The amount of money contributed by a group of students during a fundraising for a needy student was as shown in the table below.
(a) On the grid provided draw an ogive to represent the data.
(b) Use the graph to estimate:
(i) The median;
(ii) The quartile deviation;
(iii) The percentage number of students who contributed at least Ksh 750.50.
A workshop makes cupboards and tables using two artisans A and B every cupboard made requires 3 days of work by artisan A and 2 days of work by artisan B. Every table made requires 2 days of work by artisan A and 2 days of work by artisan B.
In one month artisan A worked in less than 24 while artisan B Worked for Not More Than 18 Days.
The workshop made x cupboards and y tables in that month.
(a) Write all the inequalities which must be satisfied by x and y.
(b) Represent the inequalities in (a) on the grid provided.
(c) The workshop makes a profit of Ksh 6 000 on each cupboard and Ksh4 000 on each table.
Find the number of cupboards and the number of tables that must be made for maximum profit and hence determine the maximum profit.
A ship left point P(10°S, 40°E) and sailed due East for 90 hours at an average speed of 24 knots to a point R.(Take 1 nautical mile (nm) to be 1.853 km and radius of the earth to be 6370 km)
(a) Calculate the distance between P and R in:
(b) Determine the position of point R.
(c) Find the local time, to the nearest minute, at point R when the time at P is 11:00a.m.
The figure KLMN below is a scale drawing of a rectangular piece of land of length KL = 80m
(a) On the figure, construct
(i) The locus of a point P which is both equidistant from points L and M It and from lines KL and LM.
(ii) the locus of a point Q such that ∠KQL = 90°.
(b) (i) Shade the region R bounded by the locus of Q and the Locus of points equidistant from KL and LM.
(ii) Find the area of the region R in m². (Take ℼ= 3.142).
The vertices of a triangle PQR are P(-3, 2), Q(0,-1) and R(2, -1). A transformation matrix maps triangle PQR onto triangle P’Q' R' whose vertices are P'(-7, 2), Q'(2, -1) and R’(4, -1).
Find M-1, the transformation that maps P'Q'R' onto PQR.
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