A chord subtends an angle of 72º at the centre of a circle of radius 24.5m. Calculate the perimeter of the minor segment. [Take π = \(\frac{22}{7}\)

In the diagram, BCDE is a circle with centre

A. ∠BCD = (2x + 40)°, ∠BAD = (5x - 35)º, ∠BED = (2y+ 10)° and ∠ADC=40". Find:

(a) the values of x and y;

a) Given that m = tan 30º and n = tan 45º, simplify, without using calculator, \(\frac{ m - n}{mn}\), leaving the answer in the form p + \(\sqrt{q}\)

b) There are 20 women in a bus. 15 of them wear glasses and 10 wear wristwatches. If a woman is chosen at random from the bus, find the probability that she wears both glasses and wristwatches.

The graph shows the relation of the form y = mx\(^2\) + nx + r, where m, n and r are constants.

Using the graph:

(a) state the scale used on both axes; (b) find the values of m, n and r; (c) find the gradient of the line through P and Q; (d) state the range of values of x for which y > Q.

(a) A man purchased 180 copies of a book at N250.00 each. He sold y copies at N300.00 each and the rest at a discount of 5 kobo in the Naira of the cost price.

If he made a profit of N7,125.00, find the value of y.

(b) A trader bought x bags of rice at a cost C = 24x + 103 and sold them at a price, S = \(\frac{x^2}{20} - 33x\).

Find the expression for the profit (i) If 20 bags of rice were sold,

(ii) calculate the percentage profit.