(a) Given that \(\frac{5y - x}{8y + 3x} = \frac{1}{5}\), find the value of \(\frac{x}{y}\) to two decimal places.

(b) If 3 is a root of the quadratic equation \(x^{2} + bx - 15 = 0\), determine the value of b. Find the other root.

(a) Use logarithm tables to evaluate \(\frac{15.05 \times \sqrt{0.00695}}{6.95 \times 10^{2}}\).

(b) The first 5 students to arrive in a school on a Monday morning were 2 boys and 3 girls. Of these, two were chosen at random for an assignment. Find the probability that :

(i) both were boys ; (ii) the two were of different sexes.

(a) Using a ruler and a pair of compasses only, construst \(\Delta\) ABC in which |AB| = 7cm, |BC| = 5cm and < ABC = 75°. Measure |AC|.

(b) In (a) above, locate by construction, a point D such that CD is parallel to AB and D is equidistant from points A and C. Measure < BAD.

(a) Solve the simultaneous equation : \(\log_{10} x + \log_{10} y = 4\)

                                                            \(\log_{10} x + 2\log_{10} y = 3\)

(b) The time, t, taken to buy fuel at a petrol station varies directly as the number of vehicles V on queue and jointly varies inversely as the number of pumps P available in the station. In a station with 5 pumps, it took 10 minutes to fuel 20 vehicles. Find :

(i) the relationship between t, P and V ; (ii) the time it will take to fuel 50 vehicles in the station with 2 pumps ; (iii) the number of pumps required to fuel 40 vehicles in 20 minutes.

  The solid is a cylinder surmounted by a hemispherical bowl. Calculate its

(a) total surface area ;

(b) volume (Take \(\pi = \frac{22}{7}\))