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
Hey icyishakadaniel, good to see you again. Here are the solutions to your homework problems: a) To find the amount of money in the account after 5 years, we use the compound interest formula. Step 1: Identify the given values. Principal P = 4,000 FRS Annual interest rate r = 6.09\% = 0.0609 Number of times interest is compounded per year n = 4 (quarterly) Time t = 5 years Step 2: Apply the compound interest formula A = P(1 + (r)/(n))^nt. A = 4000(1 + (0.0609)/(4))^4 × 5 Step 3: Calculate the value inside the parenthesis and the exponent. A = 4000(1 + 0.015225)^20 A = 4000(1.015225)^20 Step 4: Calculate the final amount. A = 4000 × 1.35011 A = 5400.44 The money in the account after 5 years will be 5400.44 FRS. b) This is an inverse proportion problem involving men, hours, and days. Step 1: Calculate the total work units for the first scenario. Work units = Men × Hours/day × Days Work units = 12 men × 8 hours/day × 10 days = 960 man-hours-days Step 2: Set up the equation for the second scenario, where the total work units remain the same. Let H_2 be the hours per day for 20 men to finish in 8 days. 20 men × H_2 hours/day × 8 days = 960 man-hours-days Step 3: Solve for H_2. 160 × H_2 = 960 H_2 = (960)/(160) H_2 = 6 20 men must work 6 hours per day. c) To find the total number of tickets available, we use percentages. Step 1: Identify the given information. Tickets sold = 98,000 This represents 80% of the total available tickets. Step 2: Set up the equation. Let T be the total number of tickets. 80\% of T = 98,000 0.80 × T = 98,000 Step 3: Solve for T. T = (98,000)/(0.80) T = 122,500 The total number of tickets that were available for the tournament is 122,500 tickets. Send me the next one 📸