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The event should be; mutually exclusive from the other outcome, independent from the other outcome (so its probability doesn't change ) and happen within a fixed number of trials . A good example would be th...

Because its hypothetical inverse would be 'one to many' which is not a function. This is because a single x-value would map to several y-values at the same time.

The factor theorem states that a polynomial f(x) has a factor (x-k) if and only if f(k)=0. f(2) = 3(2)^3 - 8(2)^2 + 3(2) + 2 = 3(8) - 8(4) + 6 + 2 = 24 - 32 + 8 = 0. ==> (x-2) is a factor.

Let's start by assuming that the squared root of 2 is a rational number and will prove it is irrational by contradiction.If srqt(2) is rational then it can be represented by an irreducible fraction. Let this...

let y = lnx therefore e^y = x then differentiating both sides we get: dy/dx (e^y) = 1 dy/dx = 1/(e^y) and as e^y = x dy/dx = 1/x when y = lnx