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Consider all 3-term geometric sequences with first term 1 and with common ratio the square of an integer between 1 and 1000. How many of these 1000 geometric sequences have the property that the sum of the 3 terms is prime?

PAC-MAN is a circle of radius 24 with a sector of angle π/3 removed. PAC-MAN eats circular pellets of radius 2. If PAC-MAN wants to eat pellets that have that same total area that he does, how many pellets must he eat?

Raoul wants to create a weekly schedule for going to the gym. He wants to go to the gym the same three days each week, and he wants there to be at least one day in between each of his visits. How many different ways can Raoul schedule his weekly gym visit...

Γ is a circle with chord AB. P is a point outside of Γ such that PA is tangent to Γ and ∠BPA=90∘. If AB=48 and PB=8, what is the radius of Γ?

A point P is uniformly chosen inside a regular hexagon of side length 3. For each side of the hexagon a line is drawn from P to the point on that side which is closest to P. The probability that the sum of the lengths of these segments is less than or equ...

A pair of fuzzy dice are hanging by a string in my car from the rear-view mirror. I hit the gas pedal, and while I accelerate the fuzzy dice no longer hang straight down, but instead make an angle θ of 15 degrees with respect to the vertical. How fast am...

What is the sum of all possible real values of x that satisfies the equation x x^log5 =x^3/25.

If the expression (x^2+2x−1)^8 is completely expanded, what is the sum of the coefficients of the terms with even powers of x? Details and assumptions 0 is an even number.

cant post :(

wrong

dont get it

What is the sum of all possible real values of x that satisfies the equation xlog5x=x325.

i also dunno how to do :'(

210