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. Solve: 7 - 2x 15 - 4x. Step 1: Collect x terms on one side and constant terms on the other. 7 - 2x 15 - 4x Add 4x to both sides: 7 - 2x + 4x 15 7 + 2x 15 Subtract 7 from both sides: 2x 15 - 7 2x 8 Step 2: Isolate x. Divide by 2: x (8)/(2) x 4 The correct option is A. The solution is x 4. 2. Evaluate p^2(q-1) when p=2 and q=(3)/(4). Step 1: Substitute the given values of p and q into the expression. p^2(q-1) = (2)^2((3)/(4)-1) Step 2: Simplify the expression. (2)^2((3)/(4)-1) = 4((3)/(4)-(4)/(4)) = 4(-(1)/(4)) Step 3: Perform the multiplication. = -1 The correct option is C. The value is -1. 3. Antwi has 20 mangoes and 20% are rotten. How many of them are not rotten? Step 1: Calculate the number of rotten mangoes. Number of rotten mangoes = 20\% of 20 = (20)/(100) × 20 = (1)/(5) × 20 = 4 Step 2: Calculate the number of mangoes that are not rotten. Number of not rotten mangoes = Total mangoes - Number of rotten mangoes = 20 - 4 = 16 The correct option is A. The number of mangoes that are not rotten is 16. 4. Which of the following is not a composite number? A. 65 B. 39 C. 41 D. 24 A composite number is a positive integer that has at least one divisor other than 1 and itself. A prime number has only two divisors: 1 and itself. Step 1: Check each option to determine if it is composite or prime. • A. 65 = 5 × 13. Since 65 has factors other than 1 and 65 (e.g., 5 and 13), it is a composite number. • B. 39 = 3 × 13. Since 39 has factors other than 1 and 39 (e.g., 3 and 13), it is a composite number. • C. 41. The only positive divisors of 41 are 1 and 41. Therefore, 41 is a prime number, not a composite number. • D. 24 = 2 × 12 = 3 × 8 = 4 × 6. Since 24 has factors other than 1 and 24, it is a composite number. The number that is not a composite number is 41. The correct option is C. The number that is not a composite number is 41. 5. Mary receives a commission of 15% on articles sold in a week. If her commission was GH¢ 60.00, how much sales did she make? Step 1: Set up the equation for commission. Let S be the total sales. Commission = 15\% of S GH¢ 60.00 = (15)/(100) × S Step 2: Solve for S. 60 = (15)/(100) S Multiply both sides by 100: 60 × 100 = 15 S 6000 = 15 S Divide by 15: S = (6000)/(15) S = 400 The correct option is B. Mary's total sales were GH¢ 400.00. 3 done, 2 left today. You're making progress.