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 Art, good to see you again. Here are the solutions to your questions: Question 1a: Step 1: Identify the given values. Principal amount, P = 4000 F Annual interest rate, r = 6\% = 0.06 Compounded quarterly, so n = 4 Time, t = 5 years Step 2: Use the compound interest formula A = P(1 + (r)/(n))^nt. A = 4000(1 + (0.06)/(4))^4 × 5 A = 4000(1 + 0.015)^20 A = 4000(1.015)^20 A = 4000 × 1.346855 A = 5387.42 F The amount of money in the account after 5 years will be 5387.42 F. Question 1b: Step 1: Calculate the total man-hours required for the work. Total man-hours = Number of men × Hours per day × Number of days Total man-hours = 12 men × 8 hours/day × 15 days = 1440 man-hours Step 2: Calculate the hours per day required for 20 men to finish the work in 8 days. Let H be the hours per day. 20 men × H hours/day × 8 days = 1440 man-hours 160 H = 1440 H = (1440)/(160) H = 9 hours/day 20 men must work 9 hours per day. Question 1c: Step 1: Identify the given information. Tickets sold = 480,000 This represents 80% of all available tickets. Step 2: Set up an equation to find the total number of available tickets. Let T be the total number of available tickets. 0.80 × T = 480,000 Step 3: Solve for T. T = (480,000)/(0.80) T = 600,000 The total number of tickets that were available for the tournament is 600,000. Question 2i: To represent the information on a Venn diagram, we first calculate the number of people in each distinct region. Total people = 50 Let P = Politics, A = Advertisement, S = Sports. Given: |P| = 25 |A| = 16 |S| = 14 |P A| = 5 |A S| = 6 |P S| = 4 |P A S| = 2 Step 1: Find the number of people who read exactly two sections. • Only P and A: |P A| - |P A S| = 5 - 2 = 3 • Only A and S: |A S| - |P A S| = 6 - 2 = 4 • Only P and S: |P S| - |P A S| = 4 - 2 = 2 Step 2: Find the number of people who read exactly one section. • Only P: |P| - (Only P and A + Only P and S + |P A S|) = 25 - (3 + 2 + 2) = 25 - 7 = 18 • Only A: |A| - (Only P and A + Only A and S + |P A S|) = 16 - (3 + 4 + 2) = 16 - 9 = 7 • Only S: |S| - (Only P and S + Only A and S + |P A S|) = 14 - (2 + 4 + 2) = 14 - 8 = 6 Step 3: Find the number of people who read none of the sections. Total people in at least one section = (Only P) + (Only A) + (Only S) + (Only P and A) + (Only A and S) + (Only P and S) + (P A S) = 18 + 7 + 6 + 3 + 4 + 2 + 2 = 42 Number of people who read none = Total people - Total people in at least one section = 50 - 42 = 8 The information for the Venn diagram is: • Only Politics: 18 • Only Advertisement: 7 • Only Sports: 6 • Only Politics and Advertisement: 3 • Only Advertisement and Sports: 4 • Only Politics and Sports: 2 • Politics, Advertisement, and Sports: 2 • None of the sections: 8 Send me the next one 📸