In Exercises 19-30, use the following equivalents, along with dimensional analysis, to convert the given measurement to the unit indicated. When necessary, round answers to two decimal places. 16 oz =1 lb 2000 lb = 1 T 1 oz ≈ 28 g 1 lb ≈ 0.45 kg 1 T ≈ 0.9 t 220 kg to lb
In Exercises 19-30, use the following equivalents, along with dimensional analysis, to convert the given measurement to the unit indicated. When necessary, round answers to two decimal places. 16 oz =1 lb 2000 lb = 1 T 1 oz ≈ 28 g 1 lb ≈ 0.45 kg 1 T ≈ 0.9 t 220 kg to lb
Solution Summary: The author explains how to convert 220 kg to lb using the equation.
In Exercises 19-30, use the following equivalents, along with dimensional analysis, to convert the given measurement to the unit indicated. When necessary, round answers to two decimal places.
16
oz
=1
lb
2000
lb
=
1
T
1
oz
≈
28
g
1
lb
≈
0.45
kg
1
T
≈
0.9
t
28. (a) Under what conditions do we say that two random variables X and Y are
independent?
(b) Demonstrate that if X and Y are independent, then it follows that E(XY) =
E(X)E(Y);
(e) Show by a counter example that the converse of (ii) is not necessarily true.
7. [10 marks]
Let G = (V,E) be a 3-connected graph with at least 6 vertices. Let C be a cycle in G
of length 5. We show how to find a longer cycle in G.
(a) Let x be a vertex of G that is not on C. Show that there are three C-paths
Po, P1, P2 that are disjoint except at the shared initial vertex and only intersect
C at their final vertices.
(b) Show that at least two of P0, P1, P2 have final vertices that are adjacent along C.
(c) Combine two of Po, P1, P2 with C to produce a cycle in G that is longer than C.
1. Let X and Y be random variables and suppose that A = F. Prove that
Z XI(A)+YI(A) is a random variable.
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