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If \(25^{1 - x} \times 5^{x + 2} \div (\frac{1}{125})^{x} = 625^{-1}\), find the value of x.
Express \((0.0439 \div 3.62)\) as a fraction.
If the volume of a frustrum is given as \(V = \frac{\pi h}{3} (R^2 + Rr + r^2)\), find \(\frac{\mathrm d V}{\mathrm d R}\).
A man bought a car newly for ₦1,250,000. He had a crash with the car and later sold it at the rate of ₦1,085,000. What is the percentage gain or loss of the man?
Each of the interior angles of a regular polygon is 140°. Calculate the sum of all the interior angles of the polygon.
In the diagram above, O is the centre of the circle ABC, < ABO = 26° and < BOC = 130°. Calculate < AOC.
If \(P = (\frac{Q(R - T)}{15})^{\frac{1}{3}}\), make T the subject of the formula.
Points X and Y are 20km North and 9km East of point O, respectively. What is the bearing of Y from X? Correct to the nearest degree.
Find the value of x and y in the simultaneous equation: 3x + y = 21; xy = 30
Simplify \(\frac{0.0839 \times 6.381}{5.44}\) to 2 significant figures.
If 2\(^{x + y}\) = 16 and 4\(^{x - y} = \frac{1}{32}\), find the values of x and y.
Evaluate \((\frac{6}{0.32} \div \frac{2}{0.084})^{-1}\) correct to 1 decimal place.
The weight of a day-old chick was measured to be 0.21g. If the actual weight of the chick is 0.18g, what was the percentage error in the measurement?
The angles of a polygon are given by 2x, 5x, x and 4x respectively. The value of x is
If S = (4t + 3)(t - 2), find ds/dt when t = 5 secs.
Find the value of \(\frac{(0.5436)^3}{0.017 \times 0.219}\) to 3 significant figures.
Simplify 81\(^{\frac{-3}{4}}\) x 25\(^{\frac{1}{2}}\) x 243\(^{\frac{2}{5}}\)
The simple interest on ₦8550 for 3 years at x% per annum is ₦4890. Calculate the value of x to the nearest whole number.
Tade bought 200 mangoes at 4 for ₦2.50. 30 out of the mangoes got spoilt and the remaining were sold at 2 for ₦2.40. Find the percentage profit or loss.
If P varies inversely as the square root of q, where p = 3 and q = 16, find the value of q when p = 4.