This computer science problem involves algorithmic thinking and programming concepts. The solution below explains the approach, logic, and implementation step by step.
ScanSolve AI Answer
Welcome back FUture — missed you this week. Here are the solutions to the tasks: a) Step 1: Identify the number system. The problem states the number system is less than four, meaning it could be base 2 or base 3. The rewritten pin "12 20 22 10" contains the digit '2'. Since base 2 (binary) only uses digits 0 and 1, the number system cannot be base 2. Therefore, the number system must be base 3 (ternary), which uses digits 0, 1, and 2. The number system used is base 3. Step 2: Explain why. Base 3 is used because the rewritten pin contains the digit '2', which is not allowed in base 2, and the problem states the base is less than four. Step 3: Regenerate the original pin. Each pair of digits in the rewritten pin represents an original base-10 digit. We convert each base-3 number to base 10: • First digit: 12_3 = (1 × 3^1) + (2 × 3^0) = 3 + 2 = 5_10 • Second digit: 20_3 = (2 × 3^1) + (0 × 3^0) = 6 + 0 = 6_10 • Third digit: 22_3 = (2 × 3^1) + (2 × 3^0) = 6 + 2 = 8_10 • Fourth digit: 10_3 = (1 × 3^1) + (0 × 3^0) = 3 + 0 = 3_10 The original ATM pin is 5683. b) Step 1: Determine the check intervals in minutes. The nurse checks every 2 hours, which is 2 × 60 = 120 minutes. The doctor checks every 4.5 hours, which is 4.5 × 60 = 270 minutes. Step 2: Find the least common multiple (LCM) of the check intervals. We need to find LCM(120, 270). Prime factorization of 120: 120 = 2^3 × 3 × 5 Prime factorization of 270: 270 = 2 × 3^3 × 5 LCM(120, 270) = 2^3 × 3^3 × 5 = 8 × 27 × 5 = 1080 minutes. Step 3: Convert the LCM to hours and add to the last check time. 1080 minutes = (1080)/(60) = 18 hours. They last checked together at 9:30 am. Adding 18 hours to 9:30 am: 9:30 am + 12 hours = 9:30 pm 9:30 pm + 6 hours = 3:30 am (the next day) They will check on him again at the same time at 3:30 am. c) Step 1: Calculate the time spent on resting and eating per day. Total hours in a day = 24 hours. Resting time = (3)/(8) × 24 hours = 9 hours. Eating time = (1)/(6) × 24 hours = 4 hours. Step 2: Calculate the remaining time and time spent on a healthy diet. Remaining time after resting and eating = 24 - 9 - 4 = 11 hours. Time spent having a healthy diet = (2)/(3) × 11 hours = (22)/(3) hours. Step 3: Calculate the time spent visiting the hospital per day. Time spent visiting the hospital = Remaining time - Healthy diet time Time spent visiting the hospital = 11 - (22)/(3) = (33)/(3) - (22)/(3) = (11)/(3) hours per day. Step 4: Calculate the total hours spent visiting the hospital in a week. Total hours per week = (11)/(3) hours/day × 7 days/week = (77)/(3) hours/week. (77)/(3) hours = 25 (2)/(3) hours. He spends (77)/(3) hours or 25 (2)/(3) hours visiting the hospital in a week. Send me the next one 📸