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
Step 1: Find the total cost of the items costing 48.12, 48.20, and 48.00. Formula: total cost = price_1 + price_2 + price_3 Substitute: 48.12 + 48.20 + 48.00 Add the dollars first: 48 + 48 + 48 = 144 Add the cents: 0.12 + 0.20 + 0.00 = 0.32 Total cost = 144.32 Total cost: 144.32 Step 2: How much is 8% tax on the total cost. Formula: tax = 0.08 × total cost Substitute: 0.08 × 144.32 First compute 0.01 × 144.32 = 1.4432 Then 8 × 1.4432 = 11.5456 ≈ 11.55 (rounded to nearest cent) Total to pay = 144.32 + 11.55 = 155.87 Tax: 11.55 Total payment: 155.87 Step 3: Add 146 + 302 using expanded form (no units specified). Write in expanded form: 146 = 100 + 40 + 6 302 = 300 + 0 + 2 Add hundreds: 100 + 300 = 400 Add tens: 40 + 0 = 40 Add units: 6 + 2 = 8 Combine: 400 + 40 + 8 = 448 Sum: 448 448 Step 4: Simplify (40)/(72) to test the statement k = (40)/(72) = (4)/(7). Formula: divide numerator and denominator by GCD(40,72) = 8 Substitute: (40 ÷ 8)/(72 ÷ 8) = (5)/(9) Check: (5)/(9) ≈ 0.556, (4)/(7) ≈ 0.571 (not equal) Statement is false. (5)/(9) Step 5: Cost for 30 min if 40 for 72 min. Rate per min = (40)/(72) = (5)/(9) dollars per min Cost for 30 min: (5)/(9) × 30 = (150)/(9) = 16.6 ≈ 16.67 dollars Cost: 16.67 \16.67