Contemporary Math 1.1

Determine the most probable next term in the list of numbers. 1/3,2/5,3/7,4/9,5/11

6/13

Determine the most probable next term in the following list of numbers. 6,30,150,750,3750

18750

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.

Find the next number in the sequence. 4,9,16,25,

36

What is the most probable next number in this​ list? 12,1,1,1,2,1,3 ​(Hint: Think about a clock with​ chimes)

The most probable next number is 1

Summarize the differences between deductive and inductive arguments. Give an example of each type. 1)Which of the following are properties of inductive​ arguments? Select all that apply. 2)Which of the following are properties of deductive​ arguments? Select all that apply. 3)Which of the following are examples of inductive​ arguments? Select all that apply. 4)Which of the following are examples of deductive​ arguments? Select all that apply.

1)It cannot prove its conclusion true. At​ best, it shows that its conclusion probably is true. It can be analyzed only in terms of its strength. A conclusion is formed by generalizing from a set of more specific premises. 2)A specific conclusion is deduced from a set of more general​ (or equally​ general) premises. 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. It can be valid even when its conclusion is blatantly false. 3)​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. 4)A specific conclusion is deduced from a set of more general​ (or equally​ general) premises. 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. It can be valid even when its conclusion is blatantly false.

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 the most probable next term in the list of numbers. 4​,7​,10​,13​,16

19

1)Summarize the differences between deductive and inductive arguments. Give an example of each type. 2)Which of the following are examples of deductive​ arguments? Select all that apply.

​1)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. ​2)Premise: If a figure is a​ triangle, then it has three sides. ​Premise: Squares have four sides. ​Conclusion: Squares are not triangles. ​Premise: No country is an island. ​Premise: Iceland is an island. ​Conclusion: Iceland is not a country.

Identify the pattern in the list of numbers. Then use this pattern to find the next number. 3,5,8,13,21,34

55

Use inductive reasoning to predict the next line in the sequence of computations. Then use a calculator or perform the arithmetic by hand to determine whether your conjecture is correct. 41x271=11,111 82*271=22,222 123x271=33,333 164x271=44,444

The next line in the sequence of computations is 205x271=55,555

Use inductive reasoning to predict the next line in this sequence of computations. Then use a calculator or perform the arithmetic by hand to determine whether your conjecture is correct. 2•9−2 = 16 32•9−2 = 286 432•9−2 = 3886 5432•9−2 = 48886

Make a conjecture by predicting the correct numbers in the line below. 65432•9−2= 588886 Is the conjecture​ correct? YES

Determine the most probable next term in the list of numbers. 7776,1296,216,36,6

1

Determine whether the reasoning is an example of deductive or inductive reasoning. In the sequence 9, 13​, 17​, 21​, 25​, ​..., the most probable next term is 29.

The reasoning is inductive because a general conclusion is being made from repeated observations of specific examples.

Determine whether the reasoning is an example of deductive or inductive reasoning. It has rained every day for the past six​ days, and it is raining today as well. So it will also rain tomorrow.

The reasoning is inductive because a general conclusion is being made from repeated observations of specific examples.

Determine whether the reasoning is an example of deductive or inductive reasoning. It is a fact that every student who ever attended Delgado University was accepted into graduate school. Because I am attending Delgado​ University, I can expect to be accepted to graduate​ school, too.

The reasoning is inductive because a general conclusion is being made from repeated observations of specific examples.

Identify a pattern in this list of numbers. Then use this pattern to find the next number.​ (More than one pattern might​ exist, so it is possible that there is more than one correct​ answer.) 5,8,13,20,29,40

53