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: 1. (a) Simplify w^3 × w × w^-2 Step 1: Apply the rule of exponents for multiplication, which states that when multiplying terms with the same base, you add their exponents. Remember that w is equivalent to w^1. w^3 × w^1 × w^-2 = w^3+1+(-2) Step 2: Add the exponents. w^3+1-2 = w^4-2 = w^2 The simplified expression is w^2. 1. (b) What is 21(1)/(2)\% of Le 80,000.00? Step 1: Convert the mixed percentage to a decimal. 21(1)/(2)\% = 21.5\% To use this in calculation, divide by 100. 21.5\% = (21.5)/(100) = 0.215 Step 2: Multiply the decimal by the given amount. 0.215 × Le 80,000.00 = Le 17,200.00 The amount is Le 17,200.00. 1. (c) At what rate will Le 10,000.00 earn an interest of Le 400.00 in 5 years? Step 1: Identify the given values for simple interest. The formula for simple interest is I = PRT, where I is interest, P is principal, R is rate, and T is time. Given: I = Le 400.00 P = Le 10,000.00 T = 5 years We need to find R. Step 2: Rearrange the formula to solve for R. R = (I)/(PT) Step 3: Substitute the given values into the formula. R = (400)/(10,000 × 5) Step 4: Perform the multiplication in the denominator and then the division. R = (400)/(50,000) R = (4)/(500) R = (1)/(125) R = 0.008 Step 5: Convert the decimal rate to a percentage by multiplying by 100. R = 0.008 × 100\% = 0.8\% The rate is 0.8\% per annum. 3 done, 2 left today. You're making progress.