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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You're on a roll — Here are the solutions to the problems: In Ngamongo village, a piece of work can be completed by 45 workers in 10 days. They worked for 4 days after which 15 workers were laid off. How many days could it take the remaining workers to complete the work? Step 1: Calculate the total amount of work in worker-days. Total work = Number of workers × Total days Total work = 45 workers × 10 days = 450 worker-days Step 2: Calculate the work done in the first 4 days. Work done = Number of workers × Days worked Work done = 45 workers × 4 days = 180 worker-days Step 3: Calculate the remaining work. Remaining work = Total work - Work done Remaining work = 450 worker-days - 180 worker-days = 270 worker-days Step 4: Calculate the number of remaining workers. Workers laid off = 15 Remaining workers = Original workers - Workers laid off Remaining workers = 45 - 15 = 30 workers Step 5: Calculate the time taken by the remaining workers to complete the remaining work. Time = Remaining work / Remaining workers Time = 270 worker-days30 workers = 9 days The remaining workers could take 9 days to complete the work. --- The table shows marks obtained by a form three class in a certain school. Marks (x): 2, 6, 8, 3, 1 No. of students (f): 9, 6, 8, 3, 1 Assuming the question asks for the mean mark: Step 1: Create a table to calculate fx and f. | Marks (x) | No. of students (f) | fx | |:---------:|:-------------------:|:----:| | 2 | 9 | 18 | | 6 | 6 | 36 | | 8 | 8 | 64 | | 3 | 3 | 9 | | 1 | 1 | 1 | Step 2: Calculate the sum of frequencies ( f). f = 9 + 6 + 8 + 3 + 1 = 27 Step 3: Calculate the sum of (fx) values ( fx). fx = 18 + 36 + 64 + 9 + 1 = 128 Step 4: Calculate the mean mark (x). The formula for the mean of a frequency distribution is x = ( fx)/( f). x = (128)/(27) x ≈ 4.7407 The mean mark is approximately 4.74. What's next?