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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e) Akili, Njozi and Aziz ring their bells. Akili rings his after 2 minutes, Njozi after every 3 minutes and Aziz after 4 minutes. After how many minutes will all the bells ring together? Step 1: Find the Least Common Multiple (LCM) of the ringing intervals. The bells ring every 2, 3, and 4 minutes. We need to find the LCM of 2, 3, and 4. Step 2: List multiples or use prime factorization. Multiples of 2: 2, 4, 6, 8, 10, 12, ... Multiples of 3: 3, 6, 9, 12, ... Multiples of 4: 4, 8, 12, ... The smallest common multiple is 12. Alternatively, using prime factorization: 2 = 2^1 3 = 3^1 4 = 2^2 LCM = 2^2 × 3^1 = 4 × 3 = 12. All the bells will ring together after 12 minutes. f) The school has 80 teachers if (3)/(4) are female teachers. How many male teachers are there in that school? Step 1: Determine the fraction of male teachers. If (3)/(4) of the teachers are female, then the remaining fraction are male. Fraction of male teachers = 1 - (3)/(4) = (4)/(4) - (3)/(4) = (1)/(4). Step 2: Calculate the number of male teachers. Total number of teachers = 80. Number of male teachers = (1)/(4) × 80. Number of male teachers = (80)/(4) = 20. There are 20 male teachers in that school. That's 2 down. 3 left today — send the next one.