clavin

Let f(x)=3^(171x−3)−3^(114x+2)+3^(57x+3)−1. Let S be the sum of all real values of x that satisfy f(x)=0. What is the value of 1/S?

Calvin and Dan are playing a game of chance. Calvin tosses 8 fair coins, and wins if he obtains at least 4 heads. The probability that Calvin wins can be expressed as a/b where a,b are coprime positive integers. What is the value of a+b?

For each positive integer n, let Hn=1/1 + 1/2 +⋯+ 1/n . If ∑ (up)∞ (base)(n=4) 1/n*Hn*H(n-1)= a/b for relatively prime positive integers a and b, find a+b.

Triangle ABC has an obtuse angle at B, base BC has length equal to 30 and height equal to 24. D is a point on the line segment BC and E is a point on AC such that DE∥AB. F is a point on AB such that FD∥AC. As D varies within line segment BC, what is the m...

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Triangle ABC has an obtuse angle at B, base BC has length equal to 30 and height equal to 24. (This height is taken with respect to base BC). D is a point on the line segment BC and E is a point on AC such that DE∥AB. F is a point on AB such that FD∥AC. A...

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121

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