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A twenty-something single person is planning a ski vacation. Assume that she has 3 possible destinations: New England, Utah, and Oregon. There are 3 ski areas in New England with 2 available times for 2 of the areas, and 3 times for the other area. There are 4 ski areas in Utah with 4 available times for 3 of the areas, and 3 times for the other area. There are 4 ski areas in Oregon with 4 available times for 3 of the areas, and 3 times for the other area. (A "time" refers to a weekend for which there are vacancies at the ski lodge.) A trip plan involves the selection of a location, ski area, and a time.How many possible plans are there?
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?
In a triangle ABC, if r 1 is the exradius of the excircle opposite to A, r 2 is the exradius of the excircle opposite to B and r 3 is the exradius of the excircle opposite to C
Let |G| be finite and N be a normal subgroup of G. If xN is an element of G/N and has order a power of p, show that there exists a y element of G such that |y| is a power of p and yN=xN.
Suppose that you are dealt a hand of 9 cards from a standard deck of 52 playing cards. What is the probability that you are dealt exactly 3 kings? What is the probability that you are dealt 9 cards of the same suit?
Finding the Probability from the given data - find the probability of getting no cracked candy canes.
verify that E is a constant of motion for the system of the first two equations and find the equilibria of the system of the first two equations
You have a choice to build a small new plant, do nothing (the value of this is zero), or build a large plant. We'll use Net Present Value to compute this.
Let f : [0,1]-->[0,1] be a continuous function. Show that there exists a real number x in [0,1] such that f(x)=x (apply the intermediate value theorem to the function f(x) -x).
The book value of a machine is $21,000 at the end of its fourth year of life and $14,000 at the end of its sixth year of life. What was the purchase value of the machine, assuming that "straight line depreciation" is being used.
Select and discuss two examples of real life objects that incorporate the parabolic shape. Explain why the parabolic shape was used for the objects.
Matrices are the most common and popular way to solve systems of equations. Provide an example of a matrix that can be solved using Gaussian elimination. Show specifically how row operations can be used to solve the matrix.
Also, if the variables in an equation were reversed, what would happen to the graph of the equation? This was the example I was given, how would the graph of y = x² relate to the graph of x = y²?
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