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Solve 6x\(^2\) = 5x - 1
Given that log\(_3\) 27 = 2x + 1, find the value of x.
A trader made a loss of 15% when an article was sold. Find the ratio of the selling price : cost price
If the equations x\(^2\) - 5x + 6 = 0 and x\(^2\) + px + 6 = 0 have the same roots, find the value of p.
The straight line y = mx - 4 passes through the point(-4,16). Calculate the gradient of the line
The mean of two numbers x and y is 4. Find the mean of four numbers x, 2x, y and 2y
A rectangle with width \(\frac{3}{4}\)cm and area 3 \(\frac{3}{8}\)cm\(^2\). Find the length
A local community has two newspapers: the morning tomes and the evening dispatch. The morning times is read by 45% of the households. The Evening Dispatch is read by 60% of the households. Twenty percent of the households read both papers. What is the probability that a particular household reads at least one paper?
Find the volume of a cone of radius 3.5cm and vertical height 12cm. [Take π = 22/7]
The lengths of the parallel sides of a trapezium are 9cm and 12cm. If the area of the trapezium is 105cm\(^2\), find the perpendicular distance between the parallel sides.
Find the correct to two decimal places, the volume of a sphere whose radius is 3cm. [Take π = \(\frac{22}{7}\)]
The age (years) of some members in a singing group are: 12, 47, 49, 15, 43, 41, 13, 39, 43, 41 and 36.
Find the mean
The age (years) of some members in a singing group are: 12, 47, 49, 15, 43, 41, 13, 39, 43, 41 and 36.
Find the lower quartile
Solve \(\frac{y+2}{4}\) - \(\frac{y-1}{3}\) > 1
In the diagram, triangle MNR is inscribed in circle MNR, and line PQ is a straight line. ∠MRN = 41 and = 141, find ∠QNR
Simplify \(\frac{2-18m^2}{1+3m}\)
The mean of a set of 10 numbers is 56. If the mean of the first nine numbers is 55, find the 10th number.
Mrs Gabriel is pregnant. The probability that she will give birth to a girl is 1/2 and with blue eyes is 1/4. What is the probability that she will give birth to a girl with blue eyes?
Find ∠OSN
In the diagram, MNR is a tangent to the circle centre O at N and ∠NOS = 108°. Find ∠OSN