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2303-ec1 - He theorized that every integer greater than 5...

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Math 2303 Extra Credit Write complete solutions to the problems on notebook paper. You can do any number of the problems that you want to. 1. A perfect number is one whose proper factors (i.e., all factors except the number itself) add up to the number. For example, 6 is a perfect number, since 1 + 2 + 3 = 6. Which of these numbers are perfect numbers? Justify your answers. A. 30 B. 28 C. 250 D. 496 E. 8128 2. Do this exercise: Pick a number from 1 to 10. Multiply your number by 9. Add the digits of your answer together. Subtract 5 from your answer. Now select the letter of the alphabet that corresponds to your answer (1 = A, 2 = B, 3 = C, etc.). Now write down a country that starts with that letter. Think of an animal whose first letter is the last letter of your country. Think of a fruit whose first letter is the last letter of your country. 90% of the people who do this exercise give the same answer: Denmark, Kangaroo, Orange. Can you explain why? 3. Goldbach had another conjecture.

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Unformatted text preview: He theorized that every integer greater than 5 is the sum of three prime numbers. Show that this is true for the integers from 8 through 20. 4. Here’s a method for multiplying two numbers without a calculator. It’s called duplation and mediation. Multiply 27 * 35. Take half of the first number (disregard any remainders) and double the second number: 13 ---- 70 Repeat the process until you get 1 on the left. 6 --- 140 3 --- 280 1 --- 560 Cross out any pairs where the number on the left is odd. Add the remaining numbers on the right. 27 --- 35 13 --- 70 6 --- 140 3 --- 280 1 --- 560 So, we’ll ignore the 140 and add the rest of the numbers on the right: 35 + 70 + 280 + 560 = 945 Now do the multiplication to verify. Use this method to perform each of these multiplications. Show the steps. A. 96 * 53 B. 45 * 75 C. 28 * 19 5. Find b if 43 111 = b . You must give an explanation as to how you found b . Trial and error will not get you the points!...
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2303-ec1 - He theorized that every integer greater than 5...

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