Alan

\(12+27/4 \rightarrow 12 + 6\frac{3}{4} \rightarrow 18\frac{3}{4} \)

h = (SA - 2pi*r^2)/(2pi*r)

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Brackets take priority over exponents so (-3)^2 → (-3)*(-3) → 9

Exponents take priority over negation so -3^2 → -(3^2) → -9

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Identify where the singularities are (i.e. the places where the denominator goes to zero.

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No it doesn't matter which one you use. They're just different ways of remembering the same thing! Use whichever one you are most comfortable with.

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I think Melody has read this as x^2 = 1/64.

For 2^x = 1/64 then x = -6              (2^-6 → 1/2^6 → 1/64)

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Degree of f(x)*g(x) is 8  (from x^4*2x^4 → 2x^8

Coefficient of x^2 in the product is :  (-4)*(-7) + 2t - 5 → 23 - 2t 

For this to be zero we must have t = 11.5

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Not sure what you mean Max.  If I follow your links I see the questions.

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Too many steps to include here, so here's the result given by Mathcad:

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The only way of not picking a red card after picking a blue or yellow card is to pick all the red cards first. The probability of doing this is q = 10!*35!/45!  i.e. (10/45)*(9/44)*...*(1/36)

Hence, the probability of picking a red card after picking a blue or yellow card is p = 1 - q

I've assumed the question intends all the cards to be picked; that it doesn't just refer to the 1st and 2nd cards picked.