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A tree has 11 vertices of degree 3, 12 vertices of degree 2, 10 vertices of degree 4 and the remaining vertices are of degree 1. How many vertices does it have?
Assuming that there is no cost to enter the .sweepstakes, find the expected value of the amount won for one entry. Round to the nearest tenth.
Characterize the set of all real numbers with the discrete metric as to whether it is compact, complete, or totally bounded. Use definitions only!
Consider the curve 5x3+8xy+5y2 = 45. Use implicit differentiation to calculate the derivative dy/dx. Hence determine the point/s which has/have a horizontal tangent.
A computer programming team has 12 members. How many ways can a group of 7 (out of the 12 members) be chosen to work on a special project? Explain.
Probability - Frequency Of Dice Rolls, When a pair of dice is rolled, the total will range from 2 (1,1) to 12 (6,6). It is a fact that some numbers will occur more frequently than others as the dice are rolled over and over.
Using the definition of the derivative and any standard limiting theorems, show that the derivative of (sinx)^2 is sin(2x).
Find the number of committees from the given information - How many 5 card poker hands can be performed from a deck of 52 cards?
The 4 runners on a relay team all want to run the same distance in a race. The coach says that the first runner will go 1/4 of the distance. Then the second runner will go 1/3 of the remaining distance
Let m and n be positive integers with n dividing m. Prove that the natural surjective ring projection Z/mZ ->Z/nZ is also surjective on the units:(Z/mZ)^x ->(Z/nZ)^x
Find the derivative of f(x)= (3-4x^2)/(x^2-x-6) and then determine intervals of increase/decrease,local max and min values and points of concavity or inflection.
A regression analysis
Each page of a book will contain 30in^2 of print, and each page must have 2-in margins at top and bottom and a 1-in. margin at each side.
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