In the diagram, the circle, having centre T(0;5), cuts the y-axis at P and R. The line through PO and S(-3;8) intersects the circle at N and the x-axis at M. NS =PS. MT is drawn.
In the diagram, Q(3;0), R(10; 7), S and T(0;14) are the vertices of parallelogram QRST. From T a straight line is drawn to meet QR at M(5;2). The angles of inclination of TQ and RQ are α and β respectively.
Mrs Smith has two classes, each having 30 learners. Their final marks (out of 100) for the year are represented in the box and whisker diagram below.
The amount of money, in rands, that learners spent while visiting a tuck shop at school on a specific day was recorded. The data is represented in the ogive below.
An incomplete frequency table is also given for the data.
The success rate of the Fana soccer team depends on a number of factors. The fitness of the players is one of the factors that influence the outcome of a match.
+ The probability that all the players are fit for the next match is 70%
+ If all the players are fit to play the next match, the probability of winning the match is 55%.
+ If there are players that are not fit to play the next match, the probability of winning the match is 55%.
Based on fitness alone, calculate the probability that the Fana soccer team will win the next match.
The events S and T are independentP(S and T) = 1⁄6P(S) = ¼
A piece of wire 6 metres long is cut into two pieces. One piece, x metres long, is bent to form a square. The other piece is bent into a U-shape so that it forms a rectangle BEFC when placed next to the square, as shown in the diagram below.
Calculate the value of x for which the sum of the areas enclosed by the wire will be a maximum.
On the 2nd of January 2015 a company bought a new printer for R150 000.The value of the printer decreases 20% annually on the reducing-balance method.When the book value of the printer is R49 152, the company will replace the printer.
The sketch below shows the graphs of ƒ(x) = x2 - 2x - 3 and g(x) = x - 3A and B are the x-intercepts of ƒ.The graphs of ƒ and g intersect at C and B.D is the turning point of ƒ.
The sketch below shows the graphs of ƒ(x) = log5x and g(x) = 2x - 1 + 1
T and U are the x-intercepts of g and ƒ respectively
The line y=x intersects the asymptotes of g at R, and the graph of g at V.