Simplify
\[
3^{\,n-1} \times \frac{27^{\,n+1}}{81^n}
\]

y is inversely proportional to x and y and 6 when x = 7. Find the constant of the variation

Find the gradient of the line joining the points (3, 2) and (1, 4).

Find the range of the following set of numbers 0.4, −0.4, 0.3, 0.47, −0.53, 0.2 and −0.2

Given
\[
m = N \sqrt{\frac{SL}{T}}
\]
make T the subject of the formula

Evaluate 0.00000231/0.007, and leave the answer in standard form

In the diagram MN, PQ and RS are parallel lines. What is the value of the angle marked X?

Factorize completely x²+2xy+y²+3x+3y−18.

If two graphs Y = px² + q and y = 2x² − 1 intersect at x =2, find the value of p in terms of q.

If (2√3−√2) / (√3+2√2) = m + n √ 6, find the values of m and n respectively.

Divide \(4x^3 - 3x + 1\) by \(2x - 1\)

In the figure, find x

The base in which the operation was performed was

Simplify \(\left(\sqrt[3]{64a^3}\right)^{-1}\)

The operation * on the set R of real number is defined by x * y = 3x + 2y − 1, find 3* − 1

Find the sum of the range and the mode of the set of numbers 10, 9, 10, 9, 8, 7, 7, 10, 8, 10, 8, 4, 6, 9, 10, 9, 7, 10, 6, 5

The locus of a point which is equidistant from the line PQ forms a

If \(\alpha\) and \(\beta\) are the roots of the equation
\(3x^2 + 5x - 2 = 0,\)
find the value of \(\frac{1}{\alpha} + \frac{1}{\beta}\).

A man covered a distance of 50 miles on his first trip, on a later trip he traveled 300 miles while going 3 times as fast. His new time compared with the old distance was?

Find \(\int (x^2 + 3x - 5)\, dx\)

Find the equation of the locus of a point P(x,y) such that PV = PW, where V = (1,1) and W = (3,5)

The pie chart shows the allocation of money to each sector in a farm. The total amount allocated to the farm is ₦ 80 000. Find the amount allocated to fertilizer.

A car dealer bought a second-hand car for ₦250,000 and spent ₦70,000 refurbishing it. He
then sold the car for ₦400,000. What is the percentage gain?

Evaluate 1 - (1/5×2/3)+(5+2/3)

If a rod 10cm in length was measured as 10.5cm, calculate the percentage error

Given the quadrilateral RSTO inscribed in the circle with O as centre. Find the size angle x

and given RST = 60 degrees

Evaluate \( 1 - \left(\frac{1}{5} \times \frac{2}{3}\right) + \left(5 + \frac{2}{3}\right) \)

In how many ways can the letters of the word ACCEPTANCE be arranged?

The value of x+x(x^x) when x=2

Simplify 4√27 + 5√12 − 3√75

If \( m * n = [mn - nm] \) for \( m, n \in \mathbb{R} \), evaluate \( -3 * 4 \).

Find the sum of the range and the mode of the set of numbers 10, 9, 10, 9, 8, 7, 7, 10, 8, 10, 8, 4, 6, 9, 10, 9, 10, 9, 7, 10, 6, 5

Find the sum to infinity of the series ¼, ⅛, 1/16………..

In how many ways can the word MACICITA be arranged?

What is the product of \(2x^2 - x + 1\) and \(3 - 2x\)?

Make \(S\) the subject of the relation:

\(p = s + \dfrac{sm^2}{nr}\)

In the diagram MN is a chord of a circle KMN centre O and radius 10cm. If < MON = 140°, find, correct to the nearest cm, the length of the chord MN.

In a regular polygon, each interior angle doubles its corresponding exterior angle. Find the number of sides of the polygon.

A cylindrical tank has a capacity of 3080 m³. What is the depth of the tank if the diameter of its base is 14 m²
(Take pi = 22/7)

Find the principal which amounts to ₦5,500 at a simple interest in 5 years at 2% per annum.