1.1 10, 18, 30, 32. Suggested: Odd: 1-31
Answers: #10 d; #18 y=(3/4)x+15; #30 d; #32 c
1.2 12, 18, 28, 42. Suggested: Odd: 1-57
Answers: #12 y>=(1/2)x+1; #18 no
1.3 6, 12, 20. Suggested: Odd: 1-21
Answers: #6 (6,3); #12 x=30/7, y=6/7
1.4 26, 56, 68, 78. Suggested:
Odd: 1-89
Answers: #26 m=0; #56 y=-(1/3)x; #68 7/3, 8/3, 3;
#78 y<=(3/4)x+(13/2), y<=-(7/3)x+(38/3), y>=-(4/7)x+27/7
1.5 8. Suggested: Odd:
1-9
Answer: #8 y=-1.5x+8.5
2.2 4, 10, 16, 18. Suggested: Odd: 1-25
Answers: #10 No solution; #16 y=any value, x=3y+2, z=4; #18 No solution.
2.3 20, 28, 32,38. Suggested: Odd: 1-41
Answers: #20 No; #28 First row 8 -10 2, second row -1 6 3, third
row 3 5 11; #32 -3x+4y=1, y=1.
2.4 4, 12, 20. Suggested: Odd: 1-23
Answers: #4 First row -7 3, second row 5 -2; #12 x=2, y=-3; #20 x=5,
y=-1, z=-1.
2.5 4, 6, 14. Suggested: Odd: 1-15
3.2 20,24,32. Suggested: Odd: 1-15, 19-29,
33
Answers: #20 The maximum value is 84 and it occurs at (12,0); #24 The
minimum value is 5/2 and it occurs at (2,2); #32 The maximum profit is
achieved at (30,40).
3.3 22,24,26. Suggested: Odd: 23-29
Answers: #22 The minimum cost of $67,000 is achieved at (4,3); #24
The maximum yield of $650 is achieved at (2,3,4) #26 The minimum cost is
$990.
4.2 2,12. Suggested: Odd: 5-13
Answers: #2a -6 is the only negative entry in the last row, and 1 is
the only nonzero entry above it. Pivot about the 1, first row, first column;
#2c x=5, y=12, u=0, v=0, M=40; #12 x=3, y=12, z=0, M=174.
4.3 2,4. Suggested: Odd: 1-9
Answers: #2 x=50, y=0, M=150; #4 The minimum is 20, attained
at x=0, y=0, z=20,
4.4 10,14. Suggested: Odd: 7-17
4.5 2,8,14. Suggested: Odd: 1-17
Answers: #8 x=3, y=0, M=90; u=0, v=30, M=90; #14 x=0, y=5, M=15; u=0,
v=3/2, M=15
5.2 2,4,6,14,22,32,44. Suggested:
Odd: 1-47
Answers: #2 2; #4 1; #6 6; #14 50 investors owned both stocks
and bonds; #22 Consists of points in both S and T or points in neither
S nor T; #32 Consists of points not in R or points in S but not in T.
5.3 4,12,18,24,46. Suggested:
Odd: 1-45
Answers: #4 3,5,2,4; #12 11,5,13,3,5,7,19; #18 50 workers were neither
college graduates nor union members; #24 52; #46 50.
5.4 8,20,22,32,40. Suggested:
Odd: 1-51
Answers #8 26.26.10.10.10.10=6,760,000 licence plates; #20 The number
of distinct pairs of initials is 26.26=676. Since there are 700 employees
and only 676 possible pairs of initials, at least two have the same pair;
#22 The unique letters are s,t,a,i and c. 5.4.3.2=120; #32 8.10.10=800
codes; #40 6.10.5=300 ways.
5.5 8,12,34,48,54,70. Suggested:
Odd: 1-69
Answers: #8 C(6,3)=20; #12 P(n,2); #34 C(8,5)= 56 ways; #48 There are
8 aces or kings in a deck. C(8,5)=56; #54 P(6,3)=6.5.4=120 signals; #70
Using the hint, there are 7 spots for the A's and 4 of them must be chosen.
This can be done in C(7,4)=35 ways.
5.6 4,6,24,34. Suggested: Odd:
1-39
Answers: #4 a. C(12,4)=495 samples, b. C98,4)=70 samples, c. C(8,2).C(4,2)=28.6=168
samples, d. There are C(8,3).C(4,1)=56.4=224 samples with exactly three
red balls. From part (b), there are 70 samples with all red balls. Therefore,
there are 224+70=294 samples with at least three balls; #6 a. 256 outcomes;
b. C(8,3)=56 outcomes; c. There are C(8,0)+C(8,1)=9 outcomes with no heads
or one head exactly. Therefore the number of outcomes with at least two
heads is 256-9=247 outcomes; #24 There are C(21,2)=210 ways to select the
two consonants in the sequence. There are 7!=5040 ways to arrange
the seven letters. Therefore, the number of sequences is 210.5040=1,058,400;
#34 First select the denominations of the two pairs. There are C(13,2)=78
ways to do so. There are C(4,2) ways to select two cards of one denomination.
Similarly, there are C(4,2) ways to select two cards of the other denomination.
Then select the third denomination. There are 11 ways to do this. There
are C(4,1)=4 ways to select one card within the selected denomination.
Therefore the number of "two pair" hands is 78.6.6.11.4=123,552.
5.7 22,26,36,40. Suggested: Odd:
1 -43
Answers: #26 C(13,5)=1287; #36 128-C(7,0)-C(7,1)=120 ways; #40 The
desired number is the number of all subsets of the set {1,3,5}, that is,
8.
6.3 6,10,18,24,26. Suggested: Odd: 1-25
Answers: #6 (a) 3/9, (b) 5/9, (c) 6/9; #10 (a) 0.30, 0.69, (b) 0.70,
(c) 0, (d) 0.99; #18 (a) 0.1, (b) 0.8; #24 (a) 160/737 (b) the probability
is 437/737, so that the odds are 437 to 300; #26 (a) 7 to 3.
6.4 8,10,18,30,38. Suggested: Odd: 1-39
Answers: #8 11/12; #10 5/6; #18 13/18; #30 5/16; #38 3/10.
6.5 12,24,34,48. Suggested: Odd: 1-47
Answers: #12 (a) 0.2, (b) 1/3, (c) 2/3, (d) 0.4, (e) 2/3; #24
0.1, 0.6, 0.2, 1/3; #34 (a) 0.16, (b) 0.52, (c) 0.44, (d) 0.36, (e)
0.64, (f) 0.44, (g) 0.80, (h) 0.44, (i)0.36; #48 ~0.4324
10.2 4,6,12,18. Suggested: Odd: 1-27
Answers: #4 $626.02; #6 $7360.09; #12 Balance decreases as follows:
$5000.00, $4525.00, $4047.63, $3567.87; #18 $750 a quarter is better.
10.3 4,8,14. Suggested: Odd: 1-23
Answers: #4 $3644.68; #8 a) $671.36, b) $211,408, c) $121,408, d) $14,695.50,
e) $7676.94, f) $1639.69, g) Each payment is $671.36; interest decreases
as follows: $600.00, $599.46, $598.93; applied to principal increases
as follows: $71.36, $71.90, $72.43; unpaid balance decreases as follows:
$79,928.64, $79856.74, $ 79784.31; #14 Each payment is $5454.37; interest
decreases as follows: $600.00, $308.74; applied to principal increases
as follows: $4854.37, $5145.63; unpaid balance decreases as follows: $5145.63,
$0.00.