College Algebra 9th txtbk

A-10 APPENDIX A
39. Given
centers are selected? Express the answer in terms of C n,r or
P
1 2
n,r , as appropriate, and evaluate.
2 1
L c 2 1 0 M £ 1 0§
N c
1 2 1 d 1 0 d 53. A single die is rolled 1,000 times with the frequencies of outcomes
shown in the table.
1 1
(A) What is the approximate empirical probability that the
Find, if defined: (A) LM 2N (B) ML N
number of dots showing is divisible by 3?
(B) What is the theoretical probability that the number of dots
In Problems 40 and 41, solve the system.
showing is divisible by 3?
40. x 2 3xy 3y 2 1 41. x 2 3xy y 2 1
xy 1 x 2 Number of
xy 0
dots facing up 1 2 3 4 5 6
In Problems 42 and 43, find the determinant.
3
1 0 4 4 5 6
42. 32 5 13
43. 3 2 13
45. Write a k k without summation notation and find the sum.
3 0 6
2 4 6
44. Find all real solutions to two decimal places
x 2 2xy y 2 1
9x 2 4xy y 2 15
5
k 1
2
46. Write the series using summation
notation with the summation index k starting at
2! 22
3! 23
4! 24
5! 25
6! 26
7!
k 1.
47. Find S for the geometric series 108 36 12 4 . . . .
48. Graph the solution region and indicate whether the solution region
is bounded or unbounded. Find the coordinates of each
corner point.
49. Solve the linear programming problem:
Maximize
Subject to
z 4x 9y
x 2y 14
2x y 16
x, y 0
3x 2y 12
x 2y 8
x, y 0
50. Given the system: x 1 4x 2 2x 3 k 1
2x 1 6x 2 3x 3 k 2
2x 1 5x 2 2x 3 k 3
(A) Write the system as a matrix equation of the form AX B.
(B) Find the inverse of the coefficient matrix A.
(C) Use A 1 to solve the system when k 1 1, k 2 2, and
k 3 1.
(D) Use A 1 to solve the system when k 1 2, k 2 0, and
k 3 1.
51. How many four-letter code words are possible using the first
six letters of the alphabet if no letter can be repeated? If letters
can be repeated? If adjacent letters cannot be alike?
52. A basketball team with 12 members has two centers. If 5 players
are selected at random, what is the probability that both
Frequency 160 155 195 180 140 170
54. Let a n 100(0.9) n and b n 10 0.03n. Find the least positive
integer n such that a n b n by graphing the sequences {a n } and
{b n } with a graphing calculator. Check your answer by using a
graphing calculator to display both sequences in table form.
55. Evaluate each of the following:
(A) P 25,5 (B) C(25, 5) (C) a 25
20 b
56. Expand (a 1 2b) 6 using the binomial formula.
57. Find the fifth and the eighth terms in the expansion of (3x y) 10 .
Prove each statement in Problems 58 and 59 for all positive
integers using mathematical induction.
58. P n in Problem 28 59. P n in Problem 29
60. Find the sum of all the odd integers between 50 and 500.
61. Use the formula for the sum of an infinite geometric series to
write 2.45 2.454 545 . . . as the quotient of two integers.
62. Let a for k 0, 1, . . . k a 30 , 30. Use a
k b (0.1)30k (0.9) k
graphing calculator to find the largest term of the sequence {a k }
and the number of terms that are greater than 0.01.
63. Use Cramer’s rule to solve the system for x only:
64. Use Cramer’s rule to solve the system in Problem 63 for y.
65. Use Cramer’s rule to solve the system in Problem 63 for z.
66. How many nine-digit zip codes are possible? How many of
these have no repeated digits?
67. Use mathematical induction to prove that the following statement
holds for all positive integers:
P n :
2x
x 6y 5z 16
x 2y 1
1
1 3 1
3 5 1
5 7 . . .
3z 13
1
(2n 1)(2n 1) n
2n 1
68. Three-digit numbers are randomly formed from the digits 1, 2, 3,
4, and 5. What is the probability of forming an even number if
digits cannot be repeated? If digits can be repeated?