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Unformatted text preview: normally distributed with mean 25.7 kg and standard deviation 0.50 kg. (a) What is the probability a bag selected at random will weigh less than 25.0 kg? (2) In order to reduce the number of underweight bags (bags weighing less than 25 kg) to 2.5% of the total, the mean is increased without changing the standard deviation. (b) Show that the increased mean is 26.0 kg. (3) It is decided to purchase a more accurate machine for filling the bags. The requirements for this machine are that only 2.5% of bags be under 25 kg and that only 2.5% of bags be over 26 kg. (c) Calculate the mean and standard deviation that satisfy these requirements. (3) 249 The cost of the new machine is \$5000. Cement sells for \$0.80 per kg. (d) Compared to the cost of operating with a 26 kg mean, how many bags must be filled in order to recover the cost of the new equipment? (3) (Total 11 marks) 357. Radian measure is used, where appropriate, throughout the question. Consider the function y = 3x – 2 . 2x – 5 The graph of this function has a vertical and a horizontal asymptote. (a) Write down the equation of (i) the vertical asymptote; (ii) the horizontal asymptote. (2) (b) Find dx , simplifying the answer as much as possible. dy (3) (c) How many points of inflexion does the graph of this function have? (1) (Total 7 marks) 250 358. A coin is biased so that when it is tossed the probability of obtaining heads is 2 . The coin is 3 tossed 1800 times. Let X be the number of heads obtained. Find (a) the mean of X; (b) the standard deviation of X. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 3 marks) 359. The complex number z satisfies i(z + 2) = 1 – 2z, where i = – 1 . Write z in the form z = a + bi, where a and b are real numbers. Working: Answers: ………………………………………….. (Total 3 marks) 251 360. The polynomial f(x) = x3 + 3x2 + ax + b leaves the same remainder when divided by (x – 2) as when divided by (x + 1). Find the value of a. Working: Answers: ………………………………………….. (Total 3 marks) 361. Consider the infinite geometric series 2 3 2x 2x 2x 1 + + + + ..... 3 3 3 (a) For what values of x does the series converge? (b) Find the sum of the series if x = 1.2. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 3 marks) 252 362. The function f : x a 2x +1 , x∈ x –1 , x ≠ 1. Find the inverse function, f –1, clearly stating its domain. Working: Answers: …………………………………………......... .......................................................................... (Total 3 marks) x 363. If A = 4 4 and B = 2 2 8 y , find 2 values of x and y, given that AB = BA. 4 Working: Answers: ………………………………………….. (Total 3 marks) 253 364. The line y = 16x – 9 is a tangent to the cu...
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## This note was uploaded on 06/24/2013 for the course HISTORY exam taught by Professor Apple during the Fall '13 term at Berlin Brothersvalley Shs.

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