Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Mathematics B30 Module 4 Assignment 10 Mathematics B30 269 Assignment 10 Mathematics B30 270 Assignment 10 Optional insert: Assignment #10 frontal sheet here. Mathematics B30 271 Assignment 10 Mathematics B30 272 Assignment 10 Assignment 10 Multiple Choice: Select the correct answer for each of the following and circle your answer on this question sheet. (9.1) 1. The simplified form of A. B. C. D. (9.1) 2. B. C. D. 3. 1 2 2 x 2 2 0 is ***. 2x4 x4 x4 2 x4 32 2 1 The simplified form of 1 is ***. 2 2 3 A. (9.2) 4 x 6 x 4 5 8 9 5 8 The simplest exponential form of A. a B. a C. 3 D. Mathematics B30 a 3 a 6 a is ***. a 3 2 a2 2 3 273 Assignment 10 (9.2) 4. 2 A. B. C. D. (9.2) 5. 6. 0 1 , 3 1, 3 1, 3 The solution to 5 x A. B. C. D. (9.3) The solution to 4 x 64 4 2 x is ***. 2 x 1 5 is ***. 0, 1 5 1 2 The graph of y 2 x 5 is ***. y A. B. y 5 1 x x y C. D. y 5 5 x Mathematics B30 274 x Assignment 10 (9.4) 7. The half-life of Carbon-14 is 5 760 years. If the original amount of Carbon-14 in a fossil is estimated to be 6.3 gm and the present amount is 0.8 gm, the age of the fossil is about ***. A. B. C. D. (10.1) 8. The exponential form of y log 5 x is ***. A. B. C. D. (10.1) 9. y 10 5 x x 5y x 2y 5 x 10 y The value of log 10 9 3 A. B. C. D. (10.2) 10. 45 360 years 40 000 years 25 016 years 17 149 years 3 is ***. 3 log 3 10 3.5 log 3 10 3.5 log 3 10 3 log 10 3 The domain of f x log 1 3 x is ***. A. B. C. D. Mathematics B30 1 3 1 x 3 x 0 all real numbers x 275 Assignment 10 (10.3) 11. The expression log 2 x A. B. C. D. (10.4) 12. log x 2 x 1 x 2x 1 x log x 4.69 days 5.00 days 5.69 days 56.9 days In an arithmetic sequence t 2 2 m n and t 3 3m 2n . The tenth term is ***. A. B. C. D. (11.1) 14. 3 1 x log x log 2 2 log 2 x 1 x A growth (decay) formula for a certain population is the exponential equation 1 N N 0 10 kt . If the amount N is N 0 after 3 days, the time required for 360 to 4 remain if N 0 5000 is ***. A. B. C. D. (11.1) 13. 1 1 log 1 x log x is equivalent to ***. 2 2 10 m 10 m 10 m 10 m 9n 25 n 31 n 10 n Five years after Dale invested a certain amount of money the accumulated value was $3 550 and after 7 years it was $3 988.78. After each year the accumulated value was r times the amount of the previous year. The amount originally invested was ***. A. B. C. Mathematics B30 $3 000.00 $2 811.93 $2 701.50 276 Assignment 10 D. Mathematics B30 $2 500.00 277 Assignment 10 (11.2) 15. The positive mean proportional between 36 and 9 is ***. A. B. C. D. (11.3) 16. 27 25 22.5 18 The finite sum 9 2 k 1 is ***. k 1 A. B. C. D. (11.3) 17. 17 80 81 162 The sum 12 2i k is ***. k 1 A. B. C. D. (11.4) 18. 4i 1i 0 2i 1i 2 The one convergent geometric series is ***. A. 2 2 1 2 1 2 1 ... 2 3 B. C. a a 2 a 2 a 2 ... 1 4 9 16 ... D. 1 1 1 1 ... 3 3 3 2 2 Mathematics B30 3 3 278 Assignment 10 (11.4) 19. The sum of 10 2 A. B. C. D. (12.1) 20. B. C. D. 3 cm 10 3 cm 2 2 cm 5 1 3 cm 3 The accumulated value of $100 invested for 4 years at 6% compounded quarterly is ***. A. B. C. D. (12.3) 22. infinite 20 1 12 2 25 The first blow of a hammer drives a nail 2 cm into the wood. Each following 2 blow drives the nail as far as the preceding blow did. The maximum 5 distance the nail can be driven into the wood is ***. A. (12.2) 21. 2 ... is ***. 5 $254.04 $126.90 $102.43 $124.00 If money earns 8% compounded semiannually, the amount that is to be invested today so that $500 can be withdrawn at the end of each year of investment for 5 years is ***. A. B. C. D. Mathematics B30 $2 000 $1 988 $1 798 $1 776 279 Assignment 10 (13.1) 23. One card is drawn from a standard deck of 52 playing cards. A represents the event that a red card is drawn. B represents the event that a number 10 is drawn. The number of ways A or B can happen is ***. A. B. C. D. (13.1) 24. (13.2) A committee of 3 girls and 2 boys is to be selected from a group of 6 girls and 6 boys. The number of ways this can be done is ***. A. B. C. D. (13.1) 25. (13.2) C3 6 C2 6 C3 6 C 2 12 C5 12 C3 12 C 2 6 A committee of either 3 girls and 2 boys or 4 boys and 1 girl is to be selected from a group of 7 girls and 8 boys. The number of ways this can be done is ***. A. B. C. D. (13.2) 26. 2 26 28 30 2 15 C5 7 C3 8 C 2 8 C4 7 C1 15 C5 7 C3 8 C2 8 C4 7 C1 A committee of 3 is to be chosen from 7 people to fill the positions of president, secretary, and treasurer. The number of ways this can be done is ***. A. B. C. D. Mathematics B30 C3 7 7 7 7 P3 7 6 5 4 7 280 Assignment 10 (13.2) 27. If a fair coin is tossed two times, the odds that heads will come up both times are ***. A. B. C. D. (13.3) 28. In the Venn diagram the shaded area is represented by ***. A. B. C. D. (13.4) 29. 1 to 1 3 to 1 1 to 3 1 to 4 C If the probability of event A is A. B. C. D. (13.4) 30. A B C A B C B C A B C A P A B B 1 3 , the probability of event B is , and 4 4 3 then ***. 8 events A and B are dependent events A and B are independent events A and B are virtually exclusive events A and B are random A box contains 5 red marbles, 6 white marbles and 10 blue marbles. One marble is drawn, and then, without replacing the first marble a second marble is drawn. The probability that a red marble and then a blue marble are drawn is ***. A. B. C. D. Mathematics B30 1 1 5 10 5 10 21 21 5 10 21 20 5 10 281 Assignment 10 Mathematics B30 282 Assignment 10 (13.4) 31. As in Question 30, a box contains 5 red, 6 white and 10 blue marbles. One marble is drawn, and then, without replacing the first marble a second marble is drawn. The probability that a red and blue marble are drawn is ***. A. B. C. D. (14.1) 32. The coefficients of the expansion of x y add up to ***. 6 A. B. C. D. (14.2) 33. (14.2) 34. 5 21 5 42 100 441 10 441 16 32 64 128 The middle term(s) of the expansion of 2 y b 10 A. 10 B. 10 C. 10 D. 10 C 5 2 y b , 5 5 C 5 2 y b 5 C 6 2 y b 4 10 6 5 C 5 2 y b 5 5 C 4 2 y b 6 4 The 12th term of the expansion of 2 x i 16 A. B. C. D. Mathematics B30 is(are) ***. is ***. 8 736 ix 5 8 736 ix 5 139 776 ix 5 139 776 ix 5 283 Assignment 10 (14.3) 35. In a family of 5 children the probability of having 2 girls or 3 girls is ***. A. B. C. D. (14.2) 36. (14.2) 37. The first 3 terms of the expansion of A. 81 3 729 i 2 1 944 3 B. 81 3 729 i 2 1 944 3 C. 81 3 729 i 2 1 944 3 D. 1 813 3 729 i 2 3 i 2 9 are ***. In the expansion of 5 a 2 b the coefficient of a 5 b 2 is ***. 7 A. B. C. D. (15.1) 38. (15.2) 7 8 3 8 1 2 5 8 21 1 050 2 100 262 500 On a recent quiz, the twenty-two students of Mr. Campbell received the following scores out of a total of 57. 29 43 38 44 39 48 37 46 24 51 48 51 42 50 47 54 46 49 36 44 52 45 The mean x and standard deviation , respectively, are ***. A. B. C. D. Mathematics B30 x x x x 45 .86 , 44 .28 , 43 .77 , 43 .77 , 6 .69 7 .29 7 .31 6 .87 284 Assignment 10 (15.1) 39. The median of the data in Question #38 is ***. A. B. C. D. (15.2) 40. 45 44 46 45.5 The heights for ten basketball players are given. Using the formula given in the course, the standard deviation of the data to two decimal places is ***. 188 202 A. B. C. D. (15.3) 41. 190 202 192 207 196 198 199 5.88 5.59 5.58 5.43 Given the following frequency table, the mean x of the data is ***. Class 1 2 3 4 A. B. C. D. (15.3) 42. 196 Class Interval 0-4 4-8 8-12 12-16 Frequency 3 7 6 2 9.5 6.2 7.6 7.5 From a sample, the speeds in km per hour of bicycles on a pathway are shown on the histogram. The standard deviation of the population is ***. A. B. C. D. Mathematics B30 Frequency 2.33 2.99 3.11 14 .5 f(x) 4 3 2 1 8 10 12 14 16 18 20 Speed 285 Assignment 10 x (16.1) 43. A population has a normal distribution with mean x and standard deviation . The percent of the population that lies in the interval from x to x 2 is ***. A. B. C. D. (16.1) 44. It is known that a certain population has a normal distribution with mean 50 and standard deviation 10. A sample of 200 items is drawn from that population. The approximate number of items in the sample that have values between 40 and 60 is ***. A. B. C. D. (16.1) 45. 68.26% 81.85% 84.00% 47.72% 68 95 136 190 The data represented by the curve is ***. f(x) x A. B. C. D. (16.1) 46. skewed to the left skewed to the right a normal distribution spread out further to the right The weight of northern pike fish is normally distributed with a mean weight of 2.3 kg and a standard deviation of 0.8 kg. The range of weights that you would expect 95.44% of the fish to fall between is ***. A. B. C. D. Mathematics B30 1.5 kg to 3.1 kg 0 kg to 4.6 kg 0.7 kg to 4.6 kg 0.7 kg to 3.9 kg 286 Assignment 10 (16.2) 47. The average number of frost-free days in communities throughout Saskatchewan in 1997 was 116.2 days with a standard deviation of 8.8 days. Moose Jaw recorded 122 frost free days. The z-score for Moose Jaw is ***. A. B. C. D. (16.2) 48. 0.4066 0.0934 0.9066 0.3907 During a major-league career of 25 seasons, a baseball player averaged 150 hits a season with a standard deviation of 20 hits. The number of seasons that the player had at least 170 hits was ***. A. B. C. D. (16.2) 50. 0 .66 0 .68 1 .02 1 .22 The probability of an event occurring with a z-score greater than 1.32 is ***. A. B. C. D. (16.2) 49. z z z z 1 2 3 4 The yearly Beeswax production in Saskatchewan has been recorded over the past 25 years. The mean yearly production is 156 912 pounds with a standard deviation of 39 987 pounds. The probability that in the next year the production will be greater than 175 000 pounds is ***. A. B. C. D. Mathematics B30 0.4523 0.6736 0.3413 0.3264 287 Assignment 10 Mathematics B30 288 Assignment 10