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question:Clara is a classical musician who loves performing on her cello. She has a collection of 24 music pieces she plans to practice this month. She decides to practice 3 different pieces every day. However, she also wants to dedicate every Sunday to performing her favorite piece, which she plays twice that day. If the month starts on a Monday and has 30 days in total, how many times will Clara play her favorite piece by the end of the month?
answer:To solve the problem, let's go through the details step-by-step:1. Understand the Month's Layout: - The month starts on a Monday and has 30 days. - The days of the week will cycle as follows: - Week 1: Mon (Day 1), Tue (Day 2), Wed (Day 3), Thu (Day 4), Fri (Day 5), Sat (Day 6), Sun (Day 7). - Week 2: Mon (Day 8), Tue (Day 9), Wed (Day 10), Thu (Day 11), Fri (Day 12), Sat (Day 13), Sun (Day 14). - Week 3: Mon (Day 15), Tue (Day 16), Wed (Day 17), Thu (Day 18), Fri (Day 19), Sat (Day 20), Sun (Day 21). - Week 4: Mon (Day 22), Tue (Day 23), Wed (Day 24), Thu (Day 25), Fri (Day 26), Sat (Day 27), Sun (Day 28). - Week 5: Mon (Day 29), Tue (Day 30).2. Identify Sundays: - The Sundays in this month are on Day 7, Day 14, Day 21, and Day 28.3. Determine Clara's Practice Schedule: - Clara practices her favorite piece on Sundays, playing it twice on each of those days.4. Calculate the Number of Sundays: - There are 4 Sundays in the month: Day 7, Day 14, Day 21, and Day 28.5. Calculate the Total Plays of Her Favorite Piece: - On each Sunday, Clara plays her favorite piece twice. - Therefore, for 4 Sundays, she plays her favorite piece (4 times 2 = 8) times.Thus, by the end of the month, Clara will have played her favorite piece 8 times.# 8
question:A skilled photographer at a glamping site takes 240 photos each day to capture the stunning beauty of the location. After a week of shooting, the photographer selects the best 35% of the total photos to showcase to a global audience. How many photos does the photographer select to showcase after the week of shooting?
answer:To solve the problem, we need to determine how many photos the photographer selects to showcase after a week of shooting. We'll follow these steps:1. Calculate the Total Number of Photos Taken in a Week: The photographer takes 240 photos each day. Since there are 7 days in a week, the total number of photos taken in a week is: [ 240 text{ photos/day} times 7 text{ days} = 1680 text{ photos} ]2. Determine the Percentage of Photos Selected: The photographer selects the best 35% of these photos.3. Calculate the Number of Photos Selected: To find 35% of the total photos taken, we calculate: [ 0.35 times 1680 = 588 ]Thus, the photographer selects 588 photos to showcase after the week of shooting.# 588
question:A patent lawyer named Alex offers pro-bono services to young companies who need help with intellectual property rights. This week, Alex helped 3 companies. The first company needed 6 hours of work, the second company needed twice as many hours as the first company, and the third company required 4 fewer hours than the second company. How many total hours did Alex spend helping these companies?
answer:To solve the problem, we need to calculate the total number of hours Alex spent helping the three companies.1. Determine the hours for each company: - The first company needed 6 hours. - The second company needed twice as many hours as the first company. Therefore, the second company needed: [ 2 times 6 = 12 text{ hours} ] - The third company required 4 fewer hours than the second company. Therefore, the third company needed: [ 12 - 4 = 8 text{ hours} ]2. Calculate the total hours: - Add the hours for all three companies to find the total hours Alex spent: [ 6 + 12 + 8 = 26 text{ hours} ]Thus, the total number of hours Alex spent helping the companies is 26 hours.# 26
question:Alex is a professional tennis player who uses game plans created by their student coach, Jamie, to enhance performance during matches. For an upcoming tournament, Jamie has developed a plan that includes a series of practice drills. Each drill session takes 45 minutes, and Alex needs to complete a total of 10 drills before the tournament. Additionally, Jamie suggests that Alex should spend 15 minutes analyzing each drill session to improve the next one. How many total hours will Alex spend on practice drills and analysis sessions combined before the tournament?
answer:To solve this problem, we need to calculate the total time Alex spends on both practice drills and analysis sessions. Step-by-Step Solution:1. Determine the time spent on practice drills: - Each practice drill session takes 45 minutes. - Alex needs to complete 10 drills. - Total time for drills = 10 drills × 45 minutes/drill = 450 minutes.2. Determine the time spent on analysis sessions: - Each analysis session takes 15 minutes. - Alex analyzes each of the 10 drill sessions. - Total time for analysis = 10 sessions × 15 minutes/session = 150 minutes.3. Calculate the combined total time: - Total time spent on drills and analysis = 450 minutes (drills) + 150 minutes (analysis) = 600 minutes.4. Convert total time from minutes to hours: - There are 60 minutes in an hour. - Total hours = 600 minutes ÷ 60 minutes/hour = 10 hours.Therefore, the total number of hours Alex will spend on practice drills and analysis sessions combined before the tournament is:# 10 hours
question:A manufacturing company executive wants to optimize their production process using edge computing. Currently, the company produces 500 gadgets per day. By implementing edge computing, they estimate that they can increase their production efficiency by 20%. After the implementation, they also plan to reduce the working days from 30 days to 25 days per month to save on operational costs. How many gadgets will they produce in a month after these changes are made?
answer:To solve this problem, let's go through the steps one by one:1. Current Production Calculation: - The company currently produces 500 gadgets per day.2. Efficiency Increase: - With edge computing, the production efficiency increases by 20%. - This means the new production rate per day will be 20% more than the current rate. - Calculate the increase in production per day: [ text{Increase in production per day} = 500 times 0.20 = 100 text{ gadgets} ] - Therefore, the new production rate per day is: [ 500 + 100 = 600 text{ gadgets per day} ]3. Change in Working Days: - The company plans to reduce the number of working days from 30 to 25 days per month.4. New Monthly Production Calculation: - Multiply the new daily production rate by the new number of working days: [ text{Monthly production} = 600 text{ gadgets/day} times 25 text{ days} = 15000 text{ gadgets} ]Thus, after implementing edge computing and changing the working days, the company will produce 15,000 gadgets in a month.# 15000
question:A career consultant in Toronto, who specializes in the investment and finance industry, is planning a series of workshops for aspiring financial analysts. Each workshop can accommodate a maximum of 25 participants. The consultant plans to hold 4 workshops per month over the next 3 months. If the consultant charges each participant 150 for attending a workshop, how much total revenue can the consultant expect to earn from all the workshops over the 3 months, assuming each workshop is fully booked?
answer:To solve the problem, we need to calculate the total revenue the consultant can expect to earn from all the workshops over the 3 months, assuming each workshop is fully booked.Step 1: Calculate the total number of workshops.- The consultant plans to hold 4 workshops per month.- The duration is 3 months.- Therefore, the total number of workshops = 4 workshops/month * 3 months = 12 workshops.Step 2: Calculate the maximum number of participants the consultant can accommodate in all workshops.- Each workshop can accommodate a maximum of 25 participants.- Therefore, the total number of participants for all workshops = 25 participants/workshop * 12 workshops = 300 participants.Step 3: Calculate the total revenue from all workshops.- The consultant charges 150 per participant.- Therefore, the total revenue = 300 participants * 150/participant = 45,000.Final Answer:# 45,000