This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Solve Question 6. The pie chart shows the time spent by a child during a day (24 hours) in different activities. The central angles for each activity are: • Home work: 120^ • School: 90^ • Play: 40^ • Sleep: 90^ The sum of these angles is 120^ + 90^ + 40^ + 90^ = 340^. The angle for the "Others" activity is 360^ - 340^ = 20^. A day has 24 hours. The number of hours spent on each activity is: • Home work: (120^)/(360^) × 24 hours = (1)/(3) × 24 = 8 hours • School: (90^)/(360^) × 24 hours = (1)/(4) × 24 = 6 hours • Play: (40^)/(360^) × 24 hours = (1)/(9) × 24 = (24)/(9) = (8)/(3) ≈ 2.67 hours • Sleep: (90^)/(360^) × 24 hours = (1)/(4) × 24 = 6 hours • Others: (20^)/(360^) × 24 hours = (1)/(18) × 24 = (24)/(18) = (4)/(3) ≈ 1.33 hours Step 2: Solve Question 7. The pie chart shows the number of young people liking different types of music. The central angles for each type of music are: • Folk: 101^ • Light: 144^ • Classical: 72^ The sum of these angles is 101^ + 144^ + 72^ = 317^. The angle for Semi-classical music is 360^ - 317^ = 43^. a) Which type of music is liked by the maximum number of people? The type of music with the largest central angle is liked by the maximum number of people. Comparing the angles: Folk (101^), Light (144^), Classical (72^), Semi-classical (43^). The largest angle is 144^, which corresponds to Light music. The type of music liked by the maximum number of people is Light music. b) If a total of 720 young people were surveyed, find the number of people liking semi-classical music. Number of people liking semi-classical music = Central angle for Semi-classical360^ × Total number of people Number of people liking semi-classical music = (43^)/(360^) × 720 = 43 × 2 = 86 people. c) If a company were to make CDs, how many per cent of each type would they make? This requires calculating the percentage for each music type based on its central angle. • Folk: (101^)/(360^) × 100\% ≈ 28.06\% • Light: (144^)/(360^) × 100\% = 40\% • Classical: (72^)/(360^) × 100\% = 20\% • Semi-classical: (43^)/(360^) × 100\% ≈ 11.94\% Step 3: Solve Question 8. The pie chart shows different types of programmes viewed. The central angles for each type of programme are: • News: 30^ • Informative: 90^ • Sports: 90^ • Entertainment: 144^ Note: The sum of the given angles is 30^ + 90^ + 90^ + 144^ = 364^, which is greater than 360^. We will proceed using the given angles as they are, assuming a slight inaccuracy in the diagram's angles. a) Which type of programmes are viewed the most and how much per cent? The type of programme with the largest central angle is viewed the most. Comparing the angles: News (30^), Informative (90^), Sports (90^), Entertainment (144^). The largest angle is 144^, which corresponds to Entertainment. Percentage for Entertainment = (144^)/(360^) × 100\% = 0.4 × 100\% = 40\%. The type of programme viewed the most is Entertainment, with 40\% of viewers. b) Find the percentage of the viewers for each type of programme. • News: (30^)/(360^) × 100\% = (1)/(12) × 100\% ≈ 8.33\% • Informative: (90^)/(360^) × 100\% = (1)/(4) × 100\% = 25\% • Sports: (90^)/(360^) × 100\% = (1)/(4) × 100\% = 25\% • Entertainment: (144^)/(360^) × 100\% = 40\% 3 done, 2 left today. You're making progress.