Problems 61-70 refer to the following transition matrix P and its powers A B C P = A B C .6 .3 .1 .2 .5 .3 .1 .2 .7 A B C P 2 = A B C .43 .35 .22 .25 .37 .38 .17 .27 .56 A B C P 2 = A B C .35 .348 .302 .262 .336 .402 .212 .298 .49 Find the probability of going from state B to state C in two trials.
Problems 61-70 refer to the following transition matrix P and its powers A B C P = A B C .6 .3 .1 .2 .5 .3 .1 .2 .7 A B C P 2 = A B C .43 .35 .22 .25 .37 .38 .17 .27 .56 A B C P 2 = A B C .35 .348 .302 .262 .336 .402 .212 .298 .49 Find the probability of going from state B to state C in two trials.
Problems 61-70 refer to the following transition matrix
P
and its powers
A
B
C
P
=
A
B
C
.6
.3
.1
.2
.5
.3
.1
.2
.7
A
B
C
P
2
=
A
B
C
.43
.35
.22
.25
.37
.38
.17
.27
.56
A
B
C
P
2
=
A
B
C
.35
.348
.302
.262
.336
.402
.212
.298
.49
Find the probability of going from state
B
to state
C
in two trials.
12:25 AM Sun Dec 22
uestion 6- Week 8: QuX
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Week 8: Quiz i
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Assume that a company is considering purchasing a machine for $50,000 that will have a five-year useful life and a $5,000 salvage value. The
machine will lower operating costs by $17,000 per year. The company's required rate of return is 15%. The net present value of this investment
is closest to:
Click here to view Exhibit 12B-1 and Exhibit 12B-2, to determine the appropriate discount factor(s) using the tables provided.
00:33:45
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7. [10 marks]
Let G
=
(V,E) be a 3-connected graph. We prove that for every x, y, z Є V, there is a
cycle in G on which x, y, and z all lie.
(a) First prove that there are two internally disjoint xy-paths Po and P₁.
(b) If z is on either Po or P₁, then combining Po and P₁ produces a cycle on which
x, y, and z all lie. So assume that z is not on Po and not on P₁. Now prove that
there are three paths Qo, Q1, and Q2 such that:
⚫each Qi starts at z;
• each Qi ends at a vertex w; that is on Po or on P₁, where wo, w₁, and w₂ are
distinct;
the paths Qo, Q1, Q2 are disjoint from each other (except at the start vertex
2) and are disjoint from the paths Po and P₁ (except at the end vertices wo,
W1, and w₂).
(c) Use paths Po, P₁, Qo, Q1, and Q2 to prove that there is a cycle on which x, y, and
z all lie. (To do this, notice that two of the w; must be on the same Pj.)
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
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