MAT 211 DEL TECH 1.1
Lola is thinking of a number. If you multiply her number by 64, add 7, and divide by 3, you obtain 173. What is Lola's number? Solve this problem by working backwards.
8 (173*3-7/64 = 8) work backwards
conjecture counter example
Say I flip a coin ten times, and it lands heads up every time. I might make the ______"This coin always lands heads up." But if the eleventh flip lands tails up, then that flip would be the ________ that proves my conjecture false.
What natural numbers less than 2,000 have this both horizontally and vertically symmetric?
1, 8, 11, 88, 101, 111, 181, 808, 818, 888, 1001, 1111, 1881
Predict the next three numbers in the pattern 9, 3, 1, 1/3, 1/9,
1/27, 1/81, 1/243 (Divide by three (whole #'s)(fractions * 3))
Determine the most probable next term in the list of numbers. one half 1/2, 3/4, 5/6, 7/8 9/10
11/12
Use the method of successive differences to determine the next number in the given sequence. −1, 9, 22, 38, 57, 79, 104, ___ Assuming that the pattern continues, the eighth term would be ?
132
Use patterns to complete the Heptagonal Hn=n(5n-3)/2 table below. Figurate # -- 1st 2nd 3rd 4th 5th 6th 7th 8th Heptagonal -- 1 7 ? ? ? ? ? ?
18, 34, 55, 81, 112, 148
Determine the most probable next term in the following list of numbers. 2, 4, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 2, 4, 2, 2, 2, 2
2
Determine the most probable next term in the list of numbers. 6, 9, 12, 15, 18
21
Use differences to find a pattern in the sequence. 3, 2, −2, 0, 17, 58, 132 Assuming that the pattern continues, the eighth term should be ?
248
Kathy stood on the middle rung of a ladder. She climbed up 4 rungs, moved down 3 rungs, and then climbed up 7 rungs. Then she climbed up the remaining 4 rungs to the top of the ladder. How many rungs are there in the whole ladder?
25 (4-3+7+4 =12*2 +1(middle) = 25)
Use inductive reasoning to predict the next three numbers in the pattern. 10, 13, 16, 19, 22, ...
25, 28, 31
Use patterns to complete the table below. Figurate # -- 1st 2nd 3rd 4th 5th 6th 7th 8th Triangular Tn=(n(n+1)/2) -- 1 3 6 10 15 21 ? ?
28, 36
Use patterns to complete the Hexagonal Hn=n(2n-1) table below. Figurate # -- 1st 2nd 3rd 4th 5th 6th 7th 8th Hexagonal -- 1 6 15 ? ? ? ? ?
28, 45, 66, 91, 120
Use patterns to complete the Pentagonal Pn=(n(3n-1)/2) table below. Figurate # -- 1st 2nd 3rd 4th 5th 6th 7th 8th Pentagonal -- 1 6 15 ? ? ? ? ?
35, 51, 70, 92
Find the next number in the sequence. 4, 9, 16, 25 ...
36 ( prime #'s 5, 7, 9, 11, etc)
Use patterns to complete the table below. Figurate # -- 1st 2nd 3rd 4th 5th 6th 7th 8th Square Sn=n2-- 1 4 9 16 25 ? ? ?
36, 49, 64
Use the method of Gauss to find the sum. 1 + 2 + 3 + 4 +... + 99
4950 Gauss Formula
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.) 3, 6, 11, 18, 27, 38,
51 (primes 3, 5, 7, 9, 11, 13)
Identify a pattern in the given 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, 20, 80, 320, 1280
5120
Several equations are given illustrating a suspected number pattern. Determine what the next equation would be, and verify that it is indeed a true statement. 2^2−1^2 = 2+1 3^2−2^2= 3+2 4^2−3^2= 4+3
5^2-4^2=5+4
Use patterns to complete the Octagonal On=n(3n−2n) table below. Figurate # -- 1st 2nd 3rd 4th 5th 6th 7th 8th Octagonal -- 1 ? ? ? ? ? ? ?
8, 21, 40, 65, 96, 133, 176
The word TOT is its own image when it is reflected through a vertical line through O, as shown in the figure on the right. Find other words that are their own images when reflected similarly. Select all words that are their own images when reflected similarly. A. I B. BOTOX C. TOM D. MAYAN E. AHA
A, E
Identify the premises and conclusion and determine whether deductive or inductive reasoning was used. I have 7 apples. I buy 3 more apples. I now have 10 apples.
Premises: "I have 7 apples." "I buy 3 more apples." Conclusion: "I now have 10 apples." This argument applied the general principle of addition to a specific example, 7 + 3 = 10 apples, so it is a deductive argument
Successive Differences
Process to determine the next term of a sequence using subtraction to find a common difference.
True or False There may be multiple correct explanations for the same pattern
True
Inductive reasoning
What can only lead to a probable (or more likely) result? Inductive reasoning What cannot lead to a 100% certain answer?
Select all letters you can use to create words with horizontal symmetry like BOOK
click picture for answers
A Counter Example
what is a single example that does not support the conjecture. This proves that the conjecture is false.
Inductive Reasoning (Term)
what is characterized by drawing a general conclusion (making a conjecture) from repeated observations of specific examples. The conjecture may or may not be true.
Determine the relationship between the rows of numbers to find the missing value. 16, 63, 29, 32, 61 6, 18, 18, x, 6
x=6 (top row... 1*6 = 6 (bottom row #), (6*3=18) etc.
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. Choose the correct answer below. A. The reasoning is deductive because general principles are being applied to specific examples. B. The reasoning is deductive because a general conclusion is being made from repeated observations of specific examples. C. The reasoning is inductive because a general conclusion is being made from repeated observations of specific examples. D. The reasoning is inductive because general principles are being applied to specific examples.
A. The reasoning is deductive because general principles are being applied to specific examples. Your answer is correct.
Which of the following are properties of deductive arguments? Select all that apply. A. It can be valid even when its conclusion is blatantly false. B. A specific conclusion is deduced from a set of more general (or equally general) premises. C. It cannot prove its conclusion true. At best, it shows that its conclusion probably is true. D. It can be analyzed only in terms of its strength. E. A conclusion is formed by generalizing from a set of more specific premises. 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.
A. It can be valid even when its conclusion is blatantly false. B. A specific conclusion is deduced from a set of more general (or equally general) premises. 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.
Which of the following are properties of inductive arguments? Select all that apply. A. It cannot prove its conclusion true. At best, it shows that its conclusion probably is true. B.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. C.A specific conclusion is deduced from a set of more general (or equally general) premises. D.It can be valid even when its conclusion is blatantly false. E. A conclusion is formed by generalizing from a set of more specific premises. F.It can be analyzed only in terms of its strength.
A. It cannot prove its conclusion true. At best, it shows that its conclusion probably is true. E. A conclusion is formed by generalizing from a set of more specific premises. F. It can be analyzed only in terms of its strength.
For the following sequence, determine if it is an arithmetic sequence, a geometric sequence, or neither. If it is either arithmetic or geometric, give the next two terms in the sequence. 5, 15, 45, 135, ___ ____ A. The sequence is geometric. The next two terms are 5, 15, 45, 135, ___ ____ B. The sequence is arithmetic. The next two terms are 5, 15, 45, 135, ___ ____ C. The sequence is neither arithmetic nor geometric.
A. The sequence is geometric. The next two terms are 405, 1215
Conjecture
An educated guess based on repeated observations of a particular process or pattern.
The word BOOK is still BOOK when it is reflected through a horizontal line, as shown in the figure on the right. Find other words that have the same property. Select all words that have the same property as BOOK. A. RIDE B. OHIO C. WOMB D. BID E. ECHO
B, D, E
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 two negative numbers is negative. B. 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. C. Premise: If a figure is a triangle, then it has three sides. Premise: Squares have four sides. Conclusion: Squares are not triangles. D. Premise: No country is an island. Premise: Iceland is an island. Conclusion: Iceland is not a country.
B. 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.
For the following sequence, determine if it is an arithmetic sequence, a geometric sequence, or neither. If it is either arithmetic or geometric, give the next two terms in the sequence. 7, 10, 13, 16,... A. The sequence is geometric. The next two terms are 7, 10, 13, 16, ___ ___ B. The sequence is arithmetic. The next two terms are 7, 10, 13, 16, ___ ___ C. The sequence is neither arithmetic nor geometric.
B. The sequence is arithmetic. The next two terms are 19, 22
Identify the premises and conclusion and determine whether deductive or inductive reasoning was used. All humans need air to live. I am a human. I need air to live.
Premises: "All humans need air to live." "I am a human." Conclusion: "I need air to live." This argument applied the general principle that all humans need air to a specific example, me, so it is a deductive argument.
Which of the following are examples of deductive arguments? Select all that apply. A. Premise: (−2)×(3)=−6 Premise: (−3)×(1)=−3 Premise: (−4)×(2)=−8 Conclusion: The product of two negative numbers is negative. B. 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. C. Premise: If a figure is a triangle, then it has three sides. Premise: Squares have four sides. Conclusion: Squares are not triangles. D. Premise: No country is an island. Premise: Iceland is an island. Conclusion: Iceland is not a country.
C. Premise: If a figure is a triangle, then it has three sides. Premise: Squares have four sides. Conclusion: Squares are not triangles. D. Premise: No country is an island. Premise: Iceland is an island. Conclusion: Iceland is not a country.
For the following sequence, determine if it is an arithmetic sequence, a geometric sequence, or neither. If it is either arithmetic or geometric, give the next term in the sequence. 3, 9, 12, 21, 33, 54, ___ A. The sequence is arithmetic. The next term is 3, 9, 12, 21, 33, 54, ___ B. The sequence is geometric. The next term is 3, 9, 12, 21, 33, 54, ___ C. The sequence is neither arithmetic nor geometric
C. The sequence is neither arithmetic nor geometric
Identify the argument as inductive or deductive. Every coach must know his sport well. Marty Wright is a baseball coach, so Marty Wright knows baseball well.
Deductive Reasoning
Deductive Reasoning
Deductive Reasoning If used properly ___ will lead to a 100% correct answer.
What is the most probable next term? 5, 17, 29, 41
Each number increases by 12, and this is a list of odd numbers. So 41 + 12 = 53 is the most probable next term.
What is the most probable next term? 1, 3, 5, 7
Each number increases by 2, and this is a list of odd numbers. So 7 + 2 = 9 is the most probable next term.
specific example general principle
If someone asks me, "What is the voltage drop across this 100 ohm resistor if there are 2 amps of current running through it?" I would find the voltage for this _____ by using the _____ voltage = current times resistance voltage = 2 · 100 voltage = 200 volts.
Choose which reasoning process (deductive or inductive) is shown in the following example. We examine the fingerprints of 2200 people. No two individuals in this group of people have identical fingerprints. We conclude that for all people, no two people have identical fingerprints
Inductive Reasoning
You read the newspaper daily. Lately, you have noticed more articles about increased tuition at various public and private colleges and universities. You draw the conclusion that all colleges and universities have increased tuition. Which type of reasoning is this? Are you drawing a generalization based upon specific examples (inductive) or applying a generalization to specifics (deductive)?
Inductive Reasoning
Identify the premises and conclusion and determine whether deductive or inductive reasoning was used. I am wearing clothes. All of you are wearing clothes. Therefore, everyone in Pennsylvania is wearing clothes.
Premises: "I am wearing clothes." "All of you are wearing clothes." Conclusion: "Everyone in Pennsylvania is wearing clothes." This argument draws a very general conclusion from two specific examples, so it is an inductive argument.
If you build it, they will come. You build it. Therefore, they will come. Choose the correct answer below. A. The reasoning is deductive because general principles are being applied to specific examples. B. The reasoning is deductive because a general conclusion is being made from repeated observations of specific examples. C. The reasoning is inductive because general principles are being applied to specific examples. D. The reasoning is inductive because a general conclusion is being made from repeated observations of specific examples.
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. 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 general principles are being applied to specific examples. The reasoning is inductive because a general conclusion is being made from repeated observations of specific examples. The reasoning is deductive because general principles are being applied to specific examples. The reasoning is deductive because a general conclusion is being made from repeated observations of specific examples.
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. In the sequence 9, 12, 15, 18, 21, ..., the most probable next term is 24. The reasoning is deductive because general principles are being applied to specific examples. The reasoning is inductive because general principles are being applied to specific examples. The reasoning is inductive because a general conclusion is being made from repeated observations of specific examples. The reasoning is deductive because a general conclusion is being made from repeated observations of specific examples.
The reasoning is inductive because a general conclusion is being made from repeated observations of specific examples.
It has rained every day for the past six days, and it is raining today as well. So it will also rain tomorrow. Choose the correct answer below. A. The reasoning is inductive because a general conclusion is being made from repeated observations of specific examples. B. The reasoning is deductive because a general conclusion is being made from repeated observations of specific examples. C. The reasoning is deductive because general principles are being applied to specific examples. D. The reasoning is inductive because general principles are being applied to specific examples.
The reasoning is inductive because a general conclusion is being made from repeated observations of specific examples.
A Logical Argument
__ made up of the premises and the conclusion.
Inductive reasoning is not 100% accurate
_____ reasoning is not 100% accurate.
A Premise
___can be an assumption, law, rule, widely held idea, or observation
A Conclusion
___follows from the premises by inductive or deductive reasoning.
Deductive Reasoning
___is characterized by applying general principles to specific examples.
