Problems 87 and 88 refer to the data in the following table, obtained from a random survey of 1 , 000 residents of a state. The participants were asked their political affiliations and their preferences in an upcoming election. (In the table, D = Democrat , R = Republican , and U = Unaffliliated . ) Politics. If a state resident is selected at random, what is the (empirical) probability that the resident is (A) Not affiliated with a political party or has no preference? What are the odds for this event? (B) Affiliated with a political party and prefers candidate A ? What are the odds against this event?
Problems 87 and 88 refer to the data in the following table, obtained from a random survey of 1 , 000 residents of a state. The participants were asked their political affiliations and their preferences in an upcoming election. (In the table, D = Democrat , R = Republican , and U = Unaffliliated . ) Politics. If a state resident is selected at random, what is the (empirical) probability that the resident is (A) Not affiliated with a political party or has no preference? What are the odds for this event? (B) Affiliated with a political party and prefers candidate A ? What are the odds against this event?
Problems
87
and
88
refer to the data in the following table, obtained from a random survey of
1
,
000
residents of a state. The participants were asked their political affiliations and their preferences in an upcoming election. (In the table,
D
=
Democrat
,
R
=
Republican
,
and
U
=
Unaffliliated
.
)
Politics. If a state resident is selected at random, what is the (empirical) probability that the resident is
(A) Not affiliated with a political party or has no preference? What are the odds for this event?
(B) Affiliated with a political party and prefers candidate
A
? What are the odds against this event?
EXAMPLE 3
Find
S
X
√√2-2x2
dx.
SOLUTION Let u = 2 - 2x². Then du =
Χ
dx =
2- 2x²
=
信
du
dx, so x dx =
du and
u-1/2 du
(2√u) + C
+ C (in terms of x).
Let g(z) =
z-i
z+i'
(a) Evaluate g(i) and g(1).
(b) Evaluate the limits
lim g(z), and lim g(z).
2-12
(c) Find the image of the real axis under g.
(d) Find the image of the upper half plane {z: Iz > 0} under the function g.
k
(i) Evaluate
k=7
k=0
[Hint: geometric series + De Moivre]
(ii) Find an upper bound for the expression
1
+2x+2
where z lies on the circle || z|| = R with R > 10. [Hint: Use Cauchy-Schwarz]
Chapter 8 Solutions
Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
Intro Stats, Books a la Carte Edition (5th Edition)
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