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
The problem asks to calculate the Harmonic Mean (HM) for the given set of numbers. Based on your partial work, the numbers are 4, 6, 8. The formula for the Harmonic Mean is given as HM = (n)/( 1)x. Step 1: Identify the given numbers and the count. The numbers are x = \4, 6, 8\. The count of numbers is n = 3. Step 2: Calculate the reciprocal of each number. (1)/(4), (1)/(6), (1)/(8) Step 3: Sum the reciprocals of the numbers. To sum these fractions, find a common denominator, which is 24. (1)/(x) = (1)/(4) + (1)/(6) + (1)/(8) = (6)/(24) + (4)/(24) + (3)/(24) = (6+4+3)/(24) = (13)/(24) Your calculation for the sum of reciprocals is correct. Step 4: Substitute the sum of reciprocals and the count into the Harmonic Mean formula. HM = (n)/( 1)x = (3)/(13)24 Step 5: Simplify the expression. To divide by a fraction, multiply by its reciprocal. HM = 3 × (24)/(13) = (72)/(13) Step 6: Convert the fraction to a decimal. HM ≈ 5.538 The Harmonic Mean for the given set of numbers is: 5.538 3 done, 2 left today. You're making progress.