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.
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Here are the solutions to the problems. c) Step 1: Find the reciprocal of 807. The reciprocal of 807 is (1)/(807). (1)/(807) ≈ 0.001239157 Step 2: Find the reciprocal of 0.0541. The reciprocal of 0.0541 is (1)/(0.0541). (1)/(0.0541) ≈ 18.48428835 Step 3: Evaluate the expression (2)/(807) + (4)/(0.0541). (2)/(807) + (4)/(0.0541) = 2 × (1)/(807) + 4 × (1)/(0.0541) Substitute the reciprocal values: 2 × 0.001239157 + 4 × 18.48428835 0.002478314 + 73.9371534 73.939631714 Rounding to four decimal places: 73.9396 d) Step 1: Rewrite the expression using reciprocals. The expression is (1)/(3) ( (2)/(0.6638) + (3)/(0.833) ). This can be written as: (1)/(3) ( 2 × (1)/(0.6638) + 3 × (1)/(0.833) ) Step 2: Find the reciprocals. (These values would typically be looked up in reciprocal tables.) (1)/(0.6638) ≈ 1.506478 (1)/(0.833) ≈ 1.200480 Step 3: Substitute the values and evaluate. (1)/(3) (2 × 1.506478 + 3 × 1.200480) (1)/(3) (3.012956 + 3.60144) (1)/(3) (6.614396) 2.20479866... Rounding to four decimal places: 2.2048 e) Step 1: Evaluate the numerator without using a calculator. The numerator is 12.76625 - 12.4 + 0.3 × 3. First, calculate the multiplication: 0.3 × 3 = 0.9 Next, perform the subtraction: 12.76625 - 12.4 = 0.36625 Finally, perform the addition: 0.36625 + 0.9 = 1.26625 So, the numerator is 1.26625. Step 2: Evaluate the denominator without using a calculator. The denominator is (1)/(8) of 2.56 + 3.68. First, calculate (1)/(8) of 2.56: (1)/(8) × 2.56 = (2.56)/(8) = 0.32 Next, perform the addition: 0.32 + 3.68 = 4.00 So, the denominator is 4.00. Step 3: Divide the numerator by the denominator without using a calculator. (1.26625)/(4) 1.26625 ÷ 4 = 0.3165625 0.3165625 Send me the next one 📸