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6 + 10 + 14 + 16 + 26 = 72 \(\frac{6}{72}\) x 360 = 30o Similarly others give 30o, 50o, 70o, 80o and 130o respectively

\(\begin{array}{c|c} Scores & Frequency \\\hline 55 & 1\\ 60 & 4\\ 65 & 6\\ 70 & 4\\ 75 & 1 \end{array}\) Median = 65(middle number) Mode = 65(most common) Median + Mode = 65 + 65 = 130

Vowels of letters are 6 in numbers prob. of vowel = \(\frac{6}{13}\)

59.81798 = 59.8(3 s.f) 0.0746829 = 0.0747 59.8 x 0.0747 = 4.46706 = 4.47(3s.f)

% error = \(\frac{\text{Actual error}}{\text{real value}}\) x 100 = \(\frac{5}{250}\) x 100 = 2%

(\(\frac{2}{3}\))m (\(\frac{3}{4}\))n = \(\frac{256}{729}\) \(\frac{2^m}{4^n}\) x \(\frac{3^n}{3^m}\) = \(\frac{2^{8}}{3^{6}}\) \(2^{m} \div 2^{2n} = 2^{8}; 3^{n} \div 3^{m} = 3^{-6}\) m - 2n = 8........(i) -m + n = -6........(ii) Solving the equations simultaneously m = 4, n = -2

log\(_7\)49 + log\(_7\)\(\frac{1}{7}\) = log\(_7\)7 = 1

An hexagon polygon is a six sided polygon n = 6 sum of all interior angles of hexagon polygon will be (2n - 4) x 90o = [2 x 6 - 4] x 90 = 720o If one angle is 170o and each of the remaining five angles is 5xo 5xo + 170o = 720o = 5x + 550 x = \(\frac{550}{5}\) = 110o

\(\begin{array}{c|c} x & f \\\hline 1 & 3\\ 2 & 13\\3 & 15\\ 4 & 28\\ 5 & 21\\ 6 & 10\\ 7 & 7\\ 8 & 4\end{array}\) Median is half of total frequency = 50th term 4 falls in the range = 4

Area of the paper = area of square = L x B or S2 where s = S x k Area of the paper = (2.524)2 area of the diagram = (0.524)2 area not covered = (2.524)2 - (0.524)2 = 6.370576 - 0.274576 = 6.096 = 6.10cm2 (2 s.f)

\(\sqrt[3]{\frac{27a ^{-9}}{8}}\) = \(\frac{3a^{-3}}{2}\) = \(\frac{3}{2}\) x \(\frac{1}{a^3}\) = \(\frac{3}{2a^3}\)

Circumference of PRS = \(\frac{\pi d}{2}\) = \(\frac{22}{7}\) x \(\frac{7}{1}\) x \(\frac{1}{2}\) = 11cm Side PT = 7cm, Side TR = 7cm Perimeter(PTRS) = 11cm + 7cm + 7cm = 25cm

By using cosine formula, p2 = Q2 + R2 - 2QR cos p Cos P = \(\frac{Q^2 + R^2 - p^2}{2 QR}\) = \(\frac{(3)^2 + 2(\sqrt{3})^2 - 3^2}{2\sqrt{3}}\) = \(\frac{3 + 12 - 9}{12}\) = \(\frac{6}{12}\) = \(\frac{1}{2}\) = 0.5 Cos P = 0.5 p = cos-1 0.5 = 60o = < P = 60o If < P = 60o and < Q = 30 < R = 180o - 90o angle P = 60o and angle R is 90o

\(\frac{24.57 + 25.63 + 24.32 + 26.01 + 25.77}{5}\) mean = \(\frac{126.3}{5}\) = 25.26

Speed = \(\frac{distance}{time}\) let x represent the speed, d represent distance x = \(\frac{d}{4}\) d = 4x 2x = \(\frac{600 - d}{3}\) 6x = 600 - d 6x = 600 - 4x 10x = 600 x = \(\frac{600}{10}\) = 60km/hr Since speed was doubled for the last three hours = 2 x 60km\hr = 120km\hr.