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question:The philosopher is fascinated by the symmetry in the universe and decides to conduct a thought experiment. They imagine a perfectly symmetrical garden, where each side of the garden corresponds to a different philosophical principle. The garden is a square, and each side measures 12 meters. The philosopher wants to plant trees along the perimeter of the garden, with each tree representing a fundamental idea of symmetry. They plan to plant one tree every 3 meters along the garden's perimeter.How many trees will the philosopher plant in total around the garden?
answer:To solve the problem, we will follow these steps:1. Calculate the Perimeter of the Square Garden: Since the garden is a square and each side measures 12 meters, we can calculate the perimeter using the formula for the perimeter of a square: [ text{Perimeter} = 4 times text{side length} = 4 times 12 = 48 text{ meters} ]2. Determine the Number of Trees to Plant: Trees are to be planted every 3 meters along the perimeter of the garden. To find out how many trees are needed, we divide the total perimeter by the distance between the trees: [ text{Number of trees} = frac{text{Perimeter}}{text{Distance between trees}} = frac{48}{3} = 16 ]Therefore, the philosopher will plant a total of 16 trees around the garden.# 16
question:A young Paraguayan writer admires Maybell Lebron and decides to write a collection of short stories inspired by her work. To honor Maybell, the writer plans to write a total of 15 stories. Each story will contain 7 pages.The writer dedicates 2 hours every day to writing and can complete 3 pages in that time. How many days will it take the writer to finish the entire collection of stories?
answer:To solve the problem, we need to determine how many days it will take the writer to finish the entire collection of 15 stories, each containing 7 pages.Step 1: Calculate the total number of pages.The writer plans to write 15 stories, and each story contains 7 pages. Therefore, the total number of pages is:[15 text{ stories} times 7 text{ pages per story} = 105 text{ pages}]Step 2: Determine the writing rate per day.The writer dedicates 2 hours every day to writing and can complete 3 pages in that time. Therefore, the writing rate is:[3 text{ pages per day}]Step 3: Calculate the total number of days needed.To find the total number of days required to write 105 pages, we divide the total number of pages by the number of pages the writer can complete in a day:[frac{105 text{ pages}}{3 text{ pages per day}} = 35 text{ days}]Thus, it will take the writer 35 days to complete the entire collection of stories.# 35
question:Mr. Thompson, a retired history teacher with a passion for local history and storytelling, lives near the beautiful Sierra Nevada mountain range. He often takes his grandchildren on educational hikes in the area. On one of their trips, he wants to tell them stories at exactly four different historical landmarks along the trail. The distance between the starting point and the first landmark is 2 miles. From the first to the second landmark, it's 3 miles. The distance from the second to the third landmark is 1 mile, and finally, the distance from the third landmark back to the starting point is 4 miles. If Mr. Thompson and his grandchildren walk at a steady pace of 2 miles per hour, how many hours will it take them to complete the hike and return to the starting point?
answer:To solve the problem, we need to find the total distance Mr. Thompson and his grandchildren will walk during their hike and then calculate how long it will take them given their walking pace.1. Calculate the Total Distance: - Distance from the starting point to the first landmark: 2 miles - Distance from the first landmark to the second landmark: 3 miles - Distance from the second landmark to the third landmark: 1 mile - Distance from the third landmark back to the starting point: 4 miles Add these distances together to get the total distance of the hike: [ 2 + 3 + 1 + 4 = 10 text{ miles} ]2. Calculate the Time Taken: - Mr. Thompson and his grandchildren walk at a steady pace of 2 miles per hour. - To find the time taken to walk 10 miles, use the formula: [ text{Time} = frac{text{Distance}}{text{Speed}} ] - Substitute the known values into the formula: [ text{Time} = frac{10 text{ miles}}{2 text{ miles per hour}} = 5 text{ hours} ]Thus, it will take them 5 hours to complete the hike and return to the starting point.# 5 hours
question:The head of a multinational oil company is planning to expand operations into three new countries to boost economic growth and stability. In the first country, the expected annual revenue is 150 million. In the second country, it is expected to be 200 million, and in the third country, 250 million. However, the operational costs are estimated to be 50 million in each country per year. What will be the total net annual revenue from these three countries combined after accounting for the operational costs?
answer:To find the total net annual revenue from the three countries, we need to follow these steps:1. Calculate the net revenue for each country by subtracting the operational costs from the expected annual revenue.2. Sum the net revenues of all three countries to get the total net annual revenue.Let's go through these steps:Step 1: Calculate the net revenue for each country- First Country: - Expected annual revenue = 150 million - Operational costs = 50 million - Net revenue = Expected revenue - Operational costs - Net revenue = 150 million - 50 million = 100 million- Second Country: - Expected annual revenue = 200 million - Operational costs = 50 million - Net revenue = Expected revenue - Operational costs - Net revenue = 200 million - 50 million = 150 million- Third Country: - Expected annual revenue = 250 million - Operational costs = 50 million - Net revenue = Expected revenue - Operational costs - Net revenue = 250 million - 50 million = 200 millionStep 2: Sum the net revenues of all three countries- Total net annual revenue = Net revenue from first country + Net revenue from second country + Net revenue from third country- Total net annual revenue = 100 million + 150 million + 200 million- Total net annual revenue = 450 million#450 million
question:Dr. Smith is a clinical psychologist who sees patients suffering from anxiety and depression. She schedules her appointments so that she can dedicate equal time to each patient. On Monday, Dr. Smith has 5 patients with anxiety and 3 patients with depression. If she spends 45 minutes with each anxiety patient and 60 minutes with each depression patient, how many total minutes does Dr. Smith spend with her patients on Monday?
answer:To determine the total time Dr. Smith spends with her patients on Monday, we need to calculate the time spent with patients suffering from anxiety and depression separately, and then sum these times.Step 1: Calculate the total time for anxiety patients.- Dr. Smith has 5 patients with anxiety.- She spends 45 minutes with each anxiety patient.- Therefore, the total time spent with anxiety patients is: [ 5 text{ patients} times 45 text{ minutes per patient} = 225 text{ minutes} ]Step 2: Calculate the total time for depression patients.- Dr. Smith has 3 patients with depression.- She spends 60 minutes with each depression patient.- Therefore, the total time spent with depression patients is: [ 3 text{ patients} times 60 text{ minutes per patient} = 180 text{ minutes} ]Step 3: Calculate the total time spent with all patients.- Add the time spent with anxiety patients to the time spent with depression patients: [ 225 text{ minutes} + 180 text{ minutes} = 405 text{ minutes} ]Thus, the total time Dr. Smith spends with her patients on Monday is 405 minutes.# 405
question:The school counselor, Mr. Jenkins, is organizing a series of workshops to effectively support teenage boys at the school. Each workshop can accommodate 12 students. Mr. Jenkins plans to hold a total of 8 workshops. If there are 96 teenage boys interested in attending, how many students will need to attend more than one workshop to ensure that every boy can participate at least once?
answer:To solve this problem, we need to determine how many students will need to attend more than one workshop to ensure that all 96 boys interested can participate.Step 1: Calculate the total capacity available in all workshops.Each workshop can accommodate 12 students, and Mr. Jenkins plans to hold 8 workshops. So, the total capacity is:[ 12 text{ students/workshop} times 8 text{ workshops} = 96 text{ students} ]Step 2: Compare the total number of interested boys with the total capacity.There are 96 teenage boys interested in attending, and the total capacity for all workshops is also 96 students.Step 3: Determine if all boys can attend at least once without needing to attend more than one workshop.Since the total capacity (96) matches exactly the number of interested boys (96), all boys can attend exactly one workshop without any need for any boy to attend more than once.Thus, no students need to attend more than one workshop to ensure that every boy can participate at least once.# 0