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 questions: 1. Express DXIV in Arabic numerals. Step 1: Break down the Roman numeral into its components. D = 500 X = 10 IV = 4 (since I (1) comes before V (5), it means 5 - 1 = 4) Step 2: Add the values. 500 + 10 + 4 = 514 The final answer is b) 514 2. Subtract 1543 from 2993. Step 1: Set up the subtraction. We need to calculate 2993 - 1543. Step 2: Perform the subtraction. 2993 - 1543 = 1450 The final answer is a) 1450 3. Which of the following represents the prime factors of 30? Step 1: Find the prime factors of 30. A prime factor is a prime number that divides the given number exactly. Divide 30 by the smallest prime number, 2: 30 ÷ 2 = 15 Divide 15 by the smallest prime number that divides it, which is 3: 15 ÷ 3 = 5 5 is a prime number. Step 2: List the prime factors. The prime factors of 30 are 2, 3, and 5. The final answer is a) 2, 3, 5 4. The H.C.F. of 13 and 39 is ...... Step 1: List the factors of each number. Factors of 13: 1, 13 (13 is a prime number) Factors of 39: 1, 3, 13, 39 Step 2: Identify the common factors. The common factors are 1 and 13. Step 3: Determine the highest common factor (H.C.F.). The highest common factor is 13. The final answer is d) 13 5. Which of the following is the least common multiple of 6, 5 and 4? Step 1: Find the prime factorization of each number. 6 = 2 × 3 5 = 5 (5 is a prime number) 4 = 2 × 2 = 2^2 Step 2: To find the L.C.M., take the highest power of each prime factor present in any of the numbers. The prime factors are 2, 3, and 5. Highest power of 2: 2^2 (from 4) Highest power of 3: 3^1 (from 6) Highest power of 5: 5^1 (from 5) Step 3: Multiply these highest powers together. L.C.M. = 2^2 × 3 × 5 = 4 × 3 × 5 = 12 × 5 = 60 The final answer is c) 60 6. What is 3.75 + 2.0001 + 6.3009? Step 1: Align the decimal points and add the numbers. ` 3.7500 2.0001 + 6.3009 --------- ` Step 2: Perform the addition column by column, starting from the rightmost digit. 0 + 1 + 9 = 10 (write 0, carry 1) 0 + 0 + 0 + 1 (carry) = 1 5 + 0 + 0 = 5 7 + 0 + 3 = 10 (write 0, carry 1) 3 + 2 + 6 + 1 (carry) = 12 Step 3: Combine the results. 3.75 + 2.0001 + 6.3009 = 12.0510 The final answer is a) 12.510