If (x + 1) and (x - 2) are factors of the polynomial \(g(x) = x^{4} + ax^{3} + bx^{2} - 16x - 12\), find the values of a and b.
Bottles of the same sizes produced in a factory are packed in boxes. Each box contains 10 bottles. If 8% of the bottles are defective, find, correct to two decimal places, the probability that box chosen at random contains at least 3 defective bottles.
The table shows the heights in cm of some seedlings in a certain garden.
| Height (cm) | 36-40 | 41-45 | 46-50 | 51-55 | 56-60 |
| Frequency | 3 | 9 | 21 | 12 | 5 |
(a) Draw the cumulative frequency curve for the distribution.
(b) Using the curve in (a), find thesemi-interquartile range.
A parallelogram MNQR has vertices M(4, -6), N(10, 2), Q(8, 16) and R(x, y). Find the coordinates of R.
Forces \(F_{1} (18N, 330°), F_{2} (10N, 090°)\) and \(F_{3} (25N, 180°)\) act on a body at rest. Find, correct to one decimal place, the magnitude and direction of the resultant force.
