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
You're on a roll — a) The number of votes acquired by Dalaba is (22)/(13). b) Step 1: Calculate the exact number of votes for each contestant. From part (a), we found x = (22)/(13). • Agbeke: 14x = 14 × (22)/(13) = (308)/(13) votes • Katume: 11x = 11 × (22)/(13) = (242)/(13) votes • Dalaba: x = (22)/(13) votes • Dramani: 52 votes • Quainoo: 24 votes The total number of votes is 120. Step 2: Calculate the angle for each contestant's sector in the pie chart. The total angle in a circle is 360^. The angle for each contestant is given by (votestotal votes) × 360^. • Agbeke: ((308/13)/(120)) × 360^ = (308)/(13 × 120) × 360^ = (308)/(13) × 3^ = (924)/(13)^ ≈ 71.08^ • Katume: ((242/13)/(120)) × 360^ = (242)/(13 × 120) × 360^ = (242)/(13) × 3^ = (726)/(13)^ ≈ 55.85^ • Dalaba: ((22/13)/(120)) × 360^ = (22)/(13 × 120) × 360^ = (22)/(13) × 3^ = (66)/(13)^ ≈ 5.08^ • Dramani: ((52)/(120)) × 360^ = 52 × 3^ = 156^ • Quainoo: ((24)/(120)) × 360^ = 24 × 3^ = 72^ To draw the pie chart, you would divide a circle into sectors with these angles. c) Step 1: Identify the winner of the contest. Compare the number of votes for each contestant: • Agbeke: (308)/(13) ≈ 23.69 votes • Katume: (242)/(13) ≈ 18.62 votes • Dalaba: (22)/(13) ≈ 1.69 votes • Dramani: 52 votes • Quainoo: 24 votes The contestant with the highest number of votes is Dramani, with 52 votes. Step 2: Calculate the percentage of total votes obtained by the winner. Percentage = Winner's votesTotal votes × 100\% Percentage = (52)/(120) × 100\% Percentage = (5200)/(120)\% Percentage = (520)/(12)\% Percentage = (130)/(3)\% Percentage = 43(1)/(3)\% The percentage of total votes the winner obtained is 43(1)/(3)\%. Drop the next question!