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: d) Step 1: Recall the dimensions of the semi-circular swimming pool from the previous problem. The radius (r) of the semi-circular pool is 3.5 m. The depth (h) of the pool is given as 4 m. Step 2: Calculate the area of the semi-circular base. Area of semi-circle = (1)/(2) r^2 Using ≈ (22)/(7): Area = (1)/(2) × (22)/(7) × (3.5)^2 = (1)/(2) × (22)/(7) × 12.25 = 11 × (12.25)/(7) = 11 × 1.75 = 19.25 m^2 Step 3: Calculate the volume of water. Volume = Area of base × depth = 19.25 m^2 × 4 m = 77 m^3 The volume of water in the pool is 77 m^3. 5a) Step 1: Calculate the total work units for the first scenario. Total work units = Number of men × Hours per day × Number of days = 30 men × 12 hours/day × 6 days = 2160 man-hours-days Step 2: Calculate the number of days (D_2) for the second scenario. Let M_2 = 16 men, H_2 = 9 hours/day. Total work units = M_2 × H_2 × D_2 2160 = 16 × 9 × D_2 2160 = 144 × D_2 D_2 = (2160)/(144) D_2 = 15 days Step 3: Calculate how much longer it will take. Longer time = D_2 - D_1 = 15 days - 6 days = 9 days It will take 9 days longer. 5b) i) Step 1: Identify the principal amount (P), interest rate (R), and time (T). Principal (P) = 500,000 frs Interest rate (R) = 5\% per annum = 0.05 Time (T) = 2(1)/(2) years = 2.5 years Step 2: Use the simple interest formula: I = P × R × T. I = 500,000 frs × 0.05 × 2.5 I = 25,000 frs × 2.5 I = 62,500 frs The interest Mr. Olia will have to pay is 62,500 frs. 5b) ii) Step 1: Calculate the total amount Mr. Doh will receive. Total amount = Principal + Interest = 500,000 frs + 62,500 frs = 562,500 frs Mr. Doh will receive 562,500 frs from Mr. Olia at the end of the period. 6a) Step 1: Calculate each annual expenditure item. • Tax: 25 frs per 1,000 frs of income. Annual income = 3,000,000 frs. Tax rate = (25)/(1000) = 0.025. Annual tax = 0.025 × 3,000,000 frs = 75,000 frs. • Food: 50,000 frs per month. Annual food cost = 50,000 frs/month × 12 months = 600,000 frs. • Monthly house rent: 80,000 frs per month. Annual rent = 80,000 frs/month × 12 months = 960,000 frs. • Clothing and cosmetics: 250,000 frs per annum. • Health care and transport: 100,000 frs for the year. • Miscellaneous: 76,000 frs annually. Step 2: Sum all annual expenditures. Total annual expenditure = Tax + Food + Rent + Clothing/Cosmetics + Health/Transport + Miscellaneous = 75,000 + 600,000 + 960,000 + 250,000 + 100,000 + 76,000 = 2,061,000 frs Her annual expenditure is 2,061,000 frs. Last free one today — make it count tomorrow, or type /upgrade for unlimited.