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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Here are the solutions to the problems: 1. Multiply 1.03 × 6 1.03 × 6 = 6.18 The answer is 6.18. 2. Change 72 ten to binary base To convert a base-10 number to binary, we repeatedly divide by 2 and record the remainders. 72 ÷ 2 = 36 remainder 0 36 ÷ 2 = 18 remainder 0 18 ÷ 2 = 9 remainder 0 9 ÷ 2 = 4 remainder 1 4 ÷ 2 = 2 remainder 0 2 ÷ 2 = 1 remainder 0 1 ÷ 2 = 0 remainder 1 Reading the remainders from bottom to top gives the binary number. The answer is 1001000_2. 3. Simplify 0.25 × 100 + 10 × 2.5 Step 1: Perform the multiplications. 0.25 × 100 = 25 10 × 2.5 = 25 Step 2: Perform the addition. 25 + 25 = 50 The answer is 50. 4. Subtract (2)/(3) - (1)/(4) Step 1: Find a common denominator for 3 and 4, which is 12. Step 2: Convert the fractions to have the common denominator. (2)/(3) = (2 × 4)/(3 × 4) = (8)/(12) (1)/(4) = (1 × 3)/(4 × 3) = (3)/(12) Step 3: Subtract the fractions. (8)/(12) - (3)/(12) = (8 - 3)/(12) = (5)/(12) The answer is (5)/(12). 5. Find the next number in the sequence below: 9, 3, 1, (1)/(3), ___ Observe the pattern: each term is obtained by dividing the previous term by 3. 9 ÷ 3 = 3 3 ÷ 3 = 1 1 ÷ 3 = (1)/(3) Following this pattern, the next term is: (1)/(3) ÷ 3 = (1)/(3) × (1)/(3) = (1)/(9) The next number in the sequence is (1)/(9). 6. Write 20,015 in words The number 20,015 written in words is Twenty thousand fifteen. 7. A farmer has roll of string of long [length missing], he cuts it into equal pieces, each 50 metres long. How many pieces does he get altogether? The total length of the roll of string is missing from the question. If the total length of the string roll were known (let's say L metres), the number of pieces would be calculated by dividing the total length by the length of each piece: Number of pieces = Total length of stringLength of each piece Number of pieces = L metres50 metres Without the total length of the string, the exact number of pieces cannot be determined.