The probability that South Florida will be hit by a major hurricane (category 4 or 5) in any single year is 1 16 . (Source: National Hurricane Center) a. What is the probability that South Florida will be hit by a major hurricane two years in a row? b. What is the probability that South Florida will be hit by a major hurricane in three consecutive years? c. What is the probability that South Florida will not be hit by a major hurricane in the next ten years? d. What is the probability that South Florida will be hit by a major hurricane at least once in the next ten years?
The probability that South Florida will be hit by a major hurricane (category 4 or 5) in any single year is 1 16 . (Source: National Hurricane Center) a. What is the probability that South Florida will be hit by a major hurricane two years in a row? b. What is the probability that South Florida will be hit by a major hurricane in three consecutive years? c. What is the probability that South Florida will not be hit by a major hurricane in the next ten years? d. What is the probability that South Florida will be hit by a major hurricane at least once in the next ten years?
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 11 Solutions
Thinking Mathematically, Books a la Carte Edition plus MyLab Math with Pearson eText -- Access Card Package, 4/e (7th Edition)
Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)
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