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.
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Welcome back lil — been a while! Let's pick up where you left off. Here's the solution to Question 4: 4.1.1 Calculate the value of M if the mean shoe size is 7. Step 1: List all the given shoe sizes and set up the mean formula. The shoe sizes are 6, 9, 8, 7, 6, M, 6, 8, 7, 9. There are 10 data points. The formula for the mean is: Mean = Sum of all data pointsNumber of data points 7 = (6 + 9 + 8 + 7 + 6 + M + 6 + 8 + 7 + 9)/(10) Step 2: Sum the known values and solve for M. 7 = (66 + M)/(10) Multiply both sides by 10: 7 × 10 = 66 + M 70 = 66 + M Subtract 66 from both sides: M = 70 - 66 M = 4 4.1.2 Identify the minimum value of the data. Step 1: Substitute the value of M into the data set. The data set becomes: 6, 9, 8, 7, 6, 4, 6, 8, 7, 9. Step 2: Identify the smallest value in the data set. Arranging the data in ascending order: 4, 6, 6, 6, 7, 7, 8, 8, 9, 9. The minimum value is 4. 4.2.1 Calculate the missing value C. Step 1: Identify C as the Meal Allowance and use the Total Earnings formula. From the payslip, C is the Meal Allowance. Total Earnings = Basic Salary + Incentive Pay + House Allowance + Meal Allowance (C) R14\,800.14 = R12\,000 + (16.67\% of R12\,000) + R500 + C Step 2: Calculate the Incentive Pay. Incentive Pay = 0.1667 × R12\,000 = R2\,000.40 (Assuming 16.67% is approximately 1/6, which gives R2 000. We will use R2 000.40 for precision based on the given percentage.) Step 3: Substitute the values and solve for C. R14\,800.14 = R12\,000 + R2\,000.40 + R500 + C R14\,800.14 = R14\,500.40 + C C = R14\,800.14 - R14\,500.40 C = R299.74 4.2.2 Determine the missing value D, the Net Pay. Step 1: Calculate the Total Deductions. Total Deductions = Provident Fund + Tax + Loan Total Deductions = R1\,500 + R700 + R600 Total Deductions = R2\,800 Step 2: Calculate the Net Pay (D) using Total Earnings and Total Deductions. Net Pay = Total Earnings - Total Deductions D = R14\,800.14 - R2\,800 D = R12\,000.14 Send me the next one 📸