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 problems: 10. Work out (3.6 + 11.2)/(0.144) Step 1: Calculate the sum in the numerator. 3.6 + 11.2 = 14.8 Step 2: Divide the result by the denominator. (14.8)/(0.144) To simplify the division, multiply both the numerator and the denominator by 1000 to remove the decimals: (14.8 × 1000)/(0.144 × 1000) = (14800)/(144) Step 3: Perform the division. (14800)/(144) = 102.777... Rounding to four decimal places: 102.777... ≈ 102.7778 The value is 102.7778. 11. Use a table to look for a square root of 0.8236 To find the square root of 0.8236 using a table, you would locate 0.8236 in the table's appropriate column (e.g., for square roots of numbers between 0 and 1). Calculating the square root directly: sqrt(0.8236) ≈ 0.9075241 Rounding to four decimal places, as is common for table values: sqrt(0.8236) ≈ 0.9075 The square root of 0.8236 is approximately 0.9075. 12. Evaluate: (3)/(8) of [7(3)/(5) - (1)/(3)(1(1)/(4) + 3(1)/(3) × 2(2)/(5))] Step 1: Convert all mixed numbers to improper fractions. 7(3)/(5) = (7 × 5 + 3)/(5) = (38)/(5) 1(1)/(4) = (1 × 4 + 1)/(4) = (5)/(4) 3(1)/(3) = (3 × 3 + 1)/(3) = (10)/(3) 2(2)/(5) = (2 × 5 + 2)/(5) = (12)/(5) Substitute these into the expression: (3)/(8) × [(38)/(5) - (1)/(3)((5)/(4) + (10)/(3) × (12)/(5))] Step 2: Perform the multiplication inside the innermost parentheses. (10)/(3) × (12)/(5) = (10 × 12)/(3 × 5) = (120)/(15) = 8 Step 3: Perform the addition inside the innermost parentheses. (5)/(4) + 8 = (5)/(4) + (32)/(4) = (37)/(4) The expression now becomes: (3)/(8) × [(38)/(5) - (1)/(3)((37)/(4))] Step 4: Perform the multiplication (1)/(3) × (37)/(4). (1)/(3) × (37)/(4) = (37)/(12) The expression now becomes: (3)/(8) × [(38)/(5) - (37)/(12)] Step 5: Perform the subtraction inside the square brackets. Find a common denominator for 5 and 12, which is 60. (38)/(5) - (37)/(12) = (38 × 12)/(5 × 12) - (37 × 5)/(12 × 5) = (456)/(60) - (185)/(60) = (456 - 185)/(60) = (271)/(60) The expression now becomes: (3)/(8) × (271)/(60) Step 6: Perform the final multiplication. (3)/(8) × (271)/(60) = (3 × 271)/(8 × 60) We can simplify by dividing 3 and 60 by their common factor, 3: (1 × 271)/(8 × 20) = (271)/(160) As a mixed number: 1(111)/(160) The evaluated expression is (271)/(160) or 1(111)/(160).