Daily Practice - Higher Plus

In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.

A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 2/7. Work out r.

On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?

A block has mass 280 g (to the nearest 10 g) and volume 13 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 280 g (to the nearest 10 g) and volume 13 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 (7x(n) + 2) with x(0) = 3. Work out x(1) to 3 decimal places.