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. a) Step 1: Identify prime numbers less than ten. The prime numbers less than ten are 2, 3, 5, 7. Step 2: Arrange the prime numbers in descending order to form a number. Descending order means from largest to smallest: 7, 5, 3, 2. The number formed is 7532. 7532 1. b) Step 1: Identify the second digit in the number formed in (a). The number is 7532. The second digit is 5. Step 2: Determine the total value of the second digit. The digit 5 is in the hundreds place. Its total value is 5 × 100 = 500. 500 2. Step 1: Expand the expression by distributing the numbers outside the parentheses. 4(q+6) + 7(q-3) = (4 × q) + (4 × 6) + (7 × q) + (7 × -3) = 4q + 24 + 7q - 21 Step 2: Group like terms. = (4q + 7q) + (24 - 21) Step 3: Simplify the expression. = 11q + 3 11q + 3 3. Step 1: Evaluate the product in the denominator. 0.025 × 3.6 Multiply 25 × 36: 25 × 36 = 900 Count the total number of decimal places in 0.025 (3 places) and 3.6 (1 place). The product will have 3+1=4 decimal places. So, 0.025 × 3.6 = 0.0900 = 0.09. Step 2: Substitute the product back into the expression. (5.4)/(0.09) Step 3: Eliminate the decimals by multiplying the numerator and denominator by a power of 10. To remove two decimal places from 0.09, multiply by 100. (5.4 × 100)/(0.09 × 100) = (540)/(9) Step 4: Perform the division. (540)/(9) = 60 60 3 done, 2 left today. You're making progress.