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: Determine the percentages for each region of the Venn diagram. Let E represent people who speak English and F represent people who speak French. Given information: • Percentage of people who speak both English and French, P(E F) = 12\%. • Percentage of people who speak neither language, P(E F)' = 5\%. • Percentage of people who speak only English, P(E only), is 15\% more than those who speak only French, P(F only). So, P(E only) = P(F only) + 15\%. The sum of all distinct regions must equal 100\%: P(E only) + P(F only) + P(E F) + P(E F)' = 100\% Substitute the known values: P(E only) + P(F only) + 12\% + 5\% = 100\% P(E only) + P(F only) + 17\% = 100\% P(E only) + P(F only) = 100\% - 17\% P(E only) + P(F only) = 83\% Now we have a system of two equations: 1) P(E only) + P(F only) = 83\% 2) P(E only) = P(F only) + 15\% Substitute equation (2) into equation (1): (P(F only) + 15\%) + P(F only) = 83\% 2 · P(F only) + 15\% = 83\% 2 · P(F only) = 83\% - 15\% 2 · P(F only) = 68\% P(F only) = (68\%)/(2) P(F only) = 34\% Now find P(E only) using equation (2): P(E only) = 34\% + 15\% P(E only) = 49\% The percentages for each region are: • Only English: 49\% • Only French: 34\% • Both English and French: 12\% • Neither English nor French: 5\% Step 2: Represent the information on a Venn diagram (Part a). A Venn diagram would show two overlapping circles, one for English (E) and one for French (F), within a rectangle representing the total population. The percentages for each region are: • Region E only: 49% • Region F only: 34% • Region E and F (intersection): 12% • Region outside E and F (neither): 5% Step 3: Find the percentage of people who can speak English and French (Part b). b) i) English: The percentage of people who can speak English is the sum of those who speak only English and those who speak both. P(E) = P(E only) + P(E F) P(E) = 49\% + 12\% P(E) = 61% b) ii) French: The percentage of people who can speak French is the sum of those who speak only French and those who speak both. P(F) = P(F only) + P(E F) P(F) = 34\% + 12\% P(F) = 46% Step 4: Find the number of people who can speak only French (Part c). The total population of the village is 840. The percentage of people who can speak only French is 34\%. Number of people who can speak only French = 34\% of 840. Number = 0.34 × 840 Number = 285.6 Send me the next one 📸