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
Here are the solutions for the problems: a) The sum of the interior angles of a polygon is 1440^. Calculate the number of sides of this polygon. Step 1: Recall the formula for the sum of interior angles of a polygon. The sum of the interior angles of a polygon with n sides is given by the formula: Sum = (n-2) × 180^ Step 2: Substitute the given sum into the formula and solve for n. 1440^ = (n-2) × 180^ Divide both sides by 180^: (1440)/(180) = n-2 8 = n-2 Add 2 to both sides: n = 8 + 2 n = 10 The polygon has 10 sides. b) The bar chart below shows the number of learners who got distinctions in a test in each of the Grade 9 classes. b)(i) Find the modal class. Step 1: Understand what a modal class is. The modal class is the class with the highest frequency, meaning the class with the most learners who got distinctions. Step 2: Read the number of learners for each class from the bar chart. • Class FA: 4 learners • Class FB: 8 learners • Class FC: 6 learners • Class FD: 8 learners • Class FE: 2 learners Step 3: Identify the class(es) with the highest number of learners. Both Class FB and Class FD have 8 learners, which is the highest number. The modal class is FB and FD. b)(ii) Total number of learners who got distinctions. Step 1: Sum the number of learners from all classes. Total learners = (Learners in FA) + (Learners in FB) + (Learners in FC) + (Learners in FD) + (Learners in FE) Total = 4 + 8 + 6 + 8 + 2 Step 2: Perform the addition. Total = 12 + 6 + 8 + 2 Total = 18 + 8 + 2 Total = 26 + 2 Total = 28 The total number of learners who got distinctions is 28 learners. 3 done, 2 left today. You're making progress.