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Speed = \(\frac{\text{Distance}}{\text{Time}}\) From the first statement, speed = xkm/h, t = 2hrs Therefore, distance = 2xkm From the second statement, speed = x + 2 ( since speed increased by 2km/h) and t = 3hrs distance = 3 X (x + 2) = 3x + 6 But total distance = 36km(given) Total distance = 2x + 3x + 6 = 36 i.e. (dist. from the first statement + dist. from the second statement) 5x + 6 = 36 5x = 36 - 6 = 30 x = (initial speed) = \(\frac{30}{5}\) = 6Km/h check = total distance = 36 = 2x + 3x + 6 = 12 + 18 + 6 = 36.

distance d more than 18 KM = d > 18 0r 18 < d distance d but not more than 23 KM = d \le 23 Mathematically; 18 < d \le 23

Rearrange data in increasing order: 6,7,7,7,8,8,8,9,9 and 11 First quartile (ungrouped data) = \(\frac{n + 1}{4}\)th value = \(\frac{11}{4}\) = 2.75th value = \(\frac{7 + 7}{2}\) = 7.0

∑fx = (160 * 4) + (161 * 6) + (162 * 3) + (163 * 7) + (164 * 8) + (165 * 9) =640 + 966 + 486 + 1,141 + 1,312 + 1,485 = 6,030 ∑f = 4 + 6 + 3 + 7 + 8 + 9 = 37 = \(\frac{∑fx}{∑f}\) = \(\frac{6030}{37}\) = 162.97 or 163

Total angles = 360^\circ 100 + 60 + 80 + M = 360 M = 360 - 240 = 120 Orange (M) = 120^\circ and F ( fruits in total) For Apples: \(\frac{80}{360} \times F\) = 60 F = \(\frac{60 \times 360}{80}\) F = 270 fruits in total For Orange = \(\frac{120}{360} \times 270\) = 90 oranges

\(\begin{array}{c|c} & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline 1 & 1,1 & 1,2 & 1,3 & 1,4 & 1,5 & 1,6 \\ \hline 2 & 2,1 & 2,2 & 2,3 & 2,4 & 2,5 & 2,6 \\ \hline 3 & 3,1 & 3,2 & 3,3 & 3,4 & 3,5 & 3,6 \\ \hline 4 & 4,1 & 4,2 & 4,3 & 4,4 & 4,5 & 4,6 \\ 5 & 5,1 & 5,2 & 5,3 & 5,4 & 5,5 & 5,6 \\ \hline 6 & 6,1 & 6,2 & 6,3 & 6,4 & 6,5 & 6,6\end{array}\) From the table above, event space, n(E) = 6 sample space, n(S) = 36 Hence, probability sum of scores is at least 10, is; \(\frac{n(E)}{n(S)}\) = \(\frac{6}{36}\) = \(\frac{1}{6}\)

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

Simple harmonic motion (SHM) is a special type of periodic motion where the restoring force on the moving object is directly proportional to the magnitude of the object's displacement and acts towards the object's equilibrium position.

power = \(\frac{force * distance}{time}\) → \(\frac{200 * 9}{5}\) power = 36w

Distance covered = Area under the graph D = area of square + area of trapezium D = L x L + 1/2(a+b)h D = 4 x 4 + 1/2( 4+ 10)8 D = 16 + 1/2 x 14 x 8 D = 16 + 56 D = 72m.

Calculation of velocity: V = \sqrt[V\(^2\)x + V\(^2\)\(_y\)] V\(_x\) = 40 Cos30 = 34.6 m/s V\(_y\) = 40 sin30 - 10(1) = 10 m/s V = \sqrt[34.6\(^2\) + 10\(^2\)] V = 36.02m/s

The rate of evaporation depends on temperature, presence of wind, the humidity of the surrounding, and the surface area of the liquid exposed to the atmosphere. It doesn't depend on the mass of the liquid. The larger the surface area, the more would be the rate of evaporation.

Thermistors act as a passive component in a circuit. They are an accurate, cheap, and robust way to measure temperature.

More collisions mean more force, so the pressure will increase. When the volume decreases, the pressure increases. This shows that the pressure of a gas is inversely proportional to its volume. This is shown by Boyle's law.

OPTION B is the correct answer because gravitational force is inversely proportional to the square of distance between the two bodies according to Newton's law of universal gravitation. \( F_g = G\frac{m_1m_2}{r^2}\)