A payday loan is a short-term loan that is repaid on the next payday, often by giving the lender electronic access to a personal checking account. Some states have statutes that regulate the fees that may be charged for payday loans. In Problems 87-90, express the annual interest rate as a percentage, rounded to the nearest integer. In Louisiana, charges on a payday loan may not exceed 16.75 % of the amount advanced. Find the annual interest rate if $ 350 is borrowed for 14 days at the maximum allowable charge.
A payday loan is a short-term loan that is repaid on the next payday, often by giving the lender electronic access to a personal checking account. Some states have statutes that regulate the fees that may be charged for payday loans. In Problems 87-90, express the annual interest rate as a percentage, rounded to the nearest integer. In Louisiana, charges on a payday loan may not exceed 16.75 % of the amount advanced. Find the annual interest rate if $ 350 is borrowed for 14 days at the maximum allowable charge.
A payday loan is a short-term loan that is repaid on the next payday, often by giving the lender electronic access to a personal checking account. Some states have statutes that regulate the fees that may be charged for payday loans. In Problems 87-90, express the annual interest rate as a percentage, rounded to the nearest integer.
In Louisiana, charges on a payday loan may not exceed
16.75
%
of the amount advanced. Find the annual interest rate if
$
350
is borrowed for
14
days at the maximum allowable charge.
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.)
6. [10 marks]
Let T be a tree with n ≥ 2 vertices and leaves. Let BL(T) denote the block graph of
T.
(a) How many vertices does BL(T) have?
(b) How many edges does BL(T) have?
Prove that your answers are correct.
4. [10 marks]
Find both a matching of maximum size and a vertex cover of minimum size in
the following bipartite graph. Prove that your answer is correct.
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Chapter 3 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
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