answer：First, I need to determine how many days Alex volunteers each week, which is 5 days.Next, I'll calculate the cost of buying lunch each day. Since each meal costs 10, the total cost for 5 days would be 5 multiplied by 10, which equals 50.Then, I'll calculate the cost of bringing snacks from home. Each day, the snacks cost 3, so for 5 days, the total cost is 5 multiplied by 3, which equals 15.Finally, to find out how much Alex saves by bringing snacks instead of buying lunch, I'll subtract the total snack cost from the total lunch cost: 50 minus 15 equals 35 saved each week.

answer：To determine the area allocated for the rooftop garden, I first need to calculate the total area of the rooftop.The building is rectangular, so the area is found by multiplying its length by its width.Given that the length is 120 feet and the width is 80 feet, the total area is 120 multiplied by 80, which equals 9,600 square feet.The architect wants to allocate 25% of this area for the garden. To find 25% of 9,600 square feet, I multiply 9,600 by 0.25.This calculation results in 2,400 square feet.Therefore, the area allocated for the rooftop garden is 2,400 square feet.

answer：Alright, so I need to figure out if Dr. Alicia can maintain her 8-hour sleep schedule throughout the week given her conference schedule and flight times. If she can't, I need to identify the first day she fails. Then, I also need to calculate the total number of hours she can sleep during flights if she takes short naps, ensuring her schedule remains feasible.First, let me break down the problem. Dr. Alicia has conferences each day from Monday to Friday in different cities with different time zones. After each conference, she flies to the next city, each flight taking exactly 10 hours. She needs at least 1 hour to prepare for the next conference after arriving. She sleeps exactly 8 hours each night. So, I need to check her schedule day by day, considering the time zone changes, flight durations, and preparation time to see if she can get 8 hours of sleep each night.Let me list out the details:- **Monday**: Conference in City A (UTC-5) from 9:00 AM to 5:00 PM. Then flies to City B (UTC+1), flight takes 10 hours. Needs 1 hour to prepare for Tuesday's conference.- **Tuesday**: Conference in City B (UTC+1) from 10:00 AM to 6:00 PM. Then flies to City C (UTC+9), flight takes 10 hours. Needs 1 hour to prepare for Wednesday's conference.- **Wednesday**: Conference in City C (UTC+9) from 11:00 AM to 7:00 PM. Then flies to City D (UTC-3), flight takes 10 hours. Needs 1 hour to prepare for Thursday's conference.- **Thursday**: Conference in City D (UTC-3) from 8:00 AM to 4:00 PM. Then flies to City E (UTC+3), flight takes 10 hours. Needs 1 hour to prepare for Friday's conference.- **Friday**: Conference in City E (UTC+3) from 9:00 AM to 5:00 PM. Then, I assume she might fly back, but since the problem doesn't specify beyond Friday, maybe she doesn't need to fly after Friday? Or perhaps she just stays there? The problem says "for the entire week," so maybe she doesn't fly after Friday. I'll assume she doesn't fly after Friday, so no flight on Friday night.So, starting from Monday, I need to track her time in each city, including the flight times and preparation times, and see if she can get 8 hours of sleep each night.I think the key here is to convert all the times to a common time zone, probably her home time zone, but since she's moving between different time zones, maybe it's better to convert everything to UTC and then calculate the local times accordingly.Alternatively, I can track her local time in each city, considering the flight duration and time zone changes.Wait, perhaps the best approach is to model each day as follows:1. For each day, determine the local time she starts and ends the conference.2. After the conference ends, she flies for 10 hours. So, the flight departure time is the end of the conference, and arrival time is 10 hours later in UTC, but then we need to convert that arrival time to the next city's local time.3. After arriving, she needs 1 hour to prepare, so the next conference starts 1 hour after arrival.4. Then, between the end of the previous day's conference and the start of the next day's conference, we need to calculate the time available for sleep.But wait, actually, the sleep occurs between the end of the day and the next day's start, but considering the flight and preparation time.Wait, perhaps it's better to model each transition:For example, starting from Monday:- Conference in City A (UTC-5) from 9:00 AM to 5:00 PM local time.- So, conference ends at 5:00 PM UTC-5. Then she departs for City B (UTC+1). The flight takes 10 hours.So, the flight departs at 5:00 PM UTC-5. Let's convert that to UTC: UTC-5 is 5 hours behind UTC, so 5:00 PM UTC-5 is 10:00 PM UTC.The flight takes 10 hours, so arrival in UTC is 10:00 PM + 10 hours = 8:00 AM UTC next day.Now, City B is UTC+1, so arrival time in City B is 8:00 AM UTC + 1 hour = 9:00 AM local time.She needs 1 hour to prepare, so the next conference starts at 10:00 AM local time.So, the time between arrival and the next conference is 1 hour, which is her preparation time. Therefore, the time available for sleep is from the end of the previous day's conference (5:00 PM UTC-5) to the start of the next day's conference (10:00 AM UTC+1), minus the flight and preparation time.Wait, no. Let me think again.Wait, the flight departs at 5:00 PM UTC-5 (Monday), arrives at 9:00 AM UTC+1 (Tuesday). So, the time between departure and arrival is 10 hours, which is the flight duration.But in terms of local time, she departs City A at 5:00 PM Monday, arrives in City B at 9:00 AM Tuesday.So, the time between 5:00 PM Monday UTC-5 and 9:00 AM Tuesday UTC+1 is 10 hours flight, but in terms of local time, how much time passes?Wait, perhaps it's better to convert all times to UTC to avoid confusion.So, Monday:- Conference in City A (UTC-5): 9:00 AM to 5:00 PM local.Convert to UTC: 9:00 AM UTC-5 is 2:00 PM UTC. 5:00 PM UTC-5 is 10:00 PM UTC.So, conference ends at 10:00 PM UTC on Monday.She departs immediately for City B (UTC+1). Flight takes 10 hours, so arrives at 10:00 PM + 10 hours = 8:00 AM UTC on Tuesday.Convert arrival time to City B local time: UTC+1, so 8:00 AM UTC is 9:00 AM local time in City B.She needs 1 hour to prepare, so the next conference starts at 10:00 AM local time.So, the time between arrival and the next conference is 1 hour, which is her preparation time.Therefore, the time available for sleep is from the end of Monday's conference (10:00 PM UTC) to the start of Tuesday's conference (10:00 AM UTC+1). Wait, but she arrives at 9:00 AM local time, which is 8:00 AM UTC.Wait, perhaps I need to calculate the time between the end of Monday's conference and the start of Tuesday's conference, considering the flight and preparation time.Wait, let's model it step by step:1. Monday: - Conference ends at 5:00 PM UTC-5 = 10:00 PM UTC. - Departs for City B at 10:00 PM UTC. - Flight takes 10 hours, arrives at 8:00 AM UTC on Tuesday. - Arrival in City B is 8:00 AM UTC = 9:00 AM local time. - Prep time: 1 hour, so next conference starts at 10:00 AM local time.So, the time between the end of Monday's conference (10:00 PM UTC) and the start of Tuesday's conference (10:00 AM UTC+1) is:From 10:00 PM UTC Monday to 9:00 AM UTC Tuesday is 11 hours.But she arrives at 9:00 AM local time, which is 8:00 AM UTC. Wait, no, arrival is 8:00 AM UTC, which is 9:00 AM local in City B.Wait, I think I'm getting confused.Let me try to track her schedule in UTC:- Monday: - Conference ends at 10:00 PM UTC. - Departs at 10:00 PM UTC. - Flight takes 10 hours, arrives at 8:00 AM UTC on Tuesday. - Arrival in City B is 8:00 AM UTC, which is 9:00 AM local time. - Prep time: 1 hour, so next conference starts at 10:00 AM local time.So, the time between 10:00 PM UTC Monday and 10:00 AM UTC+1 Tuesday is:From 10:00 PM UTC to 10:00 AM UTC+1 is 11 hours (since UTC+1 is one hour ahead).But she arrives at 8:00 AM UTC, which is 9:00 AM local. So, from 10:00 PM UTC Monday to 8:00 AM UTC Tuesday is 10 hours (flight time). Then, from 8:00 AM UTC to 10:00 AM UTC+1 is 2 hours (since 8:00 AM UTC is 9:00 AM local, and 10:00 AM local is 9:00 AM UTC).Wait, this is getting too convoluted. Maybe I should track her schedule in local time for each city, considering the flight duration and time zone changes.Alternatively, perhaps I should calculate the total time between the end of one conference and the start of the next, subtracting flight and preparation time, and see if the remaining time is at least 8 hours for sleep.Let me try that approach.Starting from Monday:- Conference ends at 5:00 PM UTC-5.- Departs immediately for City B (UTC+1). Flight takes 10 hours.- Arrival in City B: 5:00 PM UTC-5 + 10 hours flight = 3:00 AM UTC-5 + 10 hours = 5:00 PM + 10 hours = 3:00 AM next day UTC-5? Wait, no, that's not correct.Wait, 5:00 PM UTC-5 is 10:00 PM UTC. Adding 10 hours flight time, arrival is 8:00 AM UTC next day.Convert 8:00 AM UTC to City B (UTC+1): 9:00 AM.She needs 1 hour to prepare, so next conference starts at 10:00 AM local time.So, the time between the end of Monday's conference (5:00 PM UTC-5) and the start of Tuesday's conference (10:00 AM UTC+1) is:From 5:00 PM UTC-5 to 10:00 AM UTC+1.Convert both times to UTC:5:00 PM UTC-5 = 10:00 PM UTC.10:00 AM UTC+1 = 9:00 AM UTC.So, the time between 10:00 PM UTC Monday and 9:00 AM UTC Tuesday is 11 hours.But she departs at 10:00 PM UTC, flies for 10 hours, arrives at 8:00 AM UTC, which is 9:00 AM local in City B. Then, she prepares for 1 hour, so the next conference starts at 10:00 AM local.Therefore, the time available for sleep is from the end of Monday's conference (10:00 PM UTC) to the start of Tuesday's conference (10:00 AM UTC+1), which is 11 hours in UTC, but she is in City B, so local time is 9:00 AM to 10:00 AM, which is 1 hour. Wait, no, that doesn't make sense.Wait, perhaps I need to calculate the time between the end of the day and the start of the next day, considering the flight and preparation.Wait, maybe it's better to think in terms of when she can go to sleep and when she needs to wake up.After each conference, she flies, arrives, prepares, and then has to be ready for the next conference.So, the time between the end of the current conference and the start of the next conference is:End of current conference -> flight -> arrival -> preparation -> start of next conference.So, the total time between end of current and start of next is flight time + preparation time + time zone difference.Wait, no, time zone difference affects the local time, but the flight duration is fixed.Wait, perhaps the key is to calculate the total time between the end of one conference and the start of the next, and see if it's at least 8 hours plus any necessary preparation.Wait, let me try to model it step by step for each day.Starting from Monday:1. **Monday**: - Conference ends at 5:00 PM UTC-5. - Departs immediately for City B (UTC+1). Flight takes 10 hours. - Arrival in City B: 5:00 PM UTC-5 + 10 hours = 3:00 AM UTC-5 next day? Wait, no, because UTC-5 is behind UTC by 5 hours. Wait, 5:00 PM UTC-5 is 10:00 PM UTC. Adding 10 hours flight, arrival is 8:00 AM UTC next day. Convert to City B (UTC+1): 8:00 AM UTC is 9:00 AM local. She needs 1 hour to prepare, so next conference starts at 10:00 AM local. So, the time between the end of Monday's conference (5:00 PM UTC-5) and the start of Tuesday's conference (10:00 AM UTC+1) is: From 5:00 PM UTC-5 to 10:00 AM UTC+1. Convert both to UTC: 5:00 PM UTC-5 = 10:00 PM UTC. 10:00 AM UTC+1 = 9:00 AM UTC. So, the time between 10:00 PM UTC Monday and 9:00 AM UTC Tuesday is 11 hours. But she departs at 10:00 PM UTC, flies for 10 hours, arrives at 8:00 AM UTC, which is 9:00 AM local in City B. Then, she prepares for 1 hour, so the next conference starts at 10:00 AM local. Therefore, the time available for sleep is from the end of Monday's conference (10:00 PM UTC) to the start of Tuesday's conference (10:00 AM UTC+1), which is 11 hours in UTC, but she is in City B, so local time is 9:00 AM to 10:00 AM, which is 1 hour. Wait, that can't be right. Wait, no, she arrives at 9:00 AM local time in City B, which is 8:00 AM UTC. So, from her perspective, she arrives at 9:00 AM, needs to prepare until 10:00 AM, then the conference starts. So, the time between the end of Monday's conference (5:00 PM UTC-5) and the start of Tuesday's conference (10:00 AM UTC+1) is: From 5:00 PM UTC-5 to 10:00 AM UTC+1. Let's convert both to UTC: 5:00 PM UTC-5 = 10:00 PM UTC. 10:00 AM UTC+1 = 9:00 AM UTC. So, the time between 10:00 PM UTC Monday and 9:00 AM UTC Tuesday is 11 hours. But she is flying during this time, so she is on the plane for 10 hours, arriving at 8:00 AM UTC, which is 9:00 AM local in City B. So, from her perspective, she departs at 10:00 PM UTC, arrives at 8:00 AM UTC, which is 10 hours later. Then, she has 1 hour to prepare, so the next conference starts at 9:00 AM UTC + 1 hour = 10:00 AM UTC+1. Wait, no, arrival is 8:00 AM UTC, which is 9:00 AM local. Prep time is 1 hour, so next conference starts at 10:00 AM local. So, the time available for sleep is from the end of Monday's conference (10:00 PM UTC) to the start of Tuesday's conference (10:00 AM UTC+1), which is 11 hours in UTC, but she is in City B, so local time is 9:00 AM to 10:00 AM, which is 1 hour. Wait, that doesn't make sense because she is on the plane for 10 hours. I think I'm mixing up the time zones. Let me try a different approach. Let's track her schedule in local time for each city, considering the flight duration and time zone changes. Starting from Monday: - **Monday**: - Conference in City A (UTC-5): 9:00 AM to 5:00 PM. - Departs at 5:00 PM UTC-5 for City B (UTC+1). Flight takes 10 hours. - Arrival in City B: 5:00 PM UTC-5 + 10 hours flight = 3:00 AM UTC-5 next day? Wait, no, because UTC-5 is behind UTC by 5 hours. Wait, 5:00 PM UTC-5 is 10:00 PM UTC. Adding 10 hours flight, arrival is 8:00 AM UTC next day. Convert to City B (UTC+1): 8:00 AM UTC is 9:00 AM local. She needs 1 hour to prepare, so next conference starts at 10:00 AM local. So, the time between the end of Monday's conference (5:00 PM UTC-5) and the start of Tuesday's conference (10:00 AM UTC+1) is: From 5:00 PM UTC-5 to 10:00 AM UTC+1. Convert both to UTC: 5:00 PM UTC-5 = 10:00 PM UTC. 10:00 AM UTC+1 = 9:00 AM UTC. So, the time between 10:00 PM UTC Monday and 9:00 AM UTC Tuesday is 11 hours. But she is on the plane for 10 hours, arriving at 8:00 AM UTC, which is 9:00 AM local in City B. Then, she prepares for 1 hour, so the next conference starts at 10:00 AM local. Therefore, the time available for sleep is from the end of Monday's conference (10:00 PM UTC) to the start of Tuesday's conference (10:00 AM UTC+1), which is 11 hours in UTC, but she is in City B, so local time is 9:00 AM to 10:00 AM, which is 1 hour. Wait, that can't be right because she is on the plane for 10 hours. I think I'm overcomplicating this. Let's try to calculate the time available for sleep each night. After each conference, she flies, arrives, prepares, and then has to sleep before the next conference. So, the time available for sleep is the time between the end of the current conference and the start of the next conference, minus flight time and preparation time. Wait, no, because the flight and preparation time are part of the transition between conferences. So, the total time between the end of one conference and the start of the next is flight time + preparation time + time zone difference. Wait, perhaps not. Let me think. Let's consider the time between the end of Monday's conference and the start of Tuesday's conference. - End of Monday's conference: 5:00 PM UTC-5. - Departs immediately: 5:00 PM UTC-5. - Flight takes 10 hours, arrives at 3:00 AM UTC-5 + 10 hours = 5:00 PM + 10 hours = 3:00 AM next day UTC-5? Wait, no, because UTC-5 is behind UTC by 5 hours. Wait, 5:00 PM UTC-5 is 10:00 PM UTC. Adding 10 hours flight, arrival is 8:00 AM UTC next day. Convert to City B (UTC+1): 8:00 AM UTC is 9:00 AM local. She needs 1 hour to prepare, so next conference starts at 10:00 AM local. So, the time between the end of Monday's conference (5:00 PM UTC-5) and the start of Tuesday's conference (10:00 AM UTC+1) is: From 5:00 PM UTC-5 to 10:00 AM UTC+1. Convert both to UTC: 5:00 PM UTC-5 = 10:00 PM UTC. 10:00 AM UTC+1 = 9:00 AM UTC. So, the time between 10:00 PM UTC Monday and 9:00 AM UTC Tuesday is 11 hours. But she is on the plane for 10 hours, arriving at 8:00 AM UTC, which is 9:00 AM local in City B. Then, she prepares for 1 hour, so the next conference starts at 10:00 AM local. Therefore, the time available for sleep is from the end of Monday's conference (10:00 PM UTC) to the start of Tuesday's conference (10:00 AM UTC+1), which is 11 hours in UTC, but she is in City B, so local time is 9:00 AM to 10:00 AM, which is 1 hour. Wait, that can't be right because she is on the plane for 10 hours. I think I'm making a mistake here. Let me try to calculate the time available for sleep each night. After Monday's conference, she flies to City B, which takes 10 hours. So, she is on the plane from 5:00 PM UTC-5 (Monday) to 3:00 AM UTC-5 (Tuesday). Wait, no, because UTC-5 is behind UTC by 5 hours. Wait, 5:00 PM UTC-5 is 10:00 PM UTC. Adding 10 hours flight, arrival is 8:00 AM UTC, which is 9:00 AM local in City B. So, the time between the end of Monday's conference (10:00 PM UTC) and the start of Tuesday's conference (10:00 AM UTC+1) is 11 hours. But she is on the plane for 10 hours, so the time available for sleep is 11 hours - 10 hours flight - 1 hour preparation = 0 hours. Wait, that can't be right. Wait, no, the flight is part of the transition, so the time available for sleep is the time between the end of the conference and the start of the next conference, minus flight and preparation time. So, time available for sleep = (start of next conference - end of current conference) - (flight time + preparation time). Let's calculate that. For Monday to Tuesday: Start of next conference (Tuesday): 10:00 AM UTC+1. End of current conference (Monday): 5:00 PM UTC-5. Convert both to UTC: 5:00 PM UTC-5 = 10:00 PM UTC. 10:00 AM UTC+1 = 9:00 AM UTC. So, the time between end of Monday and start of Tuesday is from 10:00 PM UTC to 9:00 AM UTC next day, which is 11 hours. Flight time: 10 hours. Preparation time: 1 hour. So, time available for sleep = 11 hours - 10 hours - 1 hour = 0 hours. That means she has no time to sleep between Monday and Tuesday. But she needs 8 hours of sleep each night. So, she fails on Monday night. Wait, that can't be right because she needs to sleep 8 hours each night. If she has 0 hours available, she can't sleep at all, which means she fails on Monday night. But let me double-check. From Monday's conference end (10:00 PM UTC) to Tuesday's conference start (9:00 AM UTC) is 11 hours. She spends 10 hours flying and 1 hour preparing, totaling 11 hours. So, she has no time left for sleep. Therefore, she cannot get any sleep on Monday night, which means she fails on Monday. Wait, but the problem says she has conferences from Monday to Friday. So, if she can't sleep on Monday night, that would be the first day she fails. But let me check the other days to see if my calculation is correct. Let's move to Tuesday: - Conference ends at 6:00 PM UTC+1. - Departs immediately for City C (UTC+9). Flight takes 10 hours. - Arrival in City C: 6:00 PM UTC+1 + 10 hours flight = 4:00 AM UTC+1 next day. Convert to UTC: 4:00 AM UTC+1 is 3:00 AM UTC. Convert to City C (UTC+9): 3:00 AM UTC is 12:00 PM local time. She needs 1 hour to prepare, so next conference starts at 1:00 PM local. The conference in City C is from 11:00 AM to 7:00 PM local. Wait, but she arrives at 12:00 PM local, prepares until 1:00 PM, so the conference starts at 1:00 PM, which is within the scheduled 11:00 AM to 7:00 PM. So, the time between the end of Tuesday's conference (6:00 PM UTC+1) and the start of Wednesday's conference (11:00 AM UTC+9) is: Convert both to UTC: 6:00 PM UTC+1 = 5:00 PM UTC. 11:00 AM UTC+9 = 2:00 AM UTC. So, the time between 5:00 PM UTC Tuesday and 2:00 AM UTC Wednesday is 9 hours. She spends 10 hours flying, which is more than the available time. Wait, that can't be right. Wait, no, she departs at 6:00 PM UTC+1 (Tuesday), which is 5:00 PM UTC. Flight takes 10 hours, arrives at 3:00 AM UTC next day. Convert to City C (UTC+9): 3:00 AM UTC is 12:00 PM local. So, arrival is 12:00 PM local, which is 12:00 PM UTC+9. She needs 1 hour to prepare, so next conference starts at 1:00 PM local. The conference is from 11:00 AM to 7:00 PM local, so she starts at 1:00 PM, which is fine. The time between the end of Tuesday's conference (6:00 PM UTC+1) and the start of Wednesday's conference (11:00 AM UTC+9) is: From 6:00 PM UTC+1 to 11:00 AM UTC+9. Convert both to UTC: 6:00 PM UTC+1 = 5:00 PM UTC. 11:00 AM UTC+9 = 2:00 AM UTC. So, the time between 5:00 PM UTC Tuesday and 2:00 AM UTC Wednesday is 9 hours. She spends 10 hours flying, which is more than the available time. Wait, that can't be right because she departs at 5:00 PM UTC, flies for 10 hours, arrives at 3:00 AM UTC, which is 12:00 PM local in City C. So, the time between departure and arrival is 10 hours, but the time between end of Tuesday's conference and start of Wednesday's conference is 9 hours in UTC. This suggests that she arrives at 3:00 AM UTC, which is 12:00 PM local, and then needs to prepare for 1 hour, so the conference starts at 1:00 PM local. Therefore, the time available for sleep is from the end of Tuesday's conference (5:00 PM UTC) to the start of Wednesday's conference (2:00 AM UTC), which is 9 hours. She spends 10 hours flying, which is more than the available time, so she can't sleep at all, but she needs 8 hours. So, she fails again. Wait, but this seems inconsistent with the previous calculation. I think I'm making a mistake in converting the times. Let me try to calculate the time available for sleep each night. For Monday night: - Conference ends at 5:00 PM UTC-5 (10:00 PM UTC). - Departs for City B, flight takes 10 hours, arrives at 8:00 AM UTC (9:00 AM local). - Prep time: 1 hour, next conference starts at 10:00 AM local. So, the time between 10:00 PM UTC Monday and 10:00 AM UTC+1 Tuesday is 11 hours. She spends 10 hours flying and 1 hour preparing, totaling 11 hours. So, no time left for sleep. Therefore, she cannot sleep on Monday night. For Tuesday night: - Conference ends at 6:00 PM UTC+1 (5:00 PM UTC). - Departs for City C, flight takes 10 hours, arrives at 3:00 AM UTC (12:00 PM local). - Prep time: 1 hour, next conference starts at 1:00 PM local. The time between 5:00 PM UTC Tuesday and 1:00 PM UTC+9 Wednesday is: Convert 1:00 PM UTC+9 to UTC: 1:00 PM - 9 hours = 4:00 AM UTC. So, the time between 5:00 PM UTC Tuesday and 4:00 AM UTC Wednesday is 11 hours. She spends 10 hours flying and 1 hour preparing, totaling 11 hours. So, again, no time left for sleep. Wait, that can't be right because she arrives at 3:00 AM UTC, which is 12:00 PM local, and then prepares until 1:00 PM, so the conference starts at 1:00 PM. The time between the end of Tuesday's conference (5:00 PM UTC) and the start of Wednesday's conference (4:00 AM UTC) is 11 hours. She spends 10 hours flying and 1 hour preparing, so again, no time for sleep. This suggests that she cannot sleep on Tuesday night either. Wait, but the conference on Wednesday starts at 11:00 AM local, which is 2:00 PM UTC. She arrives at 3:00 AM UTC, which is 12:00 PM local, prepares until 1:00 PM local, so the conference starts at 1:00 PM local, which is 2:00 PM UTC. So, the time between the end of Tuesday's conference (5:00 PM UTC) and the start of Wednesday's conference (2:00 PM UTC) is 9 hours. She spends 10 hours flying, which is more than the available time, so she can't sleep. Wait, this is confusing. Maybe I need to approach it differently. Let me create a table for each day, tracking the end of the conference, departure time, arrival time, preparation time, and start of the next conference, and calculate the time available for sleep. Let's start with Monday: **Monday**: - Conference ends at 5:00 PM UTC-5 (10:00 PM UTC). - Departs at 10:00 PM UTC. - Flight takes 10 hours, arrives at 8:00 AM UTC (9:00 AM UTC+1). - Prep time: 1 hour, next conference starts at 10:00 AM UTC+1 (9:00 AM UTC). So, the time between 10:00 PM UTC Monday and 9:00 AM UTC Tuesday is 11 hours. She spends 10 hours flying and 1 hour preparing, totaling 11 hours. So, no time left for sleep. Therefore, she cannot sleep on Monday night. **Tuesday**: - Conference ends at 6:00 PM UTC+1 (5:00 PM UTC). - Departs at 5:00 PM UTC. - Flight takes 10 hours, arrives at 3:00 AM UTC (12:00 PM UTC+9). - Prep time: 1 hour, next conference starts at 1:00 PM UTC+9 (4:00 AM UTC). The time between 5:00 PM UTC Tuesday and 4:00 AM UTC Wednesday is 11 hours. She spends 10 hours flying and 1 hour preparing, totaling 11 hours. So, no time left for sleep. Therefore, she cannot sleep on Tuesday night. **Wednesday**: - Conference ends at 7:00 PM UTC+9 (12:00 PM UTC). - Departs at 12:00 PM UTC. - Flight takes 10 hours, arrives at 10:00 PM UTC (7:00 AM UTC-3). - Prep time: 1 hour, next conference starts at 8:00 AM UTC-3 (5:00 AM UTC). The time between 12:00 PM UTC Wednesday and 5:00 AM UTC Thursday is 17 hours. She spends 10 hours flying and 1 hour preparing, totaling 11 hours. So, time available for sleep is 17 - 11 = 6 hours. She needs 8 hours, so she fails on Wednesday night. Wait, but let me check: - Conference ends at 7:00 PM UTC+9 (12:00 PM UTC). - Departs at 12:00 PM UTC. - Flight takes 10 hours, arrives at 10:00 PM UTC (7:00 AM UTC-3). - Prep time: 1 hour, next conference starts at 8:00 AM UTC-3 (5:00 AM UTC). The time between 12:00 PM UTC Wednesday and 5:00 AM UTC Thursday is 17 hours. She spends 10 hours flying and 1 hour preparing, so 17 - 11 = 6 hours available for sleep. Since she needs 8 hours, she fails on Wednesday night. **Thursday**: - Conference ends at 4:00 PM UTC-3 (7:00 PM UTC). - Departs at 7:00 PM UTC. - Flight takes 10 hours, arrives at 5:00 AM UTC (8:00 AM UTC+3). - Prep time: 1 hour, next conference starts at 9:00 AM UTC+3 (6:00 AM UTC). The time between 7:00 PM UTC Thursday and 6:00 AM UTC Friday is 11 hours. She spends 10 hours flying and 1 hour preparing, totaling 11 hours. So, no time left for sleep. Therefore, she cannot sleep on Thursday night. **Friday**: - Conference ends at 5:00 PM UTC+3 (2:00 PM UTC). - No flight after Friday, so she can sleep from 2:00 PM UTC to the next day, but since it's the last day, she doesn't need to fly, so she can sleep as much as she wants. But since the problem is about the entire week, and she fails on Monday night, that's the first day she fails. Wait, but according to the calculations, she fails on Monday night because she has no time to sleep. Then, on Tuesday night, same issue. On Wednesday night, she only gets 6 hours, which is less than 8. So, the first day she fails is Monday. Wait, but let me confirm: On Monday night, she has 0 hours available for sleep. On Tuesday night, same. On Wednesday night, 6 hours. So, the first day she fails is Monday. But let me check the flight from Wednesday to Thursday: - Conference ends at 7:00 PM UTC+9 (12:00 PM UTC). - Departs at 12:00 PM UTC. - Flight takes 10 hours, arrives at 10:00 PM UTC (7:00 AM UTC-3). - Prep time: 1 hour, next conference starts at 8:00 AM UTC-3 (5:00 AM UTC). The time between 12:00 PM UTC Wednesday and 5:00 AM UTC Thursday is 17 hours. She spends 10 hours flying and 1 hour preparing, so 17 - 11 = 6 hours available for sleep. So, she can sleep 6 hours on Wednesday night, which is less than 8. Therefore, the first day she fails is Monday. Wait, but the problem says "for the entire week," so if she fails on Monday, that's the first day. Alternatively, maybe I made a mistake in the Monday calculation. Let me re-examine Monday: - Conference ends at 5:00 PM UTC-5 (10:00 PM UTC). - Departs at 10:00 PM UTC. - Flight takes 10 hours, arrives at 8:00 AM UTC (9:00 AM UTC+1). - Prep time: 1 hour, next conference starts at 10:00 AM UTC+1 (9:00 AM UTC). So, the time between 10:00 PM UTC Monday and 9:00 AM UTC Tuesday is 11 hours. She spends 10 hours flying and 1 hour preparing, totaling 11 hours. So, no time left for sleep. Therefore, she cannot sleep on Monday night. So, the answer to question 1 is that she fails on Monday. For question 2, assuming she can take short naps during flights, how much can she sleep during flights? Each flight is 10 hours, so she can sleep during the flight. But she needs to prepare for 1 hour after arrival. So, the total flight time is 10 hours per day, except Friday, which she doesn't fly. So, from Monday to Thursday, she has 4 flights, each 10 hours. So, total flight time is 40 hours. If she can sleep during flights, she can sleep 10 hours each day, but she needs to prepare for 1 hour after each flight. Wait, but she needs to be awake to prepare, so she can't sleep the entire flight. Wait, the problem says she can take short naps during flights, trying to maximize her sleep time. So, she can sleep as much as possible during flights, but she needs to be awake for the preparation time after arrival. So, the maximum she can sleep during flights is the flight duration minus any time needed to be awake. But since she needs 1 hour to prepare after each flight, she can sleep the entire flight time minus the preparation time. Wait, no, the preparation time is after arrival, so it's separate from the flight. So, she can sleep the entire flight duration, as the preparation time is after the flight. Therefore, she can sleep 10 hours each flight. But wait, she needs to be awake to prepare, so she can't sleep the entire flight. Wait, the problem says she needs 1 hour to prepare after arriving. So, she can sleep during the flight, but she needs to be awake for the preparation. Therefore, she can sleep the entire flight duration, as the preparation is after the flight. So, for each flight, she can sleep 10 hours. Therefore, total sleep during flights is 4 flights * 10 hours = 40 hours. But she also needs to sleep 8 hours each night, but she can't because of the schedule. Wait, but the problem says she can take short naps during flights, and she tries to maximize her sleep time during these flights as well. So, she can sleep during flights, but she still needs to get 8 hours each night. Wait, no, the problem says she needs at least 8 hours of sleep each night, regardless of naps. So, naps during flights are in addition to her nightly sleep. Wait, no, the problem says she needs at least 8 hours of sleep each night, and she can take short naps during flights to maximize her sleep. So, the naps during flights are part of her total sleep time, but she still needs 8 hours each night. Wait, no, the problem says she needs at least 8 hours of sleep each night, and she can take naps during flights to maximize her sleep. So, the naps are in addition to her nightly sleep. Wait, but that would mean she can get more than 8 hours each night, but the problem says she needs at least 8 hours. Wait, perhaps the naps are to make up for the lack of sleep during the night. So, if she can't sleep 8 hours at night, she can take naps during flights to make up for it. But the problem says she needs at least 8 hours of sleep each night, so naps during flights are in addition to that. Wait, no, the problem says she can take short naps during flights, and she tries to maximize her sleep time during these flights as well. So, the naps during flights are part of her total sleep, but she still needs to get 8 hours each night. Wait, this is confusing. Let me re-read the problem: "Dr. Alicia is a renowned conference speaker who meticulously plans her schedule to ensure she gets exactly 8 hours of sleep every night. She has a series of back-to-back conferences in different cities, each requiring long flights and varying time zone changes. For the upcoming week, her schedule is as follows: ... She needs at least 1 hour to prepare for her next conference after arriving. 1. Given her strict sleep schedule and the need to prepare for each conference, determine if Dr. Alicia can maintain her 8-hour sleep regimen for the entire week. If not, identify the first day she fails to get 8 hours of sleep. 2. Assume Dr. Alicia can take short naps during flights, and she tries to maximize her sleep time during these flights as well. Calculate the total number of hours she can sleep during flights for the entire week, ensuring her schedule remains feasible." So, for question 1, she needs exactly 8 hours of sleep each night. For question 2, she can take naps during flights to maximize sleep, but the schedule remains feasible, meaning she still needs to get 8 hours each night. Wait, but if she can take naps during flights, maybe she can get more sleep, but the problem says she needs at least 8 hours each night. So, the naps are in addition to her nightly sleep. Wait, no, the problem says she can take short naps during flights, and she tries to maximize her sleep time during these flights as well. So, the naps are part of her total sleep time, but she still needs to get 8 hours each night. Wait, perhaps the naps can help her get the required 8 hours each night, even if her schedule doesn't allow it otherwise. So, for question 2, we need to calculate the total sleep she can get during flights, assuming she can nap as much as possible, while still maintaining her schedule. So, for each flight, she can sleep as much as possible, but she needs to be awake for the preparation time after arrival. So, for each flight, she can sleep the entire flight duration, as the preparation time is after the flight. Therefore, for each flight, she can sleep 10 hours. She has 4 flights (Monday to Thursday), so 4 * 10 = 40 hours. But she also needs to sleep 8 hours each night, so the total sleep she needs is 5 days * 8 hours = 40 hours. So, if she sleeps 40 hours during flights, she can meet her sleep requirement. Wait, but she also has to sleep at night, so the total sleep would be 40 (flights) + 40 (nights) = 80 hours, which is more than the total time available. Wait, no, because the flights are during the day, and the nights are separate. Wait, perhaps the flights are during the night, so she can sleep during flights and also sleep at night. Wait, but the problem doesn't specify when the flights are, just that they take 10 hours each. So, assuming she can sleep during flights, she can get 10 hours of sleep each flight, plus 8 hours each night. But the total time available is limited. Wait, perhaps the total sleep time is the sum of sleep during flights and sleep at night, but she needs to have 8 hours each night. Wait, I'm getting confused. Let me think differently. For question 2, she can take naps during flights to maximize her sleep, but she still needs to get 8 hours each night. So, the total sleep she can get is the sum of sleep during flights and sleep at night. But the problem says "ensuring her schedule remains feasible," which means she still needs to attend conferences on time. So, the maximum sleep she can get during flights is the flight duration, which is 10 hours per flight. She has 4 flights (Monday to Thursday), so 40 hours. Additionally, she needs to sleep 8 hours each night, which is 5 nights * 8 hours = 40 hours. So, total sleep time is 80 hours. But the total time available in the week is 7 days * 24 hours = 168 hours. She spends 5 days in conferences, each day 8 hours (from 9 AM to 5 PM, etc.), so 5 * 8 = 40 hours. She spends 4 flights * 10 hours = 40 hours. She spends 4 preparation times * 1 hour = 4 hours. So, total time spent: 40 (conferences) + 40 (flights) + 4 (preparation) = 84 hours. Therefore, the remaining time is 168 - 84 = 84 hours, which is exactly the total sleep time she needs (80 hours) plus some extra. Wait, but she needs 80 hours of sleep, so she can get 80 hours of sleep, and have 4 hours extra. So, the total sleep during flights is 40 hours, and sleep at night is 40 hours, totaling 80 hours. Therefore, the answer to question 2 is 40 hours. But wait, let me check: If she sleeps 10 hours each flight, that's 40 hours. She also needs to sleep 8 hours each night, which is 40 hours. So, total sleep is 80 hours. The total time available is 168 hours. Time spent on conferences: 5 days * 8 hours = 40 hours. Time spent on flights: 4 flights * 10 hours = 40 hours. Time spent on preparation: 4 days * 1 hour = 4 hours. Total time spent: 40 + 40 + 4 = 84 hours. Therefore, remaining time: 168 - 84 = 84 hours. She needs 80 hours of sleep, so she can get 80 hours, and have 4 hours extra. Therefore, the total sleep during flights is 40 hours. So, the answer to question 2 is 40 hours. But wait, the problem says "short naps during flights," so maybe she can't sleep the entire flight. But the problem says she tries to maximize her sleep time during flights, so she can sleep as much as possible, which is 10 hours per flight. Therefore, the total sleep during flights is 40 hours. So, to summarize: 1. She fails to get 8 hours of sleep on Monday night. 2. She can sleep 40 hours during flights. But let me confirm the first part again. On Monday night, she has 0 hours available for sleep. On Tuesday night, same. On Wednesday night, 6 hours. On Thursday night, 0 hours. On Friday night, she doesn't fly, so she can sleep 8 hours. Wait, but the problem is about the entire week, so she fails on Monday. Therefore, the answers are: 1. She fails on Monday. 2. She can sleep 40 hours during flights. But let me check the flight from Thursday to Friday: - Conference ends at 4:00 PM UTC-3 (7:00 PM UTC). - Departs at 7:00 PM UTC. - Flight takes 10 hours, arrives at 5:00 AM UTC (8:00 AM UTC+3). - Prep time: 1 hour, next conference starts at 9:00 AM UTC+3 (6:00 AM UTC). The time between 7:00 PM UTC Thursday and 6:00 AM UTC Friday is 11 hours. She spends 10 hours flying and 1 hour preparing, totaling 11 hours. So, no time left for sleep. Therefore, she cannot sleep on Thursday night. On Friday night, she doesn't fly, so she can sleep 8 hours. So, the total sleep she gets is: - Monday: 0 - Tuesday: 0 - Wednesday: 6 - Thursday: 0 - Friday: 8 Total: 14 hours. But she needs 5 * 8 = 40 hours. So, she is short by 26 hours. If she can sleep during flights, she can get 40 hours during flights, plus the 14 hours at night, totaling 54 hours, which is more than 40. Wait, but the problem says she needs at least 8 hours each night, so she can't just sleep during flights and skip night sleep. Wait, no, the problem says she can take naps during flights, but she still needs to get 8 hours each night. So, the naps during flights are in addition to her nightly sleep. Therefore, the total sleep she needs is 40 hours (8 * 5), and she can get 40 hours during flights, so she can meet her requirement. Therefore, the total sleep during flights is 40 hours. So, the answers are: 1. She fails on Monday. 2. She can sleep 40 hours during flights. But wait, in the first part, she fails on Monday because she can't sleep at all. But if she can sleep during flights, maybe she can adjust. Wait, no, the first part is without considering naps during flights. The second part is assuming she can take naps. So, for question 1, she fails on Monday. For question 2, she can sleep 40 hours during flights. Therefore, the answers are: 1. The first day she fails is Monday. 2. Total sleep during flights is 40 hours.

answer：First, I'll determine the number of successful serves Emily made each day.On Monday, she successfully landed 9 serves out of 15 attempts.On Tuesday, she increased her practice by 10%. This means she attempted 15 * 1.10 = 16.5 serves. However, since the number of serves should be a whole number, I'll round it to 17 attempts. She successfully landed 12 serves.On Wednesday, she increased her practice by another 5% from Tuesday. So, she attempted 16.5 * 1.05 = 17.325 serves, which I'll round to 17 attempts. She successfully landed 14 serves.Finally, I'll add up the successful serves from all three days: 9 + 12 + 14 = 35 successful serves.

answer：First, I need to determine the total amount of money that was allocated for the 15 public infrastructure projects. Since each of the 10 funded projects received 12 million forints, the total allocated funds can be calculated by multiplying 10 by 12 million forints.Next, I'll calculate the total amount of money that was actually distributed to the 10 projects. This is done by multiplying the number of funded projects (10) by the amount each project received (12 million forints).After finding the total allocated funds, I'll identify the amount that the corrupt official embezzled. The problem states that the official took 60% of the total allocated funds for personal gain. To find this amount, I'll calculate 60% of the total allocated funds.Finally, I'll present the calculated amount that the corrupt official embezzled as the final answer.

answer：First, I need to determine the annual administrative cost after implementing the software tool. The current cost is 500,000, and the software reduces costs by 15% each year. So, the cost after the reduction is 85% of the original cost.Next, I'll calculate the new annual cost by multiplying 500,000 by 0.85, which equals 425,000.Then, I'll find the annual savings by subtracting the new cost from the original cost: 500,000 minus 425,000 equals 75,000 saved each year.Finally, to find the total savings over three years, I'll multiply the annual savings by 3, resulting in 225,000.