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In what fundamental way does the solution set of a system of linear equations differ from the solution set of a system of linear inequalities? Give examples. Discuss the important implications arising from this difference.
Expected value, indifference probabilities, expected utility, For the payoff table below, the decision maker will use P(s1) = .15, P(s2) = .5, and P(s3) = .35.
Find an example online of a graph used in real life. Please provide the link to the web page by using the link button in the editor. Describe at least one mathematical feature of the graph
Please give a short answer as to why the following is true: Let p(x) = Ax^ 2+ Bx + C. For any interval [a,b] the value of c guaranteed by the Mean Value theorem is the midpoint of the interval.
Calculate probability values.
The same experiment as in part (a) above is done with the 7 letters from CHICAGO. Find the probability that the result spells CHICAGO. Find probability that the result spells NEW YORK
Convex Sets and Linear Transformations, Prove that the following sets are convex, where E stands for the sum symbol:
Suppose that you select 2 cards without replacement from an ordinary deck of playing cards. If the first card that you select is a king, what is the probability that the second card that you select is a heart?
Let R be a PID. Consider the Diophantine equation ax+by=N where a,b and N are integers and a,b are nonzero. Suppose x_0, y_0 is a solution: ax_0+by_0=N.
The exact value of the indicated trigonometric function.
Let n >= 2 be a number. Define the graph L2(n) as follows: Vertices are ordered pairs from the set {1, ..., n}. Two vertices are adjacent if they have the same first coordinate, or the same second coordinate (but not both).
Two rainstorms occurred in one week in a certain area. In the first storm 25ml of rain fell per hour, and in the second storm 20ml of rain fell per hour. Rain fell that week for a total of 75 hours for a total rainfall of 1700ml.
Cubic Splines: Natural and Clamped, Calculate the natural cubic spline f(x) for the following data and then determine 1(1.5). (Use 3 significant digits.)
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