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##### maths questions

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Question;1. How many integers must you choose to ensure that there are at least two that have the same remainderwhen divided by 11 (make sure to explain your answer)2. How many cards must you select from a standard 52 card deck, to ensure that you have at least 3 of somekind (e.g., 3 fours, 3 kings, etc., make sure to explain your answer)3. You have 7 different pairs of drumsticks randomly thrown in a box. How many single drumsticks must yougrab (randomly, without looking) to ensure that you have at least one matched pair?4. Give the next two terms in the recursively defined sequence for all integers k >= 0:Initial conditions:x0 = 1 and x1 = 2Recurrence relation:5. Find the first four terms of the recursively defined sequence b k = 2k + bk ? 1, for all integers k greater than orequal to 2, where b1 = 3 (show your calculations, don?t just give a number)b1 =b2 =b3 =b4 =6. Calculate the first seven terms of the following Fibonacci Sequence:7. (This Problem Counts Double)8. Fill in the Exponential Smoothing Forecast column in the table below using Alpha = 0.7:Week1Actual # Collisions120Exponential Smoothing Forecast # Collisions234117487(no actual yet, still in future)9. What happens when we make the Smoothing Factor (Alpha) smaller rather than larger10. In your own words, explain how to carry out a recursive solution to the Tower of Hanoi Problem11. Suppose you invest $1,900 at an annual interest rate of r = 4% compounded monthly. What is yourinvestment worth after the first two months? (show all calculations to the nearest cent)

Paper#60618 | Written in 18-Jul-2015

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