9 (a) Pure gold costs $42 per gram. The fraction of pure gold in an object is measured in carats. 1 One carat means of the mass of an object is pure gold. 24 Henry buys a 9-carat gold bracelet weighing 16 g. The price of the bracelet is $204. Is the price of the bracelet more or less than the cost of the pure gold in it? You must show your working. [4] (b) A clock made of metals has a mass of 1080 g. The mass of each metal in the clock is in the ratio copper : zinc : other metals = 21 : 14 : 1. Calculate the mass of copper in this clock. .............................................. g [2] © UCLES 2023 0580/31/O/N/23 17 (c) There are 110 people in a group. G = { people who own gold jewellery } S = { people who own silver jewellery } 18 people own both gold jewellery and silver jewellery. 46 people own gold jewellery. 11 people own no gold jewellery and no silver jewellery. (cid:31) G S (i) Complete the Venn diagram. [2] (ii) Write down n(G+S). ................................................. [1] (iii) One of the 110 people is chosen at random. Write down the probability that this person owns gold jewellery but not silver jewellery. ................................................. [1] (d) (cid:31) E F Use set notation to describe the shaded region. ................................................. [1] © UCLES 2023 0580/31/O/N/23 [Turn over 18