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
1. Write 100 as a product of its primes. Step 1: Find the prime factors of 100. Divide 100 by the smallest prime number, 2. 100 ÷ 2 = 50 Divide 50 by 2. 50 ÷ 2 = 25 Divide 25 by the next smallest prime number, 5. 25 ÷ 5 = 5 Divide 5 by 5. 5 ÷ 5 = 1 The prime factors are 2, 2, 5, 5. Step 2: Write the prime factors as a product. 100 = 2 × 2 × 5 × 5 = 2^2 × 5^2 The product of its primes is 2^2 × 5^2. 2. Simplify the fraction (84)/(96). Step 1: Find the greatest common divisor (GCD) of 84 and 96. Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 The greatest common divisor is 12. Step 2: Divide both the numerator and the denominator by the GCD. (84 ÷ 12)/(96 ÷ 12) = (7)/(8) The simplified fraction is (7)/(8). 3. Write (5)/(8) as a decimal fraction correct to two decimal places. Step 1: Convert the fraction to a decimal. Divide 5 by 8. 5 ÷ 8 = 0.625 Step 2: Round the decimal to two decimal places. The third decimal place is 5, so round up the second decimal place. 0.625 ≈ 0.63 The decimal fraction correct to two decimal places is 0.63. 4. Calculate 30% of 500 kg. Step 1: Convert the percentage to a decimal. 30\% = (30)/(100) = 0.30 Step 2: Multiply the decimal by 500 kg. 0.30 × 500 kg = 150 kg 30% of 500 kg is 150 kg. Send me the next one 📸