Describe a way to calculate 304- 81 mentally,by using reasoning other than the common sub-0o traction algorithm. Then write a coherent sequence ofequations that correspond to your reasoning.7.12.

Subtraction becomes easy when the numbers used are whole numbers. That is subtracting 50 from 100…

Answered: Describe a way to calculate 304 – 81…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter8: Sequences And Series

Section: Chapter Questions

Problem 2T

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Carmen has learned an algorithm for subtraction. She uses it to find 54−18 as follows. 54+10=64 so 54+10=50+14 −(18+10)=−28 so −(18+10)=−(20+8) So her answer is 30+6=36. (a) What properties does Carmen's algorithm use? Is her method correct? (b) Now solve another subtraction problem, 73−36,with Carmen's algorithm. Use the traditional algorithm to check your work.
Facebook has created a new algorithm that is built to detect terrorists in the US by looking at relationships within the data. Currently 200,000,000 people use the platform in the US. 0.001% of people in the US are legitimate terrorists. The Facebook algorithm correctly identifies terrorists 93% of the time. The algorithm incorrectly identifies regular citizens as terrorists 0.07% of the time. How many people are a) Terrorists? b) Not Terrorists? c) Terrorists Identified by the Facebook algorithm? d) Terrorists not Identified by the Facebook algorithm? e) Citizens not Identified by the Facebook algorithm? f) Citizens Identified by the Facebook algorithm?
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(a) Use the division algorithm to show that any number N can be written as either N = 3k, N = 3k + 1, or N = 3k + 2. Use this to show that the product of any three consecutive integers must be divisible by 3. (In fact it must be divisible by 6. Why?) (b) Could there be integers that are neither odd or even? How would you prove that every integer must either be odd or even? [Hint: When we defined an even number we said it was of the form 2k, and an odd number is of the form 2k + 1. It is theoretically possible with this definition that a number is neither odd nor even. i.e. there might be numbers that are not picked up by this definition. Using the division algorithm with divisor 2, show that every integer must be odd or even. As a result of this, it follows that consecutive integers have “opposite parity.” That is, if one is odd, the other is even.]

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Describe a way to calculate 304 – 81 mentally, by using reasoning other than the common sub- traction algorithm. Then write a coherent sequence of equations that correspond to your reasoning. -