Y is 60 km away from X on a bearing of 135°. Z is 80 km away from X on a bearing of 225°. Find the :

(a) distance of Z from Y ;

(b) bearing of Z from Y.

Out of the 24 apples in a box, 6 are bad. If three apples are taken from the box at random, with replacement, find the probability that :

(a) the first two are good and the third is bad ;

(b) all three are bad ;

(c) all the three are good.

(a) Simplify : \(\frac{3\frac{1}{12} + \frac{7}{8}}{2\frac{1}{4} - \frac{1}{6}}\)

(b) If \(p = \frac{m}{2} - \frac{n^{2}}{5m}\) ; 

(i) make n the subject of the relation ;  (ii) find, correct to three significant figures, the value of n when p = 14 and m = -8.

(a) With the aid of four- figure logarithm tables, evaluate \((0.004592)^{\frac{1}{3}}\).

(b) If \(\log_{10} y + 3\log_{10} x = 2\), express y in terms of x.

(c) Solve the equations : \(3x - 2y = 21\)

                                        \(4x + 5y = 5\).

(a) A cylinder with radius 3.5 cm has its two ends closed, if the total surface area is \(209 cm^{2}\), calculate the height of the cylinder. [Take \(\pi = \frac{22}{7}\)].

(b)  In the diagram, O is the centre of the circle and ABC is a tangent at B. If \(\stackrel\frown{BDF} = 66°\) and \(\stackrel\frown{DBC} = 57°\), calculate, (i) \(\stackrel\frown{EBF}\) and (ii) \(\stackrel\frown{BGF}\).