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Maria and Thomas are part of a group of 8 women and 8 men who will participate in a chess tournament. The 16 players will be randomly paired up into groups of two.
(a) What is the probability that Maria and Thomas will be paired together?
(b) What is the probability that Maria will be paired with another woman?
(c) What is the probability that Maria will be paired with another woman and Thomas will be paired with another with a man?
(d) What is the probability that both Maria and Thomas are paired with a woman?
Provide a plot of temperature versus distance east. Based on its appearance, is it a good linear model for predicting temperature as a function of distance?
The probability that a basketball player will make a 3 point basket is 3/5. If he tries two 3 point shots
Suppose that Ford's performance scores really are Normally distributed. This year, managers with scores less than 31 received C's and those with scores above 595 received A's. What are the mean and standard deviation of the scores?
Explain how you would conduct the survey. What are the ethical implications if the manufacturer of Brand A toothpaste asked you to survey only its employees?
Let G be a group (finite or infinite) and let a and b in G. Let o(a) represent the order of a. Suppose G is abelian and both a and b are of finite order. Show that ab is of finite order and o(ab) divides o(a)o(b).
Let R be a ring with the property that every element is either nilpotent or invertible. If a, b, c are in R with a and b nilpotent, show that ac, ca, and a + b are nilpotent.
How many permutations are there of 12 objects taken five at a time? How is this answer related to answers in 1 and 2?
Cantor's Diagonal Argument, Here we present Cantor's diagonal argument, which proves that the cardinality of the power set 2^S
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.
Use shells to find the volume of the solid formed by revolving the region bounded by the x-axis and y=4x-x^2 about the y-axis. Sketch the area. Include a typical rectangle.
Demand for vacuum cleaners remains constant through the year.
Find the equation of the perpendicular bisector of the line drawn between two points and determine the center and radius of the circle equation.
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