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: Find the number of votes acquired by Dalaba. The total votes cast are 120. The votes for each contestant are given in the table. Let x be the number of votes for Dalaba. The sum of all votes must equal the total votes. 14 + 11 + x + 52 + 24 = 120 101 + x = 120 Subtract 101 from both sides: x = 120 - 101 x = 19 Therefore, Dalaba acquired 19 votes. a) The number of votes acquired by Dalaba is 19 votes. Step 2: Prepare data for the pie chart and identify the winner. Now we have the votes for all contestants: • Agbeke: 14 votes • Katume: 11 votes • Dalaba: 19 votes • Dramani: 52 votes • Quainoo: 24 votes Total votes: 120 To draw a pie chart, we need to calculate the angle for each contestant's sector. The total angle in a circle is 360^. Angle for each contestant = (Number of votesTotal votes) × 360^. • Agbeke: (14)/(120) × 360^ = 14 × 3^ = 42^ • Katume: (11)/(120) × 360^ = 11 × 3^ = 33^ • Dalaba: (19)/(120) × 360^ = 19 × 3^ = 57^ • Dramani: (52)/(120) × 360^ = 52 × 3^ = 156^ • Quainoo: (24)/(120) × 360^ = 24 × 3^ = 72^ Check sum of angles: 42^ + 33^ + 57^ + 156^ + 72^ = 360^. Step 3: Draw the pie chart. b) To draw the pie chart: 1. Draw a circle using a compass. 2. Mark the center of the circle. 3. Draw a radius from the center to the circumference. 4. Using a protractor, measure and draw the angles for each contestant from the previous radius. • Agbeke: 42^ • Katume: 33^ • Dalaba: 57^ • Dramani: 156^ • Quainoo: 72^ 5. Label each sector with the contestant's name and their number of votes or percentage. Step 4: Calculate the percentage of votes for the winner. The winner is the contestant with the highest number of votes. Comparing the votes: Agbeke (14), Katume (11), Dalaba (19), Dramani (52), Quainoo (24). Dramani has the highest number of votes (52), so Dramani is the winner. To find the percentage of total votes the winner obtained: Percentage = (Winner's votesTotal votes) × 100\% Percentage = ((52)/(120)) × 100\% Percentage = (5200)/(120)\% = (520)/(12)\% = (130)/(3)\% Percentage ≈ 43.33\% c) The winner obtained 43.33\% of the total votes. Send me the next one 📸