Simplify \(\frac{(\frac{2}{3} - \frac{1}{5}) - \frac{1}{3} \text{of} \frac{2}{5}}{3 - \frac{1}{1 \frac{1}{2}}}\)

\(\frac{0.0001432}{1940000}\) = k x 10ⁿ where 1 \(\leq\) k < 10 and n is a whole number. The values K and n are

P sold his bicycle to Q at a profit of 10%. Q sold it to R for N209 at a loss of 5%. How much did the bicycle cost P?

If the price of oranges was raised by \(\frac{1}{2}\)k per orange. The number of oranges a customer can buy for N2.40 will be less by 16. What is the present price of an orange?

A man invested a total of N50000 in two companies. If these companies pay dividends of 6% and 8% respectively, how much did he invest at 8% if the total yield is N3700?

Thirty boys and x girls sat for a test. The mean of the boys' scores and that of the girls were respectively 6 and 8. Find x if the total scores was 468

The cost of production of an article is made up as follows: Labour N70, Power N15, Materials N30, Miscellaneous N5. Find the angle of the sector representing Labour in a pie chart

Bola choose at random a number between 1 and 300. What is the probability that the number is divisible by 4?

Find, without using logarithm tables, the value of \(\frac{log_3 27 - log_{\frac{1}{4}} 64}{log_3 \frac{1}{81}}\)

A variable point p(x, y) traces a graph in a two-dimensional plane. (0, 3) is one position of P. If x increases by 1 unit, y increases by 4 units. The equation of the graph is

A trader in country where their currency 'MONI'(M) is in base five bought 103₅ oranges at M14₅ each. If he sold the oranges at M24₅ each, what will be his gain?

Rationalize \(\frac{5\sqrt{7} - 7\sqrt{5}}{\sqrt{7} - \sqrt{5}}\)

Simplify \(\frac{3^n - 3^{n - 1}}{3^3 \times 3^n - 27 \times 3^{n - 1}}\)

p varies directly as the square of q and inversely as r. If p = 36, when q = 3, when r = 4, find p when q = 5 and r = 2.

Factorize 6x2 - 14x - 12

A straight line y = mx meets the curve y = x2 - 12x + 40 in two distinct points. If one of them is (5, 5) find the other

The table below is drawn for a graph y = x³ - 3x + 1
\(\begin{array}{c|c} x & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\\hline y = x^3 - 3x + 1 & 1 & -1 & 3 & 1 & -1 & 3 & 1\end{array}\)
From x = -2 to x = 1, the graph crosses the x-axis in the range(s)

In a racing competition, Musa covered a distance 5x km in the first hour and (x + 10)km in the next hour. He was second to Nzozi who covered a total distance of 118km in the two hours. Which of the following inequalities is correct?

If 2x + 3y = 1 and x - 2y = 11, find (x + y)

Tunde and Shola can do a piece of work in 18 days. Tunde can do it alone in x days, whilst Shola takes 15 days longer to do it alone. Which of the following equations is satisfied by x?

If f(x) = 2(x - 3)\(^2\) + 3(x - 3) + 4 and g(y) = \(\sqrt{5 + y}\), find g [f(3)] and f[g(4)].

The quadratic equation whose roots are 1 - \(\sqrt{13}\) and 1 + \(\sqrt{13}\) is?

Find a factor which is common to all three binomial expressions 4a2 - 9b2, 8a3 + 27b3, (4a + 6b)2

If (x - 2) and (x + 1) are factors of the expression x³ + px² + qx + 1, what is the sum of p and q

A cone is formed by bending a sector of a circle having an angle of 210^o. Find the radius of the base of the cone if the diameter of the circle is 12cm.

The sides of a triangle are(x + 4)cm, xcm and (x - 4)cm, respectively If the cosine of the largest angle is \(\frac{1}{5}\), find the value of x

If a = \(\frac{2x}{1 - x}\) and b = \(\frac{1 + x}{1 - x}\), then a2 - b2 in the simplest form is

Simplify (1 + \(\frac{\frac{x - 1}{1}}{\frac{1}{x + 1}}\))(x + 2)

If pq + 1 = q² and t = \(\frac{1}{p}\) - \(\frac{1}{pq}\) express t in terms of q

The cumulative frequency function of the data below is given below by the equation y = cf(x). What is cf(5)?
\(\begin{array}{c|c} Score(n) & Frequency(f)\\\hline 3 & 30\\ 4 & 32\\ 5 & 30\\ 6 & 35\\8 & 20 \end{array}\)

A right circular cone has a base radius r cm and a vertical angle 2y^o. The height of the cone is

Two fair dice are rolled. What is the probability that both show up the same number of points.

The larger value of y for which (y - 1)² = 4y - 7 is

If sin \(\theta\) = \(\frac{x}{y}\) and 0^o < 90^o then find \(\frac{1}{tan\theta}\)

Measurements of the diameters, in centimeters, in centimeters, of 20 copper spheres are distributed as shown below
\(\begin{array}{c|c} \text{Class boundary in cm} & \text{frequency} & \\\hline 3.35 - 3.45 & 3\\ 3.45 - 3.55 & 6\\ 3.55 - 3.65 & 7\\ 3.65 - 3.75 & 4\end{array}\)
What is the mean diameter of the copper spheres?

What is the volume of this regular three dimensional figure?

Find the area of the shaded portion of the semicircular figure.

In the figure, PQRSTW is a regular hexagon. QS intersects RT at V. Calculate TVS