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first term (a) = \(\frac{5}{6}\) common difference = \(\frac{8}{6}\) - \(\frac{5}{6}\) → \(\frac{3}{6}\) or \(\frac{1}{2}\) A.P formula → T\(_n\) = a + (n - 1)d T\(_n\) = \(\frac{5}{6}\) + (19 - 1)\(\frac{1}{2}\) T\(_n\) = \(\frac{5}{6}\) + 9 → 9\(\frac{5}{6}\)

No of women wearing both purple and white shoes = 21 + 9 = 30 women. No of women wearing neither purple nor white shoes = 51 - 30 = 21 women \(\therefore\) Probability of picking a woman wearing neither purple nor white shoes = \(\frac{21}{51}\) = \(\frac{7}{17}\).

Permanent magnets are made from "hard" ferromagnetic materials such as alnico and ferrite Permanent magnets are made from special alloys (ferromagnetic materials) such as iron, nickel and cobalt, several alloys of rare-earth metals and minerals such as lodestone. When a nonmagnetic piece of steel is applied to a magnet, the atoms within it rearrange themselves in a manner that creates a permanent magnet.

Element X is aluminum of valency 3+ Element Y is oxygen of valency 2- Their combination is \(Al_{2}O_{3}\)

In the modern periodic table, the elements are listed in order of increasing atomic number. The atomic number is the number of protons in the nucleus of an atom.

s = \(\sqrt{(\frac{a^2}{x^2} - \frac{b^2}{y^2})}\) s\(^2\) = \(\frac{a^2}{x^2} - \frac{b^2}{y^2}\) \(\frac{b^2}{y^2}\) = \(\frac{a^2}{x^2}\) - s\(^2\) \(\frac{b^2}{y^2}\) = \(\frac{a^2 - s^2 x^2}{x^2}\) \(\frac{1}{y^2}\) = \((\frac{a^2 - s^2 x^2}{x^2}) \times \frac{1}{b^2}\) \(\frac{1}{y^2}\) = \(\frac{a^2 - s^2 x^2}{b^2 x^2}\) \(\therefore\) y\(^2\) = \(\frac{b^2 x^2}{a^2 - s^2 x^2}\) y = \(\sqrt{\frac{b^2 x^2}{a^2 - s^2 x^2}}\)

Using these: Loss = C.p - S.p : Percentage Loss = ( Loss X 100) \div C.p =15 %

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

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 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