Question

MATH 353

6. Find a necessary and sufficient condition on *m* and
*n* for K_{m,n} to be Hamiltonian. Prove your
answer.

Answer #1

State the sufficient and necessary condition for an undirected
graph to have an Euler cycle. Prove that if an undirected graph has
an Euler cycle then all vertex degrees are even. Show all steps and
draw a diagram it will help me understand the problem. Thanks

Learn four types of conditions:
1. Necessary condition: ask what condition must be true to
guarantee the conclusion? Conclusion doesn't follow unless a
necessary condition is met. "Sue will give birth to a healthy baby
boy." Necessary condition: Sue is pregnant. (It's not sufficient,
though, because the baby might not be healthy, might not be a boy,
might be premature.)
2. Sufficient condition: ask is this condition enough to make
the conclusion true? (But other possibilities exist).
3. Necessary and...

Find the diameters of Kn (Connected graph with n vertices), Km,n
(Bipartite graph with m and n vertices), and Cn (Cycle graph with n
vertices). For each, clearly explain your reasoning.

For what values of m, n ∈ Z>0 does the complete bipartite
graph Km,n have a perfect matching? Prove it

Discrete Math
6. Prove that for all positive integer n, there exists an even
positive integer k such that
n < k + 3 ≤ n + 2
. (You can use that facts without proof that even plus even is
even or/and even plus odd is odd.)

Assume that gcd(a, m) = 1, gcd(a, n) = 1, and gcd(m, n) = 1.
Assume that a has order s modulo m and order t modulo n. What is
the order of a modulo mn? Prove that your answer is correct

Find the minimum sample size n necessary to estimate a
population proportion p with a 95% confidence interval that has a
margin of error m = 0.03.

Find the time for orbit (days) and velocity of Mars
(km/s) if it were to make a perfectly circular orbit around sun.
Average distance from outer center of sun to center of Mars is
228x10^6km
Mass of Sun is 1.989x10^30 kg
Mass of Mars is 6.39x10^23kg
Gravitational constant G is 6.67x10^-11 N-m^2/kg^2
Answer Choices
A 687.2 days, 24.13 km/sec
B 695 days, 23.86 km/sec
C 700 days, 23.68 km/sec
D 680 days, 24.383 km/sec

You find out that the average 10th grade math score, for
Section 6 of the local high school, is 87 for the 25 students in
the class. The average test score for all 10th grade math students
across the state is 85 for 1,800 students. The standard deviation
for the state is 3.8.
Answer the following questions:
What z score do you calculate?
What is the area between the mean and the z score found in
Appendix A of the...

Data for the life of tires yields a sample standard deviation of
3645.94 km with n=18.
(a) Can you conclude, using α = 0.01, that the standard
deviation of tire life is less than 4000 kilometers? State any
necessary assumptions about the underlying distribution of the
data. Find the P-value for this test.
(b) Explain how you could answer the question in part (a) by
constructing a 99% one-sided confidence interval for σ.

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