Over a period of time Julian finds that on long-distance flights he flies economy class on 82% of flights. On the rest of the flights he flies first class. When he flies economy class, the probability that he gets a good night's sleep is x. When he flies first class, the probability that he gets a good night's sleep is 0.9.

A plate of cakes holds 12 different cakes. Find the number of ways these cakes can be shared between Alex and James i...

Pack A consists of ten cards numbered 0, 0, 1, 1, 1, 1, 1, 3, 3, 3. Pack B consists of six cards numbered 0, 0, 2, 2,...

The lengths, in centimetres, of middle fingers of women in Raneland have a normal distribution with mean u and standa...

The diagram shows part of the curve defined by the parametric equations x = t² + 4t, y = t³ – 3t². The curve has a mi...

Use the trapezium rule with three intervals to estimate the value of ∫₀^(π/4) √(1 – tan x) dx, giving your answer cor...

Expand ∛(1 – 4x) in ascending powers of x, up to and including the term in x³, simplifying the coefficients.