A car travels from calabar to Enugu, a distance of P km with an average speed of U km per hour and continues to benin, a distance of Q km, with an average speed of Wkm per hour. Find its average speed from Calabar to Benin

Solve the following equation \(\frac{2}{2r-1} - \frac{5}{3} = \frac{1}{r+2}\)

Find the derivative of the function \(y = 2 x^2(2x - 1)\) at the point \(x = -1\).

A trapezium has two parallel sides of lengths 5cm and 9cm. If the area is 91cm², find the distance between the parallel sides.

Three children shared a basket of mangoes in such a way that the first child took \(\frac{1}{4}\) of the mangoes and the second \(\frac{3}{4}\) of the remainder. What fraction of the mangoes did the third child take?

Simplify √ 27 + 3/√3

The angles of a quadrilateral are 5x-30, 4x+60, 60-x and 3x+61.find the smallest of these angles

The locus of a point which moves so that it is equidistant from two intersecting straight lines is the?

If \((x + 2)\) and \((x - 1)\) are factors of the expression \(Lx + 2kx^2 + 24\), find the values of \(L\) and \(k\).

A cylinder pipe, made of metal is 3cm thick.If the internal radius of the pipe is 10cm. Find the volume of metal used in making 3m of the pipe.

Musa borrows N10.00 at 2% per month simple interest and repays N8.00 after 4 months. How much does he still owe?

The ratio of the length of two similar rectangular blocks is 2 : 3. If the volume of the larger block is 351cm³, then the volume of the other block is?

List all integers satisfying the inequality in -2 < 2x-6 < 4

Find the mean deviation of 1, 2, 3 and 4

The angle of a sector of a circle, radius 10.5cm, is 48°, Calculate the perimeter of the sector

Simplify and express in the standard form \(\frac{0.00275 \times 0.0064}{0.025 \times 0.08}\)

Two numbers are removed at random from the numbers 1, 2, 3 and 4. What is the probability that the sum of the numbers removed is even?

Find the length of a side of a rhombus whose diagonals are 6cm and 8cm

Find the probability that a number selected at random from 41 to 56 is a multiple of 9

Simplify \(2\log \frac{2}{5} - \log \frac{72}{125} + \log 9\)

Correct \(241.34(3 \times 10^{-3})^2\) to 4 significant figures

Determine the maximum value of y=3x²-x³.

The mean of ten positive numbers is 16. When another number is added, the mean becomes 18. Find the eleventh number

4, 16, 30, 20, 10, 14 and 26 are represented on a pie chart. Find the sum of the angles of the bisectors representing all numbers equals to or greater than 16

P(-6, 1) and Q(6, 6) are the two ends of the diameter of a given circle. Calculate the radius.

Three brothers in a business deal share the profit at the end of a contract. The first received ⅓ of the profit and the second ⅔ of the remainder. If the third received the remaining N12000.00 how much profit did they share?

Factorize m³ - 2m² - m + 2

In how many ways can 2 students be selected from a group of 5 students in a debating competition?

Each of the interior angles of a regular polygon is 140°. How many sides has the polygon?

X is due east point of y on a coast. Z is another point on the coast but 6.0km due south of Y. If the distance ZX is 12km, calculate the bearing of Z from X

At what rate would a sum of N100.00 deposited for 5 years raise an interest of N7.50?

What is the n-th term of the sequence 2, 6, 12, 20...?

find the value of p if the line which passes through (-1, -p) and (-2,2) is parallel to the line 2y+8x-17=0?

What is the rate of change of the volume V of a hemisphere with respect to its radius r when r = 2?

A group of market women sell at least one of yam, plantain and maize. 12 of them sell maize, 10 sell yam and 14 sell plantain. 5 sell plantain and maize, 4 sell yam and maize, 2 sell yam and plantain only while 3 sell all the three items. How many women are in the group?

If the binary operation ∗ ∗ is defined by m ∗ ∗ n = mn + m + n for any real number m and n, find the identity of the elements under this operation

If g(x) = x² + 3x find g(x + 1) - g(x)

If w varies inversely as uv/(u+v) and is = 8 when u = 2 and v = 6, find a relationship between u, v, w.

Factorize completely 81a⁴ - 16b⁴

Find \(x\) if \(\log_{9} x = 1.5\)