Section 1-1
Legend has it that the great mathematician Carl Friedrich Gauss (1777-1855) at a very young age was told by his teacher to find the sum of the first 100 counting numbers. While his classmates toiled at the problem, Carl simply wrote down a single number and handed the correct answer in to his teacher. The young Carl explained that he observed that there were 50 pairs of numbers that each added up to 101. So the sum of all the numbers must be 50•101=5050. Use the method of Gauss to find the sum 1+2+3...+345
1+2+3...+345=59,685 because 173x345
Legend has it that the great mathematician Carl Friedrich Gauss (1777-1855) at a very young age was told by his teacher to find the sum of the first 100 counting numbers. While his classmates toiled at the problem, Carl simply wrote down a single number and handed the correct answer in to his teacher. The young Carl explained that he observed that there were 50 pairs of numbers that each added up to 101. So the sum of all the numbers must be 50•101=5050. Use the method of Gauss to find the sum 1+2+3...+630=
1+2+3...+630=198,765 because 631x315
A list of equations is given. Use the list and inductive reasoning to predict the next equation, and verify your conjecture. 3(4) =4(4−1) 3(4)+3(16)=4(16−1) 3(4)+3(16)+3(64) =4(64−1) 3(4)+3(16)+3(64)+3(256)=4(256−1)
3(4) =4(4−1) 3(4)+3(16)=4(16−1) 3(4)+3(16)+3(64) =4(64−1) 3(4)+3(16)+3(64)+3(256)=4(256−1) 3(4)+3(16)+3(64)+3(256)+3(1,024)=4(1,024-1) Simplified 4,092
Identify the pattern in the list of numbers. Then use this pattern to find the next number. 5, 7, 12, 19, 31, 50, ____
5, 7, 12, 19, 31, 50, 81 (31+50)
Which of the following are properties of inductive arguments? Select all that apply
A conclusion is formed by generalizing from a set of more specific premises. Your answer is correct. E. It can be analyzed only in terms of its strength. Your answer is correct. F. It cannot prove its conclusion true. At best, it shows that its conclusion probably is true.
Which of the following are examples of inductive arguments? Select all that apply.
A. Premise: (−2)×(3)=−6 Premise: (−3)×(1)=−3 Premise: (−4)×(2)=−8 Conclusion: The product of a negative number and a positive number is negative.
Determine whether the reasoning is an example of deductive or inductive reasoning. If the mechanic says that it will take seven days to repair your SUV, then it will actually take ten days. The mechanic says, "I figure it'll take exactly one week to fix it, ma'am." Then you can expect it to be ready ten days from now.
The reasoning is deductive because general principles are being applied to specific examples
Determine whether the reasoning is an example of deductive or inductive reasoning. If you build it, they will come. You build it. Therefore, they will come.
The reasoning is deductive because general principles are being applied to specific examples.
Determine whether the reasoning is an example of deductive or inductive reasoning. The next number in the pattern 20, 25, 30, 35, 40 is 45.
The reasoning is inductive because a general conclusion is being made from repeated observations of specific examples
Which of the following are properties of deductive arguments? Select all that apply.
Which of the following are properties of deductive arguments? Select all that apply. A. A specific conclusion is deduced from a set of more general (or equally general) premises. Your answer is correct. E. It can be valid even when its conclusion is blatantly false. Your answer is correct. F. It can be analyzed in terms of its validity and soundness. It is valid if its conclusion follows necessarily from its premises. It is sound if it is valid and its premises are true.
