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1. You dream of someday winning the lottery (don't we all). You found out about a new lottery where the winning numbers are five different numbers between 1 and 34 inclusive. To win the lottery, you must select the correct 5 numbers in the same order in which they were drawn. According to your calculations, the probability of winning are:
a. 1/33,390,720
b. 1/120
c. 120/33,390,720
d. 1/34!
2. If a person is randomly selected from your home town, the probability distribution for the number x, of siblings is as described in the following table: Is this a probability distribution? Please state the reason for your answer (the requirement that was met or not met) (Hint: The answer I am looking for has to do with the sum of the numbers)
X P(x)
0 0.24
1 0.29
2 0.24
3 0.12
4 0.06
5 0.03
Let A be a real n x n matrix. Show that a linear subspace E of R^n is A-invariant if and only if E is e^{tA} -invariant for all t in R, where e^{tA} is the exponential matrix associated to A.
Sometimes you need to find the slope of a line based on two given points. Sometimes you need to read a linear equation and determine the slope of a lone from the equation.
True or false questions.
Explain how Euler concludes from 1) that pi^2/6=1+1/4+1/9+1/16 ... . Compare the formula in 2) to Archimedes' calculation for pi. Which of these methods is more efficient and why?
Use synthetic division method to divide.
Leon drove 270 to the lodge in the same time as Pat drove 330 miles to the lodge. If Pat drove 10mph faster than Leon, how fast did each of them drive?
When is it necessary to find the least common denominator (LCD) of two rational expressions? Describe, in your own words, the process for finding the LCD of two rational expressions. How is factoring related to this process?
Calculate the companies expected gain or loss for the year
Simplifying the equation
Prove that the Cayley digraph given in Example 6 does not have a Hamiltonian circuit. Does it have a Hamiltonian path - determine if this has a Hamilton circuit
Solve the equation by graphing.
There is a linear equation that gives the annual benefit b in terms of age a for these three years. Find the equation.
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