And pq respectively consider the following symmetries

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Unformatted text preview: .............. (Total 4 marks) 241 349. The events B and C are dependent, where C is the event "a student takes Chemistry", and B is the event "a student takes Biology". It is known that P(C) = 0.4, P(B | C) = 0.6, P(B | C′) = 0.5. (a) Complete the following tree diagram. Chemistry Biology B 0.4 C B′ B C′ B′ (b) Calculate the probability that a student takes Biology. (c) Given that a student takes Biology, what is the probability that the student takes Chemistry? Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 4 marks) 242 350. The depth, y metres, of sea water in a bay t hours after midnight may be represented by the function 2π y = a + b cos k t , where a, b and k are constants. The water is at a maximum depth of 14.3 m at midnight and noon, and is at a minimum depth of 10.3 m at 06:00 and at 18:00. Write down the value of (a) a; (b) b; (c) k. Working: Answers: (a) ………………………………………….. (b) .................................................................. (c) …………………………………….......... (Total 4 marks) 351. Portable telephones are first sold in the country Cellmania in 1990. During 1990, the number of units sold is 160. In 1991, the number of units sold is 240 and in 1992, the number of units sold is 360. In 1993 it was noticed that the annual sales formed a geometric sequence with first term 160, the 2nd and 3rd terms being 240 and 360 respectively. (a) What is the common ratio of this sequence? (1) Assume that this trend in sales continues. 243 (b) How many units will be sold during 2002? (3) (c) In what year does the number of units sold first exceed 5000? (4) Between 1990 and 1992, the total number of units sold is 760. (d) What is the total number of units sold between 1990 and 2002? (2) During this period, the total population of Cellmania remains approximately 80 000. (e) Use this information to suggest a reason why the geometric growth in sales would not continue. (1) (Total 11 marks) 352. The speeds in km h–1 of cars passing a point on a highway are recorded in the following table. Speed v v ≤ 60 0 60 < v ≤ 70 7 70 < v ≤ 80 25 80 < v ≤ 90 63 90 < v ≤ 100 70 100 < v ≤ 110 71 110 < v ≤ 120 39 120 < v ≤ 130 20 130 < v ≤ 140 5 v > 140 (a) Number of cars 0 Calculate an estimate of the mean speed of the cars. (2) 244 (b) The following table gives some of the cumulative frequencies for the information above. Speed v Cumulative frequency v ≤ 60 0 v ≤ 70 7 v ≤ 80 32 v ≤ 90 95 v ≤ 100 a v ≤ 110 236 v ≤ 120 b v ≤ 130 295 v ≤ 140 300 (i) Write down the values of a and b. (ii) On graph paper, construct a cumulative frequency curve to represent this information. Use a scale of 1 cm for 10 km h–1 on the horizontal axis and a scale of 1 cm for 20 cars on the vertical axis. (5) (c) Use your graph to determ...
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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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