Math 141 Week in Review
Week 11 Problem Set Answers
1.
A. Not regular (Third column does not add up to 1.)
B. Regular
C. Not regular
2.
A. 63.03% will drink Coke and 36.97% will drink Pepsi after 2 years.
B. 62.1622% will drink Coke and 37.8378% will drink Pepsi in the long run.
3.
Equilibrium Quantity: 950 guitars; Equilibrium Price: $337.50
4.
"1 0
The row-reduced matrix is $
#0 1
R1 ! R1
!1%
"6R + R2 ! R2
' . The steps are: 1 1
R ! R2
!3&
15 2
2R2 + R1 ! R1
1
2
5.
A. (5, −3, 8)
B. No solution
7
+ 113 t, 17
+ 11
t,t ) , where t is
C. Infinitely many solutions parameterized by (! 32
11
11
any real number.
6.
a = 26, b = −13, c = 4, d = 9
7.
A. $1140.41
B. $165,123.00
C. $1111.40
8.
C(5, 3)·23·C(5, 4)·54 = 250, 000
9.
Let x = number of vases and y = number of mugs made each week.
6x + 4 y ! 42
8x + 2y " 24
Maximize P = 12x + 3y subject to:
y ! 2x
x " 0, y " 0
Corner points: (2, 4), (3, 6), (7, 0), and (3, 0). Max profit: $84 when 7 vases and 0
mugs are made. There is no clay left over.; Min profit: $36 at infinitely many
points along the line segment between (2, 4) and (3, 0). There are between 14 and
24 pieces of clay left over along this line segment.
10.
A. 43
B. 140
C. 145
84
D.
= 0.28
300
11.
12
19
10
B.
19
A.
5
10
, P(F ) =
19
19
E and F are not mutually exclusive because P(E ∩ F) ≠ 0. E and F are not
independent because P(E ∩ F) ≠ P(E)·P(F).
C. P ( E ) =
12.
y = 0.9797x + 0.6014; about 69
13.
A.
14.
0.1257
15.
E(X) = −$0.28, σ = 2.3287, Var(X) = 5.4228
16.
Need 25,675 units of food and 10,400 units of shelter.
17.
0.0033
18.
550 calendars
19.
0.0322
20.
3!·P(5, 3)·P(6, 4)·P(5, 2) = 2,592,000
21.
0.8123
22.
N = 14.92 ≈ 15, or about 3.75 years; $1000
23.
A. {2, 4}
B. {1, 6}
C. {1, 2, 3, 4, 6}
24.
y=
25.
0.2023
C(10,3)C (24,5) + C(8,4)C (26,4 ) ! C(10,3)C(8,4)C (16,1)
" 0.3312
C ( 34,8)
C (27,8)
" 0.8777
B. 1!
C(34,8)
2
x !2
9