Higher Plus

In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.

A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 5/22. Work out r.

A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 3. How many values in total?

A block has mass 720 g (to the nearest 10 g) and volume 24 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 720 g (to the nearest 10 g) and volume 24 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.

Use the iteration x(n+1) = cube root of (8x(n) + 8) with x(0) = 1. Work out x(1) to 3 decimal places.