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A talking parrot knows how to utter five distinct words, and she utters any of them with even chance. How many words does she utter on average before she utters ...

Let p(x) be a polynomial of degree 4 with real coefficients satisfying p(0)=0, p(1)=\(\frac{1}{2}\), p(2)=\(\frac{2}{3}\), p(3)=...

In the \(xyz\) coordinate system, there is a solid sphere of radius \(1\) centered at \((1,1,1)\).

Suppose the distance from a random point within the spherical volume to ...

In the \(xy\)-plane there is a disc of radius \(1\) centred at \((1,1)\).

Suppose the distance from a random point on the disc to the origin is ...

The number 21 can be written as the difference between two positive perfect squares in two different ways: ...

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