Section 4.1 Divisibility and Modular Arithmetic 87 CHAPTER 4 Number Theory and Cryptography SECTION 4.1 Divisibility and Modular Arithmetic 2. a) 1 | a since a = 1 · a. b) a | 0 since 0 = a · 0. 4. Suppose a | b ‚ so that b = at for some t ‚ and b | c‚ so that c = bs for some s. Then substituting the first equation into the second‚ we obtain c = (at)s = a(ts). This means that a | c‚ as desired. 6. Under the hypotheses‚ we have c = as and d = bt for some s and t . Multiplying
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Econometrics I Yarine Fawaz Exercises Econometrics: Set 1-Correction Computer exercises: 1) Use the data in SLEEP75.RAW from Biddle and Hamermesh (1990) to study whether there is a tradeoff between the time spent sleeping per week and the time spent in paid work. We could use either variable as the dependent variable. For concreteness‚ estimate the model sleep 0 1totwork u ‚ where sleep is minutes spent sleeping at night per week and totwrk is total minutes worked during the
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MCB 150 Lab PROBLEM SET 1 1. The data below were obtained after performance of Ex. 2 as stated in your MCB 150 lab manual. a. Estimate the number of total bacteria‚ actinomycetes‚ fungi and algae per gram (dry weight) of soil collected from the IBS garden pH: 6.0 ODW: 8.6 grams Colony Counts: PDA 10-1: 210‚ 190 AMA 10-4: 125‚ 119 SCA 10-4: 80‚ 62 10-2: 20‚ 34 10-5: 17‚ 29 10-5: 18‚ 2 Algal Medium (no. of + tubes/ no. of inoculated tubes): 10-1: 5/ 5 10-2: 5/ 5 10-3: 3/ 5 10-4:
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In our society today one of the most difficult problems we are facing is the large numbers of obesity in our children. One of the major factors in that is this; our children have become less physically active. At an early age children start watching TV‚ learn how to operate a computer‚ and play video games. Having technological skills is now a necessity in all of our lives because everything has turned "computerized‚" but the fact is that our children are relying on these types of entertainment rather
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Chapter 2 Assignment Ryan M. Kethcart INFOST-491 SEC-OL Exercises 1. Consider the statement: an individual threat agent‚ like a hacker‚ can be a factor in more than one threat category. If a hacker hacks into a network‚ copies a few files‚ defaces the Web page‚ and steals credit card numbers‚ how many different threat categories does this attack fall into? a. Overall‚ I believe this attack falls into four major threat categories: deliberate acts of trespass‚ compromises to intellectual
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Melissa Russian UNV-104 April 10‚ 2013 Jeri Jorgenson-Zwibel Exercise and Obesity Obesity has been a big problem in the US and seems to be getting bigger and bigger and now our children are starting to suffer from obesity. It is important to set a good example and show our children how to make healthy choices. A healthy lifestyle is not hard to accomplish and you will have a longer life and be happier. Exercise can also help reduce chronic diseases that are associated with obesity (Schmidt
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BE 13.8 Vertical analysis (common-size) percentages for Vallejo Company’s sales‚ cost of goods sold‚ and expenses are listed below: VERTICAL ANALYSIS 2012 2011 2010 Sales 100.0% 100.0% 100.0% Cost of goods sold 60.5 62.9 64.8 Expenses 26.0 26.6 27.5 Net Income 13.5 10.5 7.7 Did Vallejo’s net income as a percent of sales increase‚ decrease‚ or remain unchanged over the 3 year period. Provide numerical support for your answer. Sales – Cost of Goods Sold – Expenses = Net Income 100 – 64.8
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membrane? Why or Why not? 2. Did Na+Cl- move through the 50 MWCO membrane? Activity 2: 1. Are the solutes moving with or against their concentration gradient in facilitated diffusion? 2. What happened to the rate of facilitated diffusion when the number of carrier proteins was increased? 3. In the simulation you added Na+Cl- to test its effect on glucose diffusion. Explain why there was no effect. Activity 3: 1. Which membrane resulted in the greatest pressure with Na+Cl- as the solute? Why
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Exercising is one of the most important things in life. America’s number one killer is heart disease‚ which can easily be prevented by exercising. More that 1.6 billion people in the world are either overweight or obese and United States has the highest rate of obesity. Exercise not only reduces your risk for health problems and several diseases‚ but it also has an effect on overall appearance. It’s proven that exercising can improve self-esteem and confidence. Excerising has numerous benefits and
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Exercise Science Have you ever had wanted to help someone as well as keep yourself in a positive lifestyle? If you answered yes to this question than Exercise Science is probably the correct major for you. I know that searching for the right major that fits you is a very difficult and time consuming aspect of college‚ however it is one of the most important aspects of college. Your whole entire future is based on your major in college. It starts the foundation of your career. With an Exercise
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