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Simplify: \((1 - \sin \theta)(1 + \sin \theta)\).
If \(\frac{1}{5^{-y}} = 25(5^{4-2y})\), find the value of y.
A body is kept at rest by three forces \(F_{1} = (10N, 030°), F_{2} = (10N, 150°)\) and \(F_{3}\). Find \(F_{3}\).
If \(\frac{^{n}C_{3}}{^{n}P_{2}} = 1\), find the value of n.
Find the equation of the straight line that passes through (2, -3) and perpendicular to the line 3x - 2y + 4 = 0.
If \(V = \begin{pmatrix} -2 \\ 4 \end{pmatrix}\) and \(U = \begin{pmatrix} -1 \\ 5 \end{pmatrix}\), find \(|U + V|\).
Calculate the mean deviation of 1, 2, 3, 4, 5, 5, 6, 7, 8, 9.
If \(g(x) = \frac{x + 1}{x - 2}, x \neq -2\), find \(g^{-1}(2)\).
P and Q are the points (3, 1) and (7, 4) respectively. Find the unit vector along PQ.
Two out of ten tickets on sale for a raffle draw are winning tickets. If a guest bought two tickets, what is the probability that both tickets are winning tickets?
Given that \(P = \begin{pmatrix} 3 & 4 \\ 2 & x \end{pmatrix}; Q = \begin{pmatrix} 1 & 3 \\ -2 & 4 \end{pmatrix}; R = \begin{pmatrix} -5 & 25 \\ -8 & 26 \end{pmatrix}\) and PQ = R, find the value of x.
Find the upper quartile of the following scores: 41, 29, 17, 2, 12, 33, 45, 18, 43 and 5.
If \(2\sin^{2}\theta = 1 + \cos \theta, 0° \leq \theta \leq 90°\), find \(\theta\).
If \(s = 3i - j\) and \(t = 2i + 3j\), find \((t - 3s).(t + 3s)\).
A particle is acted upon by two forces 6N and 3N inclined at an angle of 120° to each other. Find the magnitude of the resultant force.
The equation of a circle is \(x^{2} + y^{2} - 8x + 9y + 15 = 0\). Find its radius.
Two bodies of masses 3kg and 5kg moving with velocities 2 m/s and V m/s respectively in opposite directions collide. If they move together after collision with velocity 3.5 m/s in the direction of the 5kg mass, find the value of V.
Express \(\frac{x^{2} + x + 4}{(1 - x)(x^{2} + 1)}\) in partial fractions.
A circular ink blot on a piece of paper increases its area at the rate \(4mm^{2}/s\). Find the rate of the radius of the blot when the radius is 8mm. \([\pi = \frac{22}{7}]\).
The sales of five salesgirls on a certain day are as follows; GH¢ 26.00, GH¢ 39.00, GH¢ 33.00, GH¢ 25.00 and GH¢ 37.00. Calculate the standard deviation if the mean sale is GH¢ 32.00.