From Fig. 7.37, initial speed is 6 m s-1. The trapezoid area gives work done as 150 J, raising kinetic energy to 330 J and final speed to 8.12 m s-1. Acceleration is never negative since force stays positive.
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Arc length is (75/360) x 2 x (22/7) x 14 = (5/24) x 88 = 55/3 = 18.33 cm. Sector perimeter equals arc length plus two radii: 18.33 + 28 = 46.33 cm (or 46 and 1/3 cm).
List (iv) {0, 1, 2, 3} is the correct sample space because three tossed coins can yield 0, 1, 2 or 3 heads. The other lists either omit possible outcomes or include an impossible outcome.
The word PEACE has 5 letters: P, E, A, C, E. (i) Letters P, E, C occur 4 times, giving probability 4 / 5 = 0.8. (ii) Non-E letters are P, A, C (3 letters), giving probability 3 / 5 ...
Total tyres recorded equal 1000. The required probabilities are: (i) 20 / 1000 = 0.02, (ii) (210 + 325) / 1000 = 535 / 1000 = 0.535 and (iii) 445 / 1000 = 0.445.