The average age of the four female teachers in a school is 40 and the average age of eight male teachers in the school is 25. Calculate the average age of the teachers in the school.

A boy bought Oranges at the rate of #24.00 for 5 and sold it at the rate of # 30.00 for 4 Oranges. Find the profit made of the ones sold

Simplify \( \dfrac{5 + \sqrt{7}}{3 + \sqrt{7}} \).

\((\sqrt{a} + \sqrt{8a})^2 = 54 + b\sqrt{2},\) a and  b are positive integers. Find the value of  a and the value of  b.

P(x, 4) and Q( 10, 8) are two points joined by a straight line in a plane. If the midpoint of the line is (9, 6), find the value of x.

PQR is a triangle such that \(|PQ| = |QR| = 8 \,\text{cm}\) and \(\angle QPR = 60^\circ\). Find the area of \(\triangle PQR\).

Find the roots of \( x^{3} - 19x - 30 = 0 \).

How many ways can 6 students be seated around a circular table?

A bag contains 7 red and 4 black identical balls. Two balls were picked at random from the bag and replaced each time. Find the probability the two balls were of same colour.

The weights of 15 students in a class are given as 25, 30, 32, 30, 42, 45, 48, 50, 52, 51, 42, 38, 40, and 42. What is the mode of the given data?

From the top of a building 10 m high, the angle of elevation of a fruit on top of a tree 25 m is \( 30^\circ \).
Calculate the horizontal distance between the building and the tree.

The Venn diagram above shows the number of students offering physics and chemistry in a class of 65. What is the probability that a student selected from the class offers physics and chemistry if every students offers at least one subject?

The mean of the numbers 13, 16, x, 18, 21, 2x, 35, is 22. Find the value of x

From a class of 5 girls and 7 boys, a committee consisting of 2 girls and 3 boys is to be formed. How many ways can this be done?

The scores of students in a test are recorded as follows: 4, 3, 3, 2, 1, 2, 5, 7, 8, 3, and 5. Find the mode of the mark.

Given that P is the set of all prime numbers between 0 and 10, and Q is the set of all odd numbers between 0 and 10. Find the union of elements in P that are not in Q and the elements in Q that are not in P.

If \( B \) varies inversely as \( C^{\tfrac{1}{3}} \) and \( C = 27 \) when \( B = 2 \), find the value of the constant of proportionality \( K \).

The sum to infinity of a GP is \(100\), find its first term if the common ratio is \(-\tfrac{1}{2}\).

In how many ways can a committee of 5 be selected from a group of 7 males and 3 females, if the committee must have one female?

Find the 7th term of the sequence -10, 50, -250 ...........

Calculate the standard deviation of the following scores 5, 4, 6, 7, and 8

How many proper and improper subsets are there in the set K = { a, b, c, d, e}?

The graph above represents inequalities

A binary operation \(\ast\) is defined on a set of real numbers by \(x \ast y = x^y\) for all real values of \(x\) and \(y\). If \(x \ast 2 = x\), find the possible values of \(x\).

U varies directly as the square root of V when U = 24, V = 9, find the value of V when U = 16.

If \( \tan \theta = \dfrac{8}{15} \), simplify
\( \dfrac{\sin \theta - \cos \theta}{\sin^{2}\theta - \sin \theta} \).

Make \(q\) the subject of the relation
\(t = \sqrt{\dfrac{pq}{r} - r^2 q}\).

Find the variance of a group of data whose standard deviation is 12.34 to the nearest whole number.

Differentiate \( \cos 25^\circ - \sin 25^\circ \).

If x is inversely proportional to y and x = 9 when y = 4, find the law containing x and y

Differentiate \( y = (5x + 1)^{4} \).

Subtract \( 14256_{7} \) from \( 20045_{7} \).

Find the perimeter of a triangle whose vertices pass through ( 3, 2), (4, 5) and (6, 2) in surd form.

Convert the number \( 10111.11_{2} \) to a mixed number.

Find \(x\) if \(\frac{16^{2+x}}{4} = 64^{x}\)

In the diagram above, T represents the construction of angle .....

The number of 144 students who registered for mathematics, physics, and chemistry in an examination are shown in the Venn diagram. How many registered for physics and mathematics?