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question:The museum curator is planning a new exhibit inspired by backpackers' stories. They decide to feature 5 different backpacking journeys, each represented by a section in the exhibit. The first section will include 12 photographs, the second section will have twice as many photographs as the first section, the third section will have 8 fewer photographs than the second section, the fourth section will have the same number of photographs as the third section, and the fifth section will include 3 more photographs than the second section. How many photographs are there in total across all five sections of the exhibit?
answer:To solve this problem, we need to determine the number of photographs in each section of the exhibit and then sum these numbers to find the total number of photographs.1. First Section: - The first section has 12 photographs.2. Second Section: - The second section has twice as many photographs as the first section. - Number of photographs in the second section = 2 * 12 = 24.3. Third Section: - The third section has 8 fewer photographs than the second section. - Number of photographs in the third section = 24 - 8 = 16.4. Fourth Section: - The fourth section has the same number of photographs as the third section. - Number of photographs in the fourth section = 16.5. Fifth Section: - The fifth section has 3 more photographs than the second section. - Number of photographs in the fifth section = 24 + 3 = 27.Now, let's find the total number of photographs across all sections by adding the photographs from each section:- Total number of photographs = (Photographs in first section) + (Photographs in second section) + (Photographs in third section) + (Photographs in fourth section) + (Photographs in fifth section)- Total number of photographs = 12 + 24 + 16 + 16 + 27Calculate the total:[12 + 24 = 36][36 + 16 = 52][52 + 16 = 68][68 + 27 = 95]The total number of photographs across all five sections is 95.# 95
question:Maria, a theatre critic based in Montevideo, Uruguay, is planning her schedule for the week to review several plays. On Monday, she reviews a play at the Teatro Solís, which lasts for 2 hours and 30 minutes. On Wednesday, she attends another play at a smaller theater that lasts for 1 hour and 45 minutes. On Friday, she has a double feature to review, with the first play lasting 1 hour and 20 minutes and the second play lasting 2 hours and 10 minutes. How many total hours and minutes does Maria spend watching plays this week?
answer:To find the total time Maria spends watching plays this week, we need to sum the durations of each play she attends. Let's break it down step-by-step:1. Monday: - Duration: 2 hours and 30 minutes2. Wednesday: - Duration: 1 hour and 45 minutes3. Friday: - First play: 1 hour and 20 minutes - Second play: 2 hours and 10 minutes - Total for Friday: 1 hour 20 minutes + 2 hours 10 minutesLet's calculate the total duration for Friday:- Convert the minutes to a common unit: - 20 minutes + 10 minutes = 30 minutes- Convert the hours to a common unit: - 1 hour + 2 hours = 3 hoursThus, the total duration for Friday is 3 hours and 30 minutes.Now, let's add up all the durations for the week:- Monday: 2 hours 30 minutes- Wednesday: 1 hour 45 minutes- Friday: 3 hours 30 minutesFirst, add up all the minutes:- 30 minutes (Monday) + 45 minutes (Wednesday) + 30 minutes (Friday) = 105 minutesConvert the total minutes to hours and minutes:- 105 minutes = 1 hour and 45 minutes (since 60 minutes = 1 hour, 105 minutes = 60 minutes + 45 minutes)Now, add up all the hours separately and include the converted hours from the minutes:- Hours from plays: 2 hours (Monday) + 1 hour (Wednesday) + 3 hours (Friday) = 6 hours- Converted hours from minutes: 1 hourThe grand total of hours is:- 6 hours + 1 hour = 7 hoursSo, the total time spent is:- 7 hours and 45 minutes#7 hours and 45 minutes
question:An art historian parent is studying a collection of Mesopotamian pottery pieces. In one section of the museum, there are 12 shelves, each displaying 8 pottery pieces. During a special exhibition, the parent learns that 3 additional shelves will be added, each holding 6 pottery pieces. Unfortunately, due to space constraints, 10 pieces from the original 96 pieces must be removed from the exhibition. How many Mesopotamian pottery pieces will be displayed in total after these changes?
answer:To solve this problem, we'll follow these steps:1. Calculate the initial number of pottery pieces: - There are 12 shelves, each displaying 8 pottery pieces. - Total initial pottery pieces = 12 shelves * 8 pieces/shelf = 96 pieces.2. Calculate the additional pottery pieces from the new shelves: - There are 3 additional shelves, each holding 6 pottery pieces. - Additional pottery pieces = 3 shelves * 6 pieces/shelf = 18 pieces.3. Calculate the total number of pottery pieces before removing any: - Total pottery pieces before removal = Initial pieces + Additional pieces - Total = 96 pieces + 18 pieces = 114 pieces.4. Remove the 10 pieces due to space constraints: - Total pottery pieces after removal = Total before removal - Removed pieces - Total after removal = 114 pieces - 10 pieces = 104 pieces.After following these steps, the total number of Mesopotamian pottery pieces displayed after the changes is:# 104
question:Nurse Practitioner Alex specializes in infectious diseases and collaborates with a pharmacist to prepare medication doses for patients. Today, Alex has 3 patients who require different dosages of a certain medication. Patient A needs 150 mg, Patient B needs 200 mg, and Patient C needs 250 mg. The pharmacist informs Alex that the medication comes in 50 mg tablets. How many tablets in total will Alex need to provide the correct dosages for all three patients?
answer:To solve this problem, we need to determine the total number of 50 mg tablets required to provide the exact dosages for all three patients: Patient A, Patient B, and Patient C.Step 1: Calculate the number of tablets needed for Patient A.- Patient A needs 150 mg.- Each tablet is 50 mg.- To find the number of tablets needed: [ text{Number of tablets for Patient A} = frac{150 text{ mg}}{50 text{ mg/tablet}} = 3 text{ tablets} ]Step 2: Calculate the number of tablets needed for Patient B.- Patient B needs 200 mg.- Each tablet is 50 mg.- To find the number of tablets needed: [ text{Number of tablets for Patient B} = frac{200 text{ mg}}{50 text{ mg/tablet}} = 4 text{ tablets} ]Step 3: Calculate the number of tablets needed for Patient C.- Patient C needs 250 mg.- Each tablet is 50 mg.- To find the number of tablets needed: [ text{Number of tablets for Patient C} = frac{250 text{ mg}}{50 text{ mg/tablet}} = 5 text{ tablets} ]Step 4: Calculate the total number of tablets needed for all patients.- Add the number of tablets needed for each patient: [ text{Total tablets} = 3 text{ (Patient A)} + 4 text{ (Patient B)} + 5 text{ (Patient C)} = 12 text{ tablets} ]# 12
question:A renewable energy advocate is giving a presentation about how switching to solar energy can help protect honeybees by reducing pollution from fossil fuels. In her presentation, she mentions that a local community plans to install solar panels that will reduce carbon emissions by 500 pounds per month. She explains that research indicates every 100 pounds reduction in carbon emissions helps save 2 honeybee colonies from the harmful effects of pollution.If the community successfully installs the solar panels, how many honeybee colonies can be saved from the harmful effects of pollution in one year?
answer:To solve this problem, we need to determine how many honeybee colonies can be saved in one year if the community installs solar panels that reduce carbon emissions by 500 pounds per month. We are given that every 100 pounds reduction in carbon emissions helps save 2 honeybee colonies.Let's follow these steps:1. Determine the monthly impact on honeybee colonies: - The solar panels reduce carbon emissions by 500 pounds per month. - For every 100 pounds reduction, 2 honeybee colonies are saved. - Therefore, for 500 pounds reduction, the number of honeybee colonies saved per month is ((500 text{ pounds}) times left(frac{2 text{ colonies}}{100 text{ pounds}}right)).2. Calculate the number of honeybee colonies saved per month: [ frac{500 times 2}{100} = 10 text{ colonies} ]3. Determine the annual impact on honeybee colonies: - Since 10 honeybee colonies are saved per month, over 12 months, the total number of colonies saved is: [ 10 text{ colonies/month} times 12 text{ months} = 120 text{ colonies} ]Thus, if the community successfully installs the solar panels, they can save 120 honeybee colonies from the harmful effects of pollution in one year.# 120
question:A tech-savvy hacker is tasked with securely sharing important information with a group of whistleblowers. To ensure security, the hacker decides to encrypt the information into data packets. Each data packet can contain up to 150 kilobytes of data. The entire information file is 1,800 kilobytes in size. Once packetized, the hacker needs to send these packets to 3 different whistleblowers. To maintain security, the hacker decides to send each whistleblower an equal number of packets. How many data packets does each whistleblower receive?
answer:To solve this problem, we need to determine the total number of data packets and then evenly distribute these packets to the three whistleblowers.Step 1: Calculate the total number of data packets.- The entire information file is 1,800 kilobytes in size.- Each data packet can contain up to 150 kilobytes of data.To find the total number of packets required, divide the total size of the file by the size of each packet:[text{Total packets} = frac{1800 text{ kilobytes}}{150 text{ kilobytes per packet}} = 12 text{ packets}]Step 2: Distribute packets evenly among whistleblowers.- There are 3 whistleblowers.To find out how many packets each whistleblower receives, divide the total number of packets by the number of whistleblowers:[text{Packets per whistleblower} = frac{12 text{ packets}}{3 text{ whistleblowers}} = 4 text{ packets}]Thus, each whistleblower receives 4 data packets.# 4