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question:Alex is a writer who specializes in experimental music and underground subcultures. They are working on a new book about the history of underground music festivals. Alex plans to attend a series of festivals over the summer to gather material for their book. They have a schedule that includes 3 small festivals, each lasting 2 days, and 4 larger festivals, each lasting 5 days. If Alex spends an average of 6 hours per day at each festival gathering information, how many total hours will Alex spend at all the festivals combined?
answer:To solve this problem, we need to calculate the total number of hours Alex will spend at all the festivals based on the given schedule.1. Calculate the total days spent at the small festivals: - There are 3 small festivals. - Each small festival lasts 2 days. - Total days spent at small festivals = Number of small festivals × Days per small festival [ 3 , text{festivals} times 2 , text{days/festival} = 6 , text{days} ]2. Calculate the total days spent at the larger festivals: - There are 4 larger festivals. - Each larger festival lasts 5 days. - Total days spent at larger festivals = Number of larger festivals × Days per larger festival [ 4 , text{festivals} times 5 , text{days/festival} = 20 , text{days} ]3. Find the total number of days spent at all festivals: - Total days at all festivals = Total days at small festivals + Total days at larger festivals [ 6 , text{days} + 20 , text{days} = 26 , text{days} ]4. Calculate the total hours spent at all festivals: - Alex spends an average of 6 hours per day gathering information. - Total hours spent = Total days at all festivals × Hours per day [ 26 , text{days} times 6 , text{hours/day} = 156 , text{hours} ]# 156
question:Jamie is a project manager who specializes in coordinating and overseeing complex multimedia campaigns. For a new campaign, Jamie is managing the production of video ads, social media posts, and online banners. The team has allocated a total of 120 hours for the entire project. The video ads require 3 times as many hours as the social media posts, and the online banners need half the hours of the social media posts. If the social media posts are planned to take 20 hours, how many hours are allocated for each type of media, and how many hours in total are actually used?
answer:To solve this problem, we will first define the variables and relationships given, and then calculate the hours allocated to each type of media.1. Define Variables: - Let ( S ) represent the hours for social media posts. - Let ( V ) represent the hours for video ads. - Let ( B ) represent the hours for online banners.2. Given Information: - The hours for social media posts are given as ( S = 20 ). - The video ads require 3 times as many hours as the social media posts: [ V = 3S ] - The online banners require half the hours of the social media posts: [ B = frac{1}{2}S ]3. Substitute the Given Value of Social Media Posts: - Since ( S = 20 ), substitute into the equations for ( V ) and ( B ): [ V = 3 times 20 = 60 ] [ B = frac{1}{2} times 20 = 10 ]4. Calculate Total Hours Used: - Add the hours for each type of media: [ text{Total hours used} = S + V + B = 20 + 60 + 10 = 90 ]5. Check Against Allocated Hours: - The project allocated a total of 120 hours, but only 90 hours are actually used based on the current plan.Thus, the hours allocated for each type of media are:- Social media posts: 20 hours- Video ads: 60 hours- Online banners: 10 hoursAnd the total hours actually used for these tasks are 90 hours.# 20 hours for social media posts, 60 hours for video ads, 10 hours for online banners, and 90 hours actually used.
question:A historian researching the Urartians wants to organize a display of ancient artifacts in a museum. She has a collection of artifacts from 3 different Urartian sites. From the first site, she has 24 clay tablets, from the second site, she has 18 bronze figurines, and from the third site, she has 36 pottery shards. She wants to create display cases, each containing the same number of artifacts, with an equal number of items from each site. What is the greatest number of display cases she can create without leaving any artifacts out?
answer:To solve this problem, we need to find the greatest number of display cases such that each case will have the same number of artifacts from each of the three different Urartian sites. This is equivalent to finding the greatest common divisor (GCD) of the number of artifacts from each site.The artifacts from the sites are:- 24 clay tablets from the first site- 18 bronze figurines from the second site- 36 pottery shards from the third siteWe need to find the GCD of 24, 18, and 36.Step 1: Prime factorization of each number- 24: The prime factorization of 24 is (2^3 times 3^1).- 18: The prime factorization of 18 is (2^1 times 3^2).- 36: The prime factorization of 36 is (2^2 times 3^2).Step 2: Identify the common prime factors- For the prime number 2, the smallest power in the factorizations is (2^1).- For the prime number 3, the smallest power in the factorizations is (3^1).Step 3: Calculate the GCD- The GCD is the product of the lowest powers of all prime factors common to each number.- Thus, the GCD is (2^1 times 3^1 = 2 times 3 = 6).Therefore, the greatest number of display cases that can be created, each containing the same number of artifacts from each site, is 6.# 6
question:Mr. Johnson, a retired firefighter, spends his time advocating for COPD awareness. This week, he plans to give educational talks at 4 different community centers. Each talk is scheduled to last 45 minutes. After each talk, Mr. Johnson spends an additional 30 minutes answering questions and distributing pamphlets about COPD prevention. How many total hours will Mr. Johnson spend at the community centers this week, including both the talks and the question-and-answer sessions?
answer:To solve this problem, we need to calculate the total time Mr. Johnson will spend at the community centers for both the talks and the question-and-answer sessions.1. Calculate the time spent on each talk: - Each talk is scheduled to last 45 minutes.2. Calculate the time spent on each question-and-answer session: - After each talk, Mr. Johnson spends an additional 30 minutes answering questions and distributing pamphlets.3. Calculate the total time spent on each community center visit: - For each community center, the total time spent is the sum of the talk and the question-and-answer session: [ 45 text{ minutes (talk)} + 30 text{ minutes (Q&A)} = 75 text{ minutes} ]4. Calculate the total time for 4 community centers: - Since Mr. Johnson plans to give talks at 4 different community centers, we multiply the time spent per community center by 4: [ 75 text{ minutes/center} times 4 text{ centers} = 300 text{ minutes} ]5. Convert the total time from minutes to hours: - There are 60 minutes in an hour, so we convert the total time in minutes to hours: [ frac{300 text{ minutes}}{60 text{ minutes/hour}} = 5 text{ hours} ]Thus, Mr. Johnson will spend a total of 5 hours at the community centers this week.# 5
question:A historian specializing in medieval monarchies is collaborating with a museum librarian to create an exhibition on royal history. They have decided to display artifacts from 4 different medieval monarchies. For each monarchy, they plan to exhibit 5 royal crowns, 6 pieces of royal clothing, and 8 ancient documents. If the museum has enough space to display a total of 100 artifacts, how many more artifacts can they add to the exhibition?
answer:To solve the problem, we need to determine how many artifacts will be displayed initially and how many more can be added to reach the maximum capacity of 100 artifacts.Step 1: Calculate the number of each type of artifact for one monarchy.- For each monarchy, there are: - 5 royal crowns - 6 pieces of royal clothing - 8 ancient documentsStep 2: Calculate the total number of artifacts per monarchy.- Total artifacts per monarchy = 5 crowns + 6 clothing + 8 documents = 19 artifacts.Step 3: Calculate the total number of artifacts for 4 monarchies.- Total artifacts for 4 monarchies = 4 * 19 = 76 artifacts.Step 4: Determine the remaining space for additional artifacts.- The total space available is 100 artifacts.- Space left for additional artifacts = 100 - 76 = 24 artifacts.Thus, the number of additional artifacts that can be added to the exhibition is 24.# 24
question:Dr. Ellis, a professional zoologist, is conducting a study on a group of rare birds in a wildlife reserve. To ensure accurate data, she wants to double-check the number of birds reported by her team. Her team reports that they observed 24 blue jays, 18 cardinals, and 32 sparrows in one part of the reserve. However, she knows from past experience that her team often overestimates by about 10% due to counting errors. How many birds did Dr. Ellis actually observe in that part of the reserve, according to her corrected estimate?
answer:To solve this problem, we need to adjust the reported counts of each type of bird by reducing each count by 10%, as the team typically overestimates by this amount.1. Blue Jays: - Reported count = 24 - Overestimated by 10%, so we need to reduce the count by 10%. - Reduction = 10% of 24 = 0.1 × 24 = 2.4 - Corrected count = 24 - 2.4 = 21.62. Cardinals: - Reported count = 18 - Overestimated by 10%, so we need to reduce the count by 10%. - Reduction = 10% of 18 = 0.1 × 18 = 1.8 - Corrected count = 18 - 1.8 = 16.23. Sparrows: - Reported count = 32 - Overestimated by 10%, so we need to reduce the count by 10%. - Reduction = 10% of 32 = 0.1 × 32 = 3.2 - Corrected count = 32 - 3.2 = 28.8Finally, we sum the corrected counts to find the total number of birds Dr. Ellis actually observed:- Total corrected number of birds = 21.6 (Blue Jays) + 16.2 (Cardinals) + 28.8 (Sparrows)- Total corrected number of birds = 66.6Thus, according to Dr. Ellis's corrected estimate, the actual number of birds observed is:# 66.6