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question:Alex is an attention-to-detail pharmaceutical document specialist who assists in the collation of documents for licensing applications. For a new project, Alex needs to compile a total of 120 document pages. Each application requires 8 different types of documents: safety reports, efficacy studies, manufacturing protocols, ingredient lists, regulatory compliance forms, clinical trial results, patient information leaflets, and quality assurance certificates. Each type consists of 5 pages, but due to an oversight, Alex has only received 3 pages for each type. How many additional pages does Alex need to request to complete the full set of documents for the application?
answer:To solve this problem, let's break it down step-by-step:1. Determine the pages needed for each type of document: - There are 8 different types of documents. - Each type of document should have 5 pages. Total pages needed = 8 types × 5 pages/type = 40 pages.2. Determine the pages Alex currently has: - Alex has received 3 pages for each type. - Therefore, for 8 types of documents, Alex currently has: Total pages Alex has = 8 types × 3 pages/type = 24 pages.3. Calculate the additional pages Alex needs to request: - To find the additional pages required, subtract the pages Alex currently has from the pages needed: Additional pages needed = Total pages needed - Total pages Alex has Additional pages needed = 40 pages - 24 pages = 16 pages.Thus, Alex needs to request 16 additional pages to complete the full set of documents for the application.# 16
question:Dr. Smith is a public health researcher studying the impact of travel on health. She is conducting a study in three different cities to understand how travel frequency affects people's health. In City A, 150 people travel at least once a week for work, and 60 people travel for leisure every month. In City B, 200 people travel weekly for work, and 80 people travel monthly for leisure. In City C, 250 people travel weekly for work, and 100 people travel monthly for leisure. Dr. Smith wants to know the total number of people across all three cities who travel either for work or leisure. How many people in total travel in a month considering those who travel weekly for work also travel four times a month?
answer:To find the total number of people traveling in a month across all three cities, we need to consider both those who travel weekly for work and those who travel monthly for leisure. Here is the step-by-step breakdown: City A:- People traveling weekly for work: 150 - Since they travel weekly, they make 4 trips in a month.- People traveling monthly for leisure: 60Total unique travelers in City A:- All people traveling for work are also traveling for leisure, so we need to add both groups together without counting anyone twice.- Total: 150 (work) + 60 (leisure) = 210 people City B:- People traveling weekly for work: 200 - Since they travel weekly, they make 4 trips in a month.- People traveling monthly for leisure: 80Total unique travelers in City B:- Total: 200 (work) + 80 (leisure) = 280 people City C:- People traveling weekly for work: 250 - Since they travel weekly, they make 4 trips in a month.- People traveling monthly for leisure: 100Total unique travelers in City C:- Total: 250 (work) + 100 (leisure) = 350 people Total across all cities:- City A: 210 people- City B: 280 people- City C: 350 peopleTotal number of unique people traveling in a month across all cities:- Total: 210 + 280 + 350 = 840 people# 840
question:Detective Hawthorne, known for his suspenseful and dramatic flair, is investigating a series of mysterious thefts at the local museum. During his investigation, he notices a peculiar pattern: the thief seems to strike every 3 days, stealing exactly 5 valuable pieces each time. Detective Hawthorne shares his observations with his partner, emphasizing the importance of details in cracking the case."If we don't catch the thief soon," he muses dramatically, "we'll have to calculate how many pieces they would have stolen by the end of a 30-day month. But remember, we started tracking from the first day of the month. We must be precise in our calculations to ensure we don't miss any crucial detail."How many valuable pieces will the thief have stolen by the end of the 30-day month, assuming they continue at the same rate?
answer:To find out how many valuable pieces the thief will have stolen by the end of the 30-day month, given the pattern of thefts, we can break down the problem as follows:1. Determine the Frequency of Thefts: The thief strikes every 3 days. 2. Calculate the Number of Thefts in 30 Days: To find out how many thefts occur in 30 days, we divide 30 by 3. [ text{Number of thefts} = frac{30}{3} = 10 ]3. Determine the Number of Pieces Stolen Per Theft: The thief steals 5 valuable pieces each time they strike.4. Calculate the Total Number of Pieces Stolen: Multiply the number of thefts by the number of pieces stolen per theft. [ text{Total pieces stolen} = 10 times 5 = 50 ]So, by the end of a 30-day month, the thief will have stolen a total of 50 valuable pieces.# 50
question:Attorney Lex, who moonlights as a pun-loving nerd, was preparing for a case and decided to use some playful math to lighten the mood. He had a collection of 20 law books and 15 comic books, each filled with his favorite punny jokes. He decided to organize them on his shelf in a pattern: for every 2 law books, he places 3 comic books next to them. If Lex continues this pattern consistently, how many books will he have left unorganized after using as many books as possible from his collection?
answer:To solve this problem, let's start by determining the pattern Lex is using to organize his books and then calculate how many books will be left unorganized.1. Identify the Pattern: - For every 2 law books, Lex places 3 comic books. - This means each complete pattern uses 2 + 3 = 5 books in total.2. Determine How Many Full Patterns Can Be Formed: - Lex has 20 law books and 15 comic books.3. Calculate Full Patterns Using Law Books: - With 20 law books, since each pattern uses 2 law books, the maximum number of full patterns he can form is: [ text{Max patterns using law books} = frac{20}{2} = 10 ]4. Calculate Full Patterns Using Comic Books: - With 15 comic books, since each pattern uses 3 comic books, the maximum number of full patterns he can form is: [ text{Max patterns using comic books} = frac{15}{3} = 5 ]5. Determine the Limiting Factor: - The number of full patterns is limited by the resource that runs out first. In this case, it's the comic books, allowing only 5 full patterns.6. Calculate the Total Number of Books Used in the Patterns: - Each full pattern uses 5 books. - Total books used in 5 patterns: [ text{Total books used} = 5 times 5 = 25 ]7. Calculate the Total Number of Books: - Lex has a total of 20 law books + 15 comic books = 35 books.8. Calculate Unorganized Books: - The number of books left unorganized is the total number of books minus the number of books used in the patterns: [ text{Unorganized books} = 35 - 25 = 10 ]Thus, Lex will have 10 books left unorganized after using as many books as possible from his collection.# 10
question:A contractor is collaborating with a blogger to renovate a series of five large rooms in a house. The contractor estimates that they need 20 gallons of paint to cover the walls of one room. To attract more followers, the blogger suggests filming the renovation of one of the rooms, which will require an additional 5 gallons of paint for touch-ups and decorations. How many gallons of paint does the contractor need in total to complete the renovation of all five rooms and the additional filming requirements for one of them?
answer:To solve this problem, we need to calculate the total amount of paint needed for the renovation and filming requirements. Here are the steps to find the solution:1. Determine the paint needed for each room without filming additional requirements: The contractor estimates 20 gallons of paint per room. There are 5 rooms in total. [ text{Total paint for rooms without filming} = 5 times 20 = 100 text{ gallons} ]2. Calculate the additional paint required for filming one room: The blogger suggests filming the renovation of one room, which requires an additional 5 gallons of paint. [ text{Additional paint for filming} = 5 text{ gallons} ]3. Combine the paint requirements: Add the additional paint needed for filming to the paint needed for all five rooms. [ text{Total paint needed} = 100 + 5 = 105 text{ gallons} ]The total amount of paint required to complete the renovation of all five rooms, including the additional filming requirements for one of them, is 105 gallons.# 105
question:Sarah is an English-speaking public health worker who is implementing a vaccination campaign in a rural area of Benin. Her team plans to visit 8 villages over the course of 4 weeks. Each village has an average population of 150 people. Sarah's goal is to vaccinate 70% of the population in each village. If her team can vaccinate 50 people per day, how many days will it take for them to achieve their goal of vaccinating 70% of the total population in all 8 villages?
answer:To solve the problem, we need to determine the total number of people that need to be vaccinated and calculate the number of days required to vaccinate them, given the team's daily vaccination capacity.Step 1: Calculate the total population across all villages.Each village has an average population of 150 people. There are 8 villages in total.[text{Total population} = 150 times 8 = 1200 text{ people}]Step 2: Calculate the target number of people to be vaccinated.Sarah's goal is to vaccinate 70% of the population in each village. Therefore, we need to find 70% of the total population.[text{Target vaccinations} = 1200 times 0.70 = 840 text{ people}]Step 3: Determine the number of days required to vaccinate the target population.The team can vaccinate 50 people per day.[text{Number of days} = frac{840}{50} = 16.8]Since the number of days must be a whole number, Sarah's team will need 17 days to meet their vaccination goal, since they cannot work for a fraction of a day.Therefore, the total number of days required is:# 17