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
Here are the solutions to the problems: 1. Find the value of 1.57 - 0.42 leaving the answer as a mixed fraction in simplified form. Step 1: Convert the decimals to fractions. 1.57 = (157)/(100) 0.42 = (42)/(100) Step 2: Subtract the fractions. (157)/(100) - (42)/(100) = (157 - 42)/(100) = (115)/(100) Step 3: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 5. (115 ÷ 5)/(100 ÷ 5) = (23)/(20) Step 4: Convert the improper fraction to a mixed fraction. (23)/(20) = 1 (3)/(20) The value is 1 (3)/(20). 2. Oscar refuels his car every two days; Morris refuels his car after every four days while Millicent refuels her car after every ten days. If they all refueled their cars on 20^th March, on which date will they refuel their cars together again? Step 1: Find the least common multiple (LCM) of 2, 4, and 10 to determine how many days it will be until they refuel together again. Prime factorization: 2 = 2^1 4 = 2^2 10 = 2^1 × 5^1 The LCM is 2^2 × 5^1 = 4 × 5 = 20. They will refuel together again after 20 days. Step 2: Calculate the date 20 days after March 20th. March has 31 days. Days remaining in March from March 20th: 31 - 20 = 11 days. Remaining days to count in the next month: 20 - 11 = 9 days. The next month is April. So, they will refuel together on April 9th. The date is April 9th. 3. Use logarithms only to evaluate, correct to 4 decimal places: (12.78 33.45^(9.0