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a)A graph has six vertices, every two of which are joined by an edge. Each edge is colored red or white. Show that the graph contains a monochromatic triangle (a triangle all of whose vertices have the same color.) Is the result true for a graph with 5 vertices?
b)A graph has six vertices, every two of which are joined by an edge. Each vertex is colored red or white. Show that the graph contains at least two monochromatic triangles.
c)A graph has six vertices, every two of which are joined by an edge. Each edge is colored red or white. Show that the graph contains at least two monochromatic triangles.
There were 116 fewer blue balloons than white ones. How many balloons of each color did Marty inflate?
Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the curves x=4y^2-y^3 and x=0 about the x-axis.
Find the probability that a male resident who was newly diagnosed with AIDS in 1998 contracted it via homosexual contact. Find the probability that a female resident who was newly diagnosed with AIDS in 1998 contracted it via intravenous drug use.
A weight-loss program guarantees, "You'll lose weight within two weeks or we'll refund your money plus $10!" Using α = 5%, perform the sign test of the median paired difference to determine whether the median weight of these twelve participants decre..
What is the WACC for this financing?
Apply normal distribution methods to approximate this binomial distribution.
A firm has an opportunity to invest $80000 today that will yield $92000 in one year. if the interest rates are 5% what is the net present value (NPV0 of this interest?
Calculate probability values.
Circle O and circle P are externally tangent circles. Circle O is tangent to circle P at T, OT = 12, TP = 6. AB is a common external tangent line to both circles. Find AB.
Assume that the field is algebraically closed and has zero characteristic, G is finite and representations are finite-dimensional.
Suppose that derivative of the function f is given by f'(x) = 3x and suppose that the point (4,2) is on the graph of f. Write an equation of a line tangent to the graph of f at the point (4,2)
State the research and null hypotheses to test whether or not doctors in this HMO have less experience than the national average at alpha=0.05
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