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 to the questions you sent. Question (c) The table shows the number of packages purchased from a store. (i) Copy and complete the table. The completed table is: |c|c|c| Packages (x) & Customers (f) & fx \\ 0 & 0 & 0 \\ 1 & 4 & 4 \\ 2 & 4 & 8 \\ 3 & 8 & 24 \\ 4 & 2 & 8 \\ 5 & 1 & 5 \\ (ii) Calculate the mean number of packages purchased. Step 1: Calculate the sum of customers ( f). f = 0 + 4 + 4 + 8 + 2 + 1 = 19 Step 2: Calculate the sum of fx ( fx). fx = 0 + 4 + 8 + 24 + 8 + 5 = 49 Step 3: Calculate the mean using the formula Mean = ( fx)/( f). Mean = (49)/(19) ≈ 2.5789 The mean number of packages purchased is 2.58 (rounded to 2 decimal places). (iii) Find the total number of customers. The total number of customers is the sum of the frequencies ( f). Total customers = 0 + 4 + 4 + 8 + 2 + 1 = 19 The total number of customers is 19. (iv) What is the total number of packages purchased? The total number of packages purchased is the sum of fx ( fx). Total packages = 0 + 4 + 8 + 24 + 8 + 5 = 49 The total number of packages purchased is 49. (v) If a package costs GHe 43.50, how much did the store make? Step 1: Use the total number of packages purchased from part (iv). Total packages = 49. Step 2: Multiply the total packages by the cost per package. Total earnings = 49 × GHe 43.50 Total earnings = GHe 2131.50 The store made GHe 2131.50. Question (d) (i) Find the sum of 16.702, 923.5 and 2.7208, leaving your answer in standard form. Step 1: Add the numbers. 16.702 + 923.5 + 2.7208 = 942.9228 Step 2: Convert the sum to standard form (A × 10^n, where 1 |A| < 10). 942.9228 = 9.429228 × 10^2 The sum in standard form is 9.429228 × 10^2. (ii) Factorize completely: 12ab - 6b + 8a - 4. Step 1: Group the terms. (12ab - 6b) + (8a - 4) Step 2: Factor out the common factor from each group. 6b(2a - 1) + 4(2a - 1) Step 3: Factor out the common binomial (2a - 1). (2a - 1)(6b + 4) Step 4: Factor out the common factor from the second binomial. (2a - 1)2(3b + 2) Step 5: Rearrange for the final factored form. 2(2a - 1)(3b + 2) The completely factorized expression is 2(2a - 1)(3b + 2). 3 done, 2 left today. You're making progress.