[This problem is worth 5 points.]
A fair coin is flipped 10 times. Find the probability that there are no consecutive tosses that come up heads.
Tuesday, August 7, 2012
Monday, August 6, 2012
Problem #40
[This problem is worth 4 points.]
Let k be an integer such that 36 + k, 300 + k, and 596 + k are the squares of three consecutive terms of an arithmetic sequence. Find k.
Let k be an integer such that 36 + k, 300 + k, and 596 + k are the squares of three consecutive terms of an arithmetic sequence. Find k.
Thursday, August 2, 2012
Problem #39
[This problem is worth 3 points.]
The polynomial x2 + bx + c is a factor of both x4 + 6x2 + 25 and 3x4 + 4x2 + 28x + 5. What are b and c?
The polynomial x2 + bx + c is a factor of both x4 + 6x2 + 25 and 3x4 + 4x2 + 28x + 5. What are b and c?
Wednesday, August 1, 2012
Solution #36
We factor into (π - 3)(π - 4). The first factor is positive and the second is negative, so the product is negative.
Problem #38
[This problem is worth 6 points.]
What is the area of the largest square in the Cartesian coordinate plane such that the interior of the square contains at most 3 points of the form (a,b), where a and b are both integers?
What is the area of the largest square in the Cartesian coordinate plane such that the interior of the square contains at most 3 points of the form (a,b), where a and b are both integers?
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