Daily Practice - Higher Plus

A bag holds 7 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?

A histogram has four 20-wide classes from 0, with frequency densities 1, 3, 2, 0.5. Which class contains the median?

A block has mass 300 g (to the nearest 10 g) and volume 23 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 300 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.

Solve x² + y² = 841 and y = x + 1 simultaneously.Solve x^2 + y^2 = 841 and y = x + 1 simultaneously.

y is directly proportional to √x. When x = 36, y = 48. Work out y when x = 81.y is directly proportional to sqrt(x). When x = 36, y = 48. Work out y when x = 81.