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To calculate Mean: add up all the numbers ⇒ 3+5+8+k+14+17 = 47 + k then divide by how many numbers there are ⇒ 6 The Mean is already given as 11 11 = (47 + k) / 6 Cross multiply to solve for k : k = (6 X 11) - 47 k = 19

From the figure above, Tan\(\theta\) = \(\frac{\text{O}}{\text{A}}\) Tan 68º = \(\frac{\text{x}}{20}\) x = Tan 68º x 20 = 49.501m to 3 d.p Height of Storey building = 49.501 + 4.5 = 54. 001 ≈ 54m to the nearest metre.

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

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

n(A U B) = n(A) + n(B) - n(A n B) n(A U B) = 6 + 5 - 2 = 9

Total ratio = 3 + 5 + 8 = 16 Total orange shared = x Smallest share received = 45 The orange shared = \(\frac{3}{16} \times\) x = 45 3x = 16 x 45 x = 16 x 15 = 240 oranges

\(t^2\) + kt + \(\frac{25}{4}\) The general form of quadratic expression = ax\(^2\) + bx + c comparing \(t^2\) + kt + \(\frac{25}{4}\) and the general form a = 1, b = k and c = \(\frac{25}{4}\) using: b\(^2\) = 4ac we can find the value of k. ( note: there is/are another way(s) to find the value of k) k\(^2\) = 4 x 1 x \(\frac{25}{4}\) k\(^2\) = 25 taking the square root of both sides k = 5

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)

VOLUME of CUBE = \(L^3\) 8000 = \(L^3\) L = \(\sqrt[3]{8000}\) = 20 S. A. CUBE = 6\(L^2\) S. A. CUBE = 6 x 20 x 20 = 2400\(cm^2\)

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

To find the probability that two beads drawn (with replacement) are of the same color, we consider two cases: both red and both white. Beads = 5, White beads = 7, Total beads = 12 Both Red: \(P(\text{Red}) = \frac{5}{12}, \quad P(\text{Both Red}) = \frac{5}{12} \times \frac{5}{12} = \frac{25}{144}\) Both White: \(P(\text{White}) = \frac{7}{12}, \quad P(\text{Both White}) = \frac{7}{12} \times \frac{7}{12} = \frac{49}{144}\) Total Probability of Same Color: \(P(\text{Same Color}) = \frac{25}{144} + \frac{49}{144} = \frac{74}{144} = \frac{37}{72}\) The probability that the two beads are the same color is \( \frac{37}{72}\).

\(\sqrt{6a^{-2}} \times \sqrt{24a^6}\) = \(\sqrt{6a^{-2} \times 24a^6}\) = \(\sqrt{144a^4}\) = \pm12a\(^2\).

9\(^x\) = 729 3\(^2\)\(^x\) = 3\(^6\) 2x = 6 x = 3

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