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From the diagram r\(^2\) = B\(^2\) + 15\(^2\) = 64 + 225 r = \(\sqrt{289}\) = 17cm

Perimeter of the sector = \(2r + \frac{\theta}{360} \times 2\pi r\) = \(2(14) + \frac{135}{360} \times 2 \times \frac{22}{7} \times 14\) = \(28 + 33\) = 61 cm

S.D = \(\sqrt{Variance}\) = \(\sqrt{25}\) = 5

< T = \(\frac{x}{1}\) = 25o (PQ = QT) < SQR = 2(25o) = 50o (sum of interior angle) < Q + < R + < S = 180o 50o + 75o + < S = 180o = 125o + < S = 180o < S = 180o - 125o = 55o

Using cosine formula (t\(\sqrt{3}\))2 = t2 + t2 - 2t2 cos\(\theta\) 3t2 = 2t2 - 2t2 cos\(\theta\) = 2t2(1 - cos\(\theta\)) 1 - cos\(\theta\) = \(\frac{3t^2}{2t^2}\) = \(\frac{3}{2}\) cos = 1 - \(\frac{3}{2} = -\frac{1}{2}\) \(\theta\) = cos-1(-\(\frac{1}{2}\)) = 120o and 240o N.B 0 \(\geq\) \(\theta\) 360

From the diagram above, the bearing of X from Y is 330º (The bearing from Y to X is the opposite direction of the bearing from X to Y. Since bearings are measured clockwise, to find the reverse bearing, you need to add 180^\circ to the original bearing and then adjust for any values over 360^\circ)

To find the length of the arc, we use the formula: \(\text{Length of arc} = \frac{\theta}{360^\circ} \times 2\pi r\) Given: \(\theta = 75^\circ \) Diameter = 7cm, r = \(\frac{7}{2}\) = 3.5 cm. \(\pi = \frac{22}{7}\) Calculate the circumference of the circle: \(\text{Circumference} = 2\pi r = 2 \times \frac{22}{7} \times 3.5\) Calculating: \(= 2 \times \frac{22}{7} \times \frac{7}{2} = 22 \text{ cm}\) Calculate the length of the arc: \(\text{Length of arc} = \frac{75}{360} \times 22\) Calculating: \(= \frac{75 \times 22}{360} = \frac{1650}{360} \approx 4.5833 \text{ cm}\) The length of the arc is approximately 4.58 cm

to calculate for the high of the pole, we use sohcahtoa Let the height of the pole be x. Tan32º = \(\frac{opp}{adj}\) Tan32º = \(\frac{x}{68}\) x = Tan32º x 68 = 42.5m ( to 1 d.p)

No expanded working has been attached for this question yet. The verified answer is Option E.

let one bottle of mirinda cost = #x, a bottle of malt will cost #3x 4 bottles of mirinda will cost = #4x, then 5 bottles of malt cost = #15x total cost = 4x + 15x = 380 x = 380/19 = 20, therefore a bottle of mirinda cost = #20 then a bottle of mirinda will cost 3 x 20 = #60.00

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SP = #4600, profit % = 15 % profit = \(\frac{SP - CP}{CP}\) X 100 \(\frac{15}{100} = \frac{4600 - CP}{CP}\) 15CP = 460000 - 100CP 15CP + 100CP = 460000 CP = \(\frac{460000}{115}\) = #4000 Cost price of article = #4000 OR Profit % = 100 + 15 = 115 CP = \(\frac{4600 \times 100}{115}\) = #4000

To express 0.03785 in standard form to 3 significant figures: * Identify significant figures: 3.785 * Round to 3 figures: 3.79. * Write in standard form: 3.79 \times 10\(^{-2}\) Final answer: 3.79\times10\(^{−2}\)​

0^\circ ∠ \theta ∠ 90º, From the diagram above, the adjacent by Pythagoras theorem = 3 Cos \theta = \(\frac{\text{adj}}{\text{hyp}}\) = \(\frac{3}{5}\) Tan \theta = \(\frac{\text{opp}}{\text{adj}}\) = \(\frac{4}{3}\) cos \theta + tan \theta = \(\frac{3}{5}\) + \(\frac{4}{3}\) = \(\frac{29}{15}\)

using cosine rule, \(cos\theta\) = \(\frac{28^2 + 15^2 - 21^2}{2\times28\times15}\) = \(\frac{568}{840}\) \(\theta = cos^{-1}\) = 47.5^\circ