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question:Alex and Jamie used to be fierce rivals on the tennis court, but now they are the best of friends and support each other in all tournaments. Alex is preparing for an upcoming tournament and plans to practice 5 days a week. Each practice session lasts 2 hours. Jamie, being a supportive friend, joins Alex for 3 of those practice sessions each week to offer encouragement and tips. If the tournament is in 4 weeks, how many total hours will Alex and Jamie practice together by the time the tournament starts?
answer:To solve the problem, we need to calculate the total hours Alex and Jamie practice together over the 4 weeks leading up to the tournament.1. Determine the number of practice sessions per week: Alex practices 5 days a week, with each session lasting 2 hours. - Total hours Alex practices alone each week: [ 5 text{ sessions/week} times 2 text{ hours/session} = 10 text{ hours/week} ]2. Calculate the number of sessions Alex and Jamie practice together each week: Jamie joins Alex for 3 sessions each week. - Total hours Alex and Jamie practice together each week: [ 3 text{ sessions/week} times 2 text{ hours/session} = 6 text{ hours/week} ]3. Calculate the total hours they practice together over 4 weeks: Multiply the weekly practice hours by the number of weeks: - Total hours Alex and Jamie practice together over 4 weeks: [ 6 text{ hours/week} times 4 text{ weeks} = 24 text{ hours} ]Thus, by the time the tournament starts, Alex and Jamie will have practiced together for a total of 24 hours.# 24
question:Dr. Martinez, a medical researcher, is developing a new imaging technique to study the human brain. She uses a special scanner that can capture 3D images of the brain in different layers. Each layer is 2 millimeters thick. If the total thickness of the brain is 140 millimeters, how many layers does Dr. Martinez's scanner need to capture to visualize the entire brain?
answer:To determine how many layers Dr. Martinez's scanner needs to capture, we need to divide the total thickness of the brain by the thickness of each layer. Here's the step-by-step solution:1. Identify the total thickness of the brain: The problem states that the total thickness of the brain is 140 millimeters.2. Identify the thickness of each layer: Each layer that the scanner captures is 2 millimeters thick.3. Calculate the number of layers needed: To find the number of layers, divide the total thickness of the brain by the thickness of each layer. [ text{Number of layers} = frac{text{Total thickness of the brain}}{text{Thickness of each layer}} = frac{140 text{ mm}}{2 text{ mm/layer}} ]4. Perform the division: [ frac{140}{2} = 70 ]Therefore, Dr. Martinez's scanner needs to capture 70 layers to visualize the entire brain.# 70
question:Niranjan Kaushik, an Indian-born film director, screenwriter, and advertising professional, is planning a new film project. He has a total budget of 100,000 for the project. Niranjan decides to allocate his budget as follows: 40% for filming, 25% for post-production, 15% for marketing, and the remaining amount for miscellaneous expenses. How much money is allocated for miscellaneous expenses?
answer:To solve this problem, we need to calculate the amounts allocated to each budget category and then determine the amount left for miscellaneous expenses.1. Total Budget: 100,0002. Filming Allocation: - Filming is allocated 40% of the total budget. - Calculation: (0.40 times 100,000 = 40,000) - So, 40,000 is allocated for filming.3. Post-Production Allocation: - Post-production is allocated 25% of the total budget. - Calculation: (0.25 times 100,000 = 25,000) - So, 25,000 is allocated for post-production.4. Marketing Allocation: - Marketing is allocated 15% of the total budget. - Calculation: (0.15 times 100,000 = 15,000) - So, 15,000 is allocated for marketing.5. Miscellaneous Expenses Allocation: - Miscellaneous expenses are allocated the remaining percentage of the budget. - First, calculate the total allocated so far: [ 40,000 text{ (filming)} + 25,000 text{ (post-production)} + 15,000 text{ (marketing)} = 80,000 ] - Subtract the total allocated from the total budget to find the miscellaneous expenses: [ 100,000 - 80,000 = 20,000 ]Therefore, the amount allocated for miscellaneous expenses is 20,000.# 20,000
question:Professor Smith, an art history professor at the University of Edinburgh, is curating an exhibition that explores the connection between art and science. For the exhibition, she selects 12 paintings that each include a scientific element. She wants to display these paintings in the gallery in such a way that each painting is accompanied by 3 scientific artifacts. If Professor Smith has collected a total of 45 scientific artifacts for the exhibition, how many paintings will have to share the scientific artifacts with other paintings?
answer:To solve this problem, we need to determine how many paintings will have to share the scientific artifacts with other paintings, given that there are 12 paintings and 45 scientific artifacts, with each painting accompanied by 3 artifacts.Let's break down the problem:1. Calculate the Total Number of Artifacts Required: Each painting requires 3 scientific artifacts. Therefore, for 12 paintings, the total number of artifacts required is: [ 12 times 3 = 36 ] This is the number of artifacts needed if each painting were to have its unique set of 3 artifacts.2. Compare the Required Artifacts to Available Artifacts: We are given that there are 45 scientific artifacts available. Since 45 is greater than 36, there are more than enough artifacts available to meet the requirement for each painting to have 3 artifacts. However, since the problem implies that some paintings share artifacts, we need to determine how many paintings will have to share.3. Calculate the Surplus of Artifacts: The surplus of artifacts is: [ 45 - 36 = 9 ] This means there are 9 additional artifacts beyond the 36 required to distribute 3 unique artifacts per painting.4. Determine the Number of Shared Artifacts: Since each painting requires 3 artifacts, and we have a surplus of 9 artifacts, we can deduce that these 9 extra artifacts allow some paintings to share among them.5. Calculate How Many Paintings Share Artifacts: Since each painting is supposed to have 3 unique artifacts, but due to sharing, some paintings can share these extra 9 artifacts, no painting has to share because the 9 surplus allows for flexibility, not a necessity to share.Thus, since the problem provides more artifacts than needed without specifying any constraint on sharing (such as needing to reduce the number of different artifacts), all paintings can technically have their own set of artifacts without any required sharing due to the sufficient surplus.In conclusion, based on the problem's available information, no painting necessarily has to share artifacts due to the surplus.# 0
question:Emily, a college student majoring in mass communication, is planning a themed movie night for her friends to watch episodes of "The Handmaid's Tale." She decides to prepare red cloaks and white bonnets as costumes for her 8 friends. Each cloak costs 15 and each bonnet costs 10. Emily also wants to prepare popcorn for everyone. A bag of popcorn costs 3, and she wants to buy 2 bags per person. If she has already received 50 from her friends to help cover the costs, how much more money does Emily need to cover the total cost of the costumes and popcorn?
answer:To solve the problem, we need to calculate the total costs for the costumes and popcorn, and then determine how much more money Emily needs after accounting for the 50 she has already received.1. Cost of Costumes: - Emily has 8 friends, and each will need one cloak and one bonnet. - Total number of cloaks needed = 8 - Total number of bonnets needed = 8 - Cost per cloak = 15 - Cost per bonnet = 10 - Total cost for cloaks = 8 cloaks × 15/cloak = 120 - Total cost for bonnets = 8 bonnets × 10/bonnet = 80 - Total cost for costumes = Total cost of cloaks + Total cost of bonnets - Total cost for costumes = 120 + 80 = 2002. Cost of Popcorn: - Emily wants to buy 2 bags of popcorn per person. - Total number of people = 8 friends + Emily = 9 people - Total number of popcorn bags needed = 9 people × 2 bags/person = 18 bags - Cost per bag of popcorn = 3 - Total cost for popcorn = 18 bags × 3/bag = 543. Total Cost: - Total cost = Total cost for costumes + Total cost for popcorn - Total cost = 200 (costumes) + 54 (popcorn) = 2544. Money Emily Already Has: - Emily has received 50 from her friends.5. Amount of Additional Money Needed: - Additional money needed = Total cost - Money Emily already has - Additional money needed = 254 - 50 = 204Emily needs an additional 204 to cover the total cost of the costumes and popcorn.# 204
question:Emma is a talented singer-songwriter who is trying to overcome her stage fright by performing at small local venues. She has planned a series of performances to gradually build her confidence. In the first week, she performs at 2 venues. Each venue allows her to sing 3 songs. In the second week, she feels braver and adds 2 more venues to her schedule, with each venue still allowing her to sing 3 songs. By the third week, Emma decides to challenge herself even more and performs at 5 venues, maintaining the same number of songs per venue. How many songs does Emma perform in total over these three weeks?
answer:To determine the total number of songs Emma performs over the three weeks, we will calculate the number of songs for each week separately and then sum those values.Week 1:- Emma performs at 2 venues.- Each venue allows her to sing 3 songs.- Total songs in Week 1 = (2 text{ venues} times 3 text{ songs/venue} = 6 text{ songs}).Week 2:- Emma adds 2 more venues, so she performs at (2 + 2 = 4) venues.- Each venue allows her to sing 3 songs.- Total songs in Week 2 = (4 text{ venues} times 3 text{ songs/venue} = 12 text{ songs}).Week 3:- Emma performs at 5 venues.- Each venue allows her to sing 3 songs.- Total songs in Week 3 = (5 text{ venues} times 3 text{ songs/venue} = 15 text{ songs}).Total Songs Over Three Weeks:- Total songs = Songs in Week 1 + Songs in Week 2 + Songs in Week 3- Total songs = (6 + 12 + 15 = 33).# 33