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 for problems 6a, 6b, 7a, 7b, 8a, and 8b. Problem 6a: Step 1: Let the unknown number be N. Step 2: Translate the problem into an equation: "3.5% of a number is 3.5". 0.035 × N = 3.5 Step 3: To find N, divide both sides by 0.035: N = (3.5)/(0.035) Step 4: Simplify the division: N = (35)/(0.35) = (3500)/(35) = 100 The number is 100. Problem 6b: Step 1: Evaluate the numerator: 0.01 × 0.04 = 0.0004 Step 2: Rewrite the expression with the evaluated numerator: (0.0004)/(0.0002) Step 3: Perform the division: (0.0004)/(0.0002) = 2 Step 4: Express the answer in standard form (scientific notation). Standard form requires a number between 1 and 10 multiplied by a power of 10. 2 = 2 × 10^0 The value is 2 × 10^0. Problem 7a: Step 1: Identify the given information: Number of girls = 375 Ratio of boys to girls = 4:5 Step 2: Let the number of boys be B. Set up a proportion based on the ratio: Number of boysNumber of girls = (4)/(5) (B)/(375) = (4)/(5) Step 3: Solve for B by multiplying both sides by 375: B = (4)/(5) × 375 Step 4: Perform the multiplication: B = 4 × (375)/(5) = 4 × 75 B = 300 The number of boys in the school is 300. Problem 7b: Step 1: Identify the given values for simple interest calculation: Principal (P) = ₦650.00 Time (T) = 2 years Rate (R) = 6% per annum = 0.06 Step 2: Use the formula for simple interest: Simple Interest (SI) = (P × R × T)/(100) Step 3: Substitute the values into the formula: SI = (650 × 6 × 2)/(100) Step 4: Perform the multiplication in the numerator: SI = (650 × 12)/(100) SI = (7800)/(100) Step 5: Perform the division: SI = ₦78.00 The simple interest is ₦78.00. Problem 8a: Step 1: This is an inverse proportion problem. Let M be the number of men and D be the number of days. The total work is constant, so M_1 D_1 = M_2 D_2. Step 2: Identify the given values: M_1 = 6 men D_1 = 4 days M_2 = 8 men D_2 = ? days Step 3: Substitute the values into the formula: 6 × 4 = 8 × D_2 24 = 8 D_2 Step 4: Solve for D_2 by dividing both sides by 8: D_2 = (24)/(8) D_2 = 3 It will take 8 men 3 days to finish the same work. Problem 8b: Step 1: Find the prime factorization of 60. 60 = 2 × 30 = 2 × 2 × 15 = 2^2 × 3 × 5 Step 2: For a number to be a perfect square, all the exponents in its prime factorization must be even. Step 3: In the prime factorization of 60 (2^2 × 3^1 × 5^1), the exponent of 2 is even (2), but the exponents of 3 and 5 are odd (1). Step 4: To make the exponents of 3 and 5 even, we need to multiply by 3^1 and 5^1. Step 5: The smallest number to multiply by is 3 × 5 = 15. 60 × 15 = (2^2 × 3 × 5) × (3 × 5) = 2^2 × 3^2 × 5^2 = (2 × 3 × 5)^2 = 30^2 = 900, which is a perfect square. The smallest number by which 60 must be multiplied to be a perfect square is 15. 3 done, 2 left today. You're making progress.