Answer these questions

7. A 10m long diving board is positioned over a pool like the diagram below, with a large weight on one end to stop the board from tipping. 2m (a) The board is rated so that divers weighing up to 150kg can stand on the very edge. When this happens, the board is on the point of tipping around the pivot closest to the pool. Calculate the mass of the large weight on the end of the board. [5] (b) Explain how all of your modelling assumptions affected your calculations. [2]8. A non-uniform rod AB, of mass 10kg and length am, has the end at A attached to a smooth hinge. A force of 51N is applied at point B, making an angle of 1150 with the rod. The rod is held in equilibrium 25 above the horizontal. Given that the Centre of Mass of AB is 3m from B, find the value of x. B 51N 250 A [4] 9. THROWBACK: Given that P(A) = 0.5, P(B)-0.35 and P(An B)-0.24, find: (a) P(AUB) [2] (b) P(A'|B) [2] Given that the events B and C are mutually exclusive, the events A and C are independent and that P(An C) = 0.14, (c) Find P(C) [2] (d) Draw a Venn diagram to illustrate the events A, B and C, showing the proba- bilities for each region [4]