700 different people enter the contest.
6 different people win a shirt.
Shirts with the same design are indistinguishable from one another.
The order in which the shirts are handed out does not matter.
How many different ways can the shirts be handed out? No need to simplify your answer.
You must explain your answer.
SEQUENCE
UPVOTE WILL BE GIVEN. PLEASE WRITE THE COMPLETE SOLUTIONS LEGIBLY.
Use deductive reasoning to show that the following procedure
produces a number that is three times the original number.
Procedure: Pick a number. Multiply the number by 6, add 10 to the
product, divide the sum by 2, and subtract by 5.
Hint: Let n represent the original number.
Chapter 1 Solutions
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