In all problems involving days,a 360 -day year is assumed. When annual rates are requested as an answer, express, express the rate as a percentage, correct to three decimal places, unless directed otherwise. Round dollar amounts to the nearest cent. If $ 5 , 000 is loaned for 9 months at a 6.2 % annual rate, how much interest is earned?
In all problems involving days,a 360 -day year is assumed. When annual rates are requested as an answer, express, express the rate as a percentage, correct to three decimal places, unless directed otherwise. Round dollar amounts to the nearest cent. If $ 5 , 000 is loaned for 9 months at a 6.2 % annual rate, how much interest is earned?
In all problems involving days,a
360
-day year is assumed. When annual rates are requested as an answer, express, express the rate as a percentage, correct to three decimal places, unless directed otherwise. Round dollar amounts to the nearest cent.
If
$
5
,
000
is loaned for
9
months at a
6.2
%
annual rate, how much interest is earned?
Give an example of a graph with at least 3 vertices that has exactly 2 automorphisms(one of which is necessarily the identity automorphism). Prove that your example iscorrect.
3. [10 marks]
Let Go (Vo, Eo) and G₁
=
(V1, E1) be two graphs that
⚫ have at least 2 vertices each,
⚫are disjoint (i.e., Von V₁ = 0),
⚫ and are both Eulerian.
Consider connecting Go and G₁ by adding a set of new edges F, where each new edge
has one end in Vo and the other end in V₁.
(a) Is it possible to add a set of edges F of the form (x, y) with x € Vo and y = V₁ so
that the resulting graph (VUV₁, Eo UE₁ UF) is Eulerian?
(b) If so, what is the size of the smallest possible F?
Prove that your answers are correct.
Let T be a tree. Prove that if T has a vertex of degree k, then T has at least k leaves.
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Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
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