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Find the sum of the first 20 terms of the sequences, -7, - 3, 1, . . . . .
In a truth table, if p is true and q is false, which of the following notations is false
The parents of 7 out of every 10 students in a class are farmers. If 12 students were selected at random, find the probability that the parents of 8 of them will be farmers.
The line x + y + 4 = 0 makes an angle of \(\theta\) with the x-axis. Find the value of \(\theta\)
The scores of some students in a class test are 4, 6, 1, 8, 9, 5, and 2. Calculate, correct to one decimal place, the mean deviation of their scores.
Given that y = 2x - 1 and Δx = 0.1, find Δ y
The gradient of a curve is given by 3x\(^2\) - 8x + 2. If the curve passes through P(0, 4), find the equation of the curve.
Find, correct to the nearest degree, the acute angle between 3x - y - 5 = 0, and 7x - y - 3 = 0
If y\(^2\) + 2xy - 8 = 0, find \(\frac{dy}{dx}\)
In triangle XYZ, |XY| = 10cm, |YZ| = 9 cm and |XZ| = 7 cm. If XZY = \(\alpha\), find the value of cos \(\alpha\).
In how many ways can 12 people be seated on a bench if only 5 spaces are available?
A body of mass 80 kg moving with a velocity of 25 ) ms\(^{-1}\) collides with another moving in the opposite direction at 10 ms\(^{-1}\). After collision, both bodies moved with a common velocity of 12.8 ms\(^{-1}\). Calculate, correct to the nearest whole number, the mass of the second body.
If \(\begin{pmatrix} 6 & 4 \\ 7 & 5 \end{pmatrix}\) \(\begin{pmatrix} 2 \\ m \end{pmatrix}\) = 2\(\begin{pmatrix} 12 \\ 14.5 \end{pmatrix}\), find the value of m.
How many three-digit numbers can be formed from the digits 2, 3, 4, 5, 6, 7, and 8 if repetition is not allowed?
Given that f(x) = x\(^2\) + 3x + 1, find the value of x at the turning point.
Find the coefficient of y\(^2\) in the binomial expansion of (y - 2x)\(^5\).
The point P(-3, 5) lies on a line which is perpendicular to 2x - 4y + 3 = 0. Find the equation of the line.
A particle of mass 40 kg is kept on a smooth plane inclined at an angle of 30º to the horizontal by a force up the plane. find, correct to one decimal place, the magnitude of the normal reaction of the plane of the particle.[Take g = 10 ms\(^{-2}\)]
Find the range of values of x for which 9x - 1 > 14x\(^2\)
A particle starts from rest accelerates at 4ms\(^{-2}\). Find the distance covered after 4 seconds.