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
I will continue solving question 3 based on the information provided in our previous interaction, as question 3 is not visible in the current photo. a) To illustrate the information in a Venn diagram, we first need to find the values. Step 1: Define variables and set up the equation. Let M be the set of candidates who took Maths and E be the set of candidates who took English. Given: Total candidates = 44 Number of candidates who took Maths, |M| = x Number of candidates who took English, |E| = 3x Number of candidates who took both, |M E| = (1)/(3)|M| = (1)/(3)x The formula for the union of two sets is: |M E| = |M| + |E| - |M E| Step 2: Substitute the given values into the formula and solve for x. Assuming all 44 candidates took at least one subject: 44 = x + 3x - (1)/(3)x 44 = 4x - (1)/(3)x To combine the terms on the right side, find a common denominator: 44 = (12x)/(3) - (x)/(3) 44 = (11x)/(3) Multiply both sides by 3: 44 × 3 = 11x 132 = 11x Divide by 11: x = (132)/(11) x = 12 Step 3: Calculate the number of candidates for each section. Number of candidates who took Maths, |M| = 12 Number of candidates who took English, |E| = 3 × 12 = 36 Number of candidates who took both, |M E| = (1)/(3) × 12 = 4 Number of candidates who took Maths only: 12 - 4 = 8 Number of candidates who took English only: 36 - 4 = 32 Step 4: Illustrate the Venn diagram. • Draw two intersecting circles. Label one circle 'M' for Maths and the other 'E' for English. • In the intersection region (M E), write the number of candidates who took both subjects: 4. • In the part of circle M that does not overlap with E (Maths only), write the number of candidates who took Maths only: 8. • In the part of circle E that does not overlap with M (English only), write the number of candidates who took English only: 32. 3 done, 2 left today. You're making progress.