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A. Use inductive reasoning to find a pattern and predict the number or figure in the list. Then make a reasonable conjecture of the following: 1) 1,2,4, 7,11, 16, 22, 29? 2) 9, 12,11,14, 13,16, 15, 18? 3) -2, 3, -4,5, -6,7?

A. Use inductive reasoning to find a pattern and predict the number or figure in the list. Then make a reasonable conjecture of the following: 1) 1,2,4, 7,11, 16, 22, 29? 2) 9, 12,11,14, 13,16, 15, 18? 3) -2, 3, -4,5, -6,7?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Module 3 PROBLEM SOLVING AND REASONING Gauge Your Learning! A. Use inductive reasoning to find a pattern and predict the number or figure in the list. Then make a reasonable conjecture of the following: 1) 1, 2, 4, 7,11,16, 22,29? 2) 9,12,11,14, 13, 16, 15, 18? 3) -2,3, -4,5, -6,7? 4) 2,5, 10, 17, 25? 5) B. Find a counterexample to show that each statement is false. 6) The sum of any three odd numbers is even. 7) When an even number is added to the product of two odd numbers, the result will be even. 8) When an odd number is squared and divided by 2, the result will be a whole number. C. Use inductive reasoning to make a conjecture about a rule that relates the number you selected to the final answer. Prove your conjecture by using deductive reasoning. 9) Pick a number: Double it: Subtract 20 from the answer: Divided by 2: Subtract the original number: Result: 10) Pick a number: Multiply it by 9: Add 21: Divided by 3: Subtract three times the original number: Result: D. Determine whether the following statements are inductive or deductive reasoning. Write our answer after each statement. 11) Every time you eat peanuts, you start to cough. You are allergic to peanuts. 12) 1 All brown dogs in the park today are small dogs. Therefore, all small dogs must be brown. 13) All brown dogs in the park today are small dogs. Therefore, all small dogs must be brown.
Transcribed Image Text:Module 3 PROBLEM SOLVING AND REASONING Gauge Your Learning! A. Use inductive reasoning to find a pattern and predict the number or figure in the list. Then make a reasonable conjecture of the following: 1) 1, 2, 4, 7,11,16, 22,29? 2) 9,12,11,14, 13, 16, 15, 18? 3) -2,3, -4,5, -6,7? 4) 2,5, 10, 17, 25? 5) B. Find a counterexample to show that each statement is false. 6) The sum of any three odd numbers is even. 7) When an even number is added to the product of two odd numbers, the result will be even. 8) When an odd number is squared and divided by 2, the result will be a whole number. C. Use inductive reasoning to make a conjecture about a rule that relates the number you selected to the final answer. Prove your conjecture by using deductive reasoning. 9) Pick a number: Double it: Subtract 20 from the answer: Divided by 2: Subtract the original number: Result: 10) Pick a number: Multiply it by 9: Add 21: Divided by 3: Subtract three times the original number: Result: D. Determine whether the following statements are inductive or deductive reasoning. Write our answer after each statement. 11) Every time you eat peanuts, you start to cough. You are allergic to peanuts. 12) 1 All brown dogs in the park today are small dogs. Therefore, all small dogs must be brown. 13) All brown dogs in the park today are small dogs. Therefore, all small dogs must be brown.
Module 3 PROBLEM SOLVING AND REASONING 14) The chair in the living room is red. The chair in the dining room is red. The chair in the bedroom is red. All the chairs in the house are red. 15) Every day so far, the sun has risen in the East and set in the West. The sun will probably continue to rise in the East and set in the West. 16) A consumer products company accepts the premise that professional women are overloaded with family and work responsibilities and strapped for time. From this, they can be successful marketing hair coloring product that can be applied in less time than their competition's hair coloring product. 17) The first two kids I met at my new school were nice to me. The students at this school are really nice. 18) A supermarket manager believes candy products are an impulse buy. She decides that she can sell more by placing candy displays close to store entry paths. 19) The first three candies that I ate out of the bag were chocolates. All of the candy in the bag is chocolate. 20) A recruiter conducts a study of recent hires who have achieved success and stayed on with the organization. She finds that they graduated from three local colleges, so she decides to focus recruiting efforts on those schools. 21) A food products company identifies a trend that shows consumers to favor organic products. Its marketing department deduces it can boost sales by increasing the size of the lettering for the word "organic" when redesigning their packaging. 22) A salesperson presents testimonials of current customers to suggest to prospective clients that her products are high quality and worth the purchase. 23) A bartender becomes aware that customers give her higher tips when she shares personal information, so she intentionally starts to divulge personal information when it feels appropriate to do so. 24) Cacti are plants and all plants perform photosynthesis; therefore, cacti perform photosynthesis. 25) We had rained each day for the last five days, so it will rair
Transcribed Image Text:Module 3 PROBLEM SOLVING AND REASONING 14) The chair in the living room is red. The chair in the dining room is red. The chair in the bedroom is red. All the chairs in the house are red. 15) Every day so far, the sun has risen in the East and set in the West. The sun will probably continue to rise in the East and set in the West. 16) A consumer products company accepts the premise that professional women are overloaded with family and work responsibilities and strapped for time. From this, they can be successful marketing hair coloring product that can be applied in less time than their competition's hair coloring product. 17) The first two kids I met at my new school were nice to me. The students at this school are really nice. 18) A supermarket manager believes candy products are an impulse buy. She decides that she can sell more by placing candy displays close to store entry paths. 19) The first three candies that I ate out of the bag were chocolates. All of the candy in the bag is chocolate. 20) A recruiter conducts a study of recent hires who have achieved success and stayed on with the organization. She finds that they graduated from three local colleges, so she decides to focus recruiting efforts on those schools. 21) A food products company identifies a trend that shows consumers to favor organic products. Its marketing department deduces it can boost sales by increasing the size of the lettering for the word "organic" when redesigning their packaging. 22) A salesperson presents testimonials of current customers to suggest to prospective clients that her products are high quality and worth the purchase. 23) A bartender becomes aware that customers give her higher tips when she shares personal information, so she intentionally starts to divulge personal information when it feels appropriate to do so. 24) Cacti are plants and all plants perform photosynthesis; therefore, cacti perform photosynthesis. 25) We had rained each day for the last five days, so it will rair
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