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1. Prove the following statement using the method of contradiction:
There are no positive integer solutions to the Diophantine equation x2 - y2 = 1.
2. Prove the following statement using contraposition: If n, is a positive integer such that n(mod 3) = 2, then n is not a perfect square.
3. Find a solution (if it exists) to the linear diophantine equation 234x + 65y = 325.
4. Prove that the sum to n terms of the sequence
5. Prove using mathematical induction, that n3 - 7n + 3 is divisible by 3 for each integer n > 0.
6. The terms of a sequence are given recursively as
7. In each case decide whether the statement is true or false.
The dimensions of a rectangle are such that its length is 5 in more than its width. If the length were doubled and if the width were decreased by 2 in., the area would be increased by 52 in squared. What are the length and width of the rectangle?
Suppose that 40% of a company's television sets are manufactured at a plant in Portland and 60% at a plant in Houston. Of those made in Portland, 4% are defective, and of those made in Houston 9% are defective.
An archer has probability 0.3 of hitting a certain target. What is the probability of hitting the target exactly two times in four attempts?
Sketch a possible parabolic path of your arrows flight if your shoulder height is 53 inches.
If Mark makes the tee time, then there is a 0.8 chance that Rene will then make the tee time. What is the probability that Rene will make the tee time but Mark will not?
The weight of a randomly chosen American passenger car is a uniformly distributed random variable ranging from 4,400 pounds to 6,500 pounds.
Profit for each big shelf is $85 and for each medium shelf is $75. What is the constraint on money to invest?
What is the elongation in the (2, 2, 1) direction? What is the change of angle between two perpendicular lines (in the undeformed state) in the directions (2, 2, 1) and (3, 0, 6)?
Explain in simple terms how solving linear equations is similar and different than solving linear inequalities. Cite and explain three examples.
Explaining how to derive the formula for the distance between two points -Prepare an essay of 1,000 words explaining how to derive the formula for the distance between two points in analytic geometry 3-space.
ow large a sample must be selected if he wants to be 99 percent confident of finding whether the true mean differs from the sample mean by 2.5 hours?
Find the break-even point for the firm
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