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question:Alex is a PhD candidate researching queer representation in sci-fi movies. They are analyzing a collection of 60 sci-fi movies released over the past decade. Out of these, 25 movies prominently feature queer characters, while the rest do not. Alex wants to create a presentation highlighting the percentage of movies with queer representation. Additionally, Alex plans to watch 3 movies per day to finish the entire collection. How many days will it take Alex to watch all the movies, and what percentage of the movies feature queer characters?
answer:To solve this problem, we need to calculate two things: the percentage of movies with queer representation and the number of days it will take Alex to watch all the movies.Step 1: Calculate the percentage of movies with queer representation.We know that:- Total number of movies = 60- Number of movies featuring queer characters = 25The percentage of movies with queer representation is given by the formula:[text{Percentage} = left( frac{text{Number of movies with queer characters}}{text{Total number of movies}} right) times 100]Substitute the values into the formula:[text{Percentage} = left( frac{25}{60} right) times 100]Calculate the fraction:[frac{25}{60} = 0.4167]Multiply by 100 to convert to percentage:[0.4167 times 100 = 41.67%]Therefore, 41.67% of the movies feature queer characters.Step 2: Calculate the number of days it will take Alex to watch all the movies.Alex plans to watch 3 movies per day. Therefore, the number of days required is given by:[text{Number of days} = frac{text{Total number of movies}}{text{Number of movies watched per day}}]Substitute the values into the equation:[text{Number of days} = frac{60}{3}]Calculate the division:[frac{60}{3} = 20]Thus, it will take Alex 20 days to watch all the movies.# 20 days, 41.67%
question:Jasmine is a business analyst who studies music industry trends in the Asian market. She is analyzing the growth of streaming service subscriptions across three countries: South Korea, Japan, and China. Last year, the number of new subscribers was as follows: South Korea had 240,000 new subscribers, Japan had 180,000, and China had 480,000. This year, each of these countries saw an increase in new subscribers by 15%, 10%, and 20%, respectively. Calculate the total number of new subscribers across these three countries this year.
answer:To solve the problem, we need to calculate the number of new subscribers for each country this year by applying the given percentage increases to last year's figures. Then, we can sum up the results to get the total number of new subscribers across the three countries.1. South Korea: - Last year's new subscribers: 240,000 - Increase: 15% - This year's new subscribers = Last year's subscribers + (15% of last year's subscribers) [ text{This year's new subscribers for South Korea} = 240,000 + left(0.15 times 240,000right) ] [ = 240,000 + 36,000 = 276,000 ]2. Japan: - Last year's new subscribers: 180,000 - Increase: 10% - This year's new subscribers = Last year's subscribers + (10% of last year's subscribers) [ text{This year's new subscribers for Japan} = 180,000 + left(0.10 times 180,000right) ] [ = 180,000 + 18,000 = 198,000 ]3. China: - Last year's new subscribers: 480,000 - Increase: 20% - This year's new subscribers = Last year's subscribers + (20% of last year's subscribers) [ text{This year's new subscribers for China} = 480,000 + left(0.20 times 480,000right) ] [ = 480,000 + 96,000 = 576,000 ]4. Total number of new subscribers this year: - Sum the new subscribers from all three countries: [ text{Total new subscribers} = 276,000 + 198,000 + 576,000 ] [ = 1,050,000 ]# 1,050,000
question:Sarah, an orthodontic patient who previously used the Herbst device to correct her bite, now has a new set of braces. Every month, she visits her orthodontist for adjustments, which take about 30 minutes each. If Sarah's treatment plan involves 18 months of wearing braces and she has already completed 5 months, how many more hours will she spend at the orthodontist for adjustments during the remainder of her treatment?
answer:To solve the problem, we need to determine how many more hours Sarah will spend at the orthodontist for adjustments during the remainder of her treatment. Let's break it down step-by-step:1. Total Duration of the Treatment: Sarah's treatment plan involves wearing braces for a total of 18 months.2. Completed Duration: Sarah has already completed 5 months of her treatment.3. Remaining Duration: To find out how many months are left in her treatment, subtract the completed months from the total duration: [ text{Remaining months} = 18 - 5 = 13 text{ months} ]4. Monthly Adjustment Time: Each orthodontic adjustment visit takes about 30 minutes.5. Total Adjustment Time in Minutes: Calculate the total time in minutes for the remaining 13 months: [ text{Total time in minutes} = 13 times 30 = 390 text{ minutes} ]6. Convert Minutes to Hours: Since 1 hour is 60 minutes, convert the total time from minutes to hours: [ text{Total time in hours} = frac{390}{60} = 6.5 text{ hours} ]Therefore, Sarah will spend a total of 6.5 more hours at the orthodontist for adjustments during the remainder of her treatment.# 6.5
question:Brent Telano's old friend, who prefers paper maps over GPS and finds calculators a bit puzzling, decides to visit three different local shops to buy some items. At the first shop, they buy 5 notebooks for 2 each. At the second shop, they purchase 3 packs of pencils, with each pack costing 1.50. At the third shop, they see a sale and get 2 erasers for 0.75 each. They are puzzled by how much money they have spent in total. Can you help them calculate the total cost of their purchases?
answer:To calculate the total cost of Brent Telano's old friend's purchases, we need to find the cost from each shop and then sum them up.1. First Shop: - They buy 5 notebooks, each costing 2. - Total cost at the first shop = Number of notebooks × Cost per notebook - Total cost at the first shop = 5 × 2 = 102. Second Shop: - They purchase 3 packs of pencils, each pack costing 1.50. - Total cost at the second shop = Number of packs × Cost per pack - Total cost at the second shop = 3 × 1.50 = 4.503. Third Shop: - They buy 2 erasers, each costing 0.75. - Total cost at the third shop = Number of erasers × Cost per eraser - Total cost at the third shop = 2 × 0.75 = 1.504. Total Cost: - Add up the costs from each shop to find the total expenditure. - Total cost = Cost from first shop + Cost from second shop + Cost from third shop - Total cost = 10 + 4.50 + 1.50 = 16.00# 16.00
question:Professor Wave, a skeptical physics professor who researches sound waves, decided to conduct a small experiment to test the effectiveness of yoga on improving concentration. Even though he is unfamiliar with yoga, he invites a yoga instructor to his lab. The instructor suggests a simple exercise where participants hum at a frequency of 256 Hz, which is known to have calming effects.To put this to the test, Professor Wave records the time it takes for two groups of students to solve a set of puzzles. Group A, which practices the humming exercise for 5 minutes, takes an average of 25 minutes to solve the puzzles. Group B, which does not practice the exercise, takes an average of 30 minutes.Professor Wave is curious to calculate the total time spent on both the yoga exercise and solving puzzles for Group A. What is the total time, in minutes, that Group A spends from the start of the yoga exercise to the end of solving the puzzles?
answer:To determine the total time spent by Group A from the start of the yoga exercise to the end of solving the puzzles, follow these steps:1. Identify the time spent on the yoga exercise: Group A practices the humming exercise for 5 minutes.2. Identify the time spent on solving puzzles: After practicing the humming exercise, Group A takes an average of 25 minutes to solve the puzzles.3. Calculate the total time: The total time spent by Group A includes both the time spent on the yoga exercise and the time spent solving the puzzles. Therefore, the total time is the sum of these two durations: [ text{Total Time} = text{Time spent on yoga exercise} + text{Time spent solving puzzles} ] [ text{Total Time} = 5 text{ minutes} + 25 text{ minutes} ]4. Compute the total time: [ text{Total Time} = 30 text{ minutes} ]Therefore, the total time that Group A spends from the start of the yoga exercise to the end of solving the puzzles is 30 minutes.# 30
question:Dr. Green, a botanist specializing in horticulture, is conducting an experiment to increase the yield of tomato plants by using a new cultivation technique. She has 120 tomato plants divided equally into 4 different test plots. Each plot is treated with a different genetic enhancement method. After several months, Dr. Green measures the average yield of tomatoes per plant in each plot. Plot A produces 15 tomatoes per plant, Plot B produces 18 tomatoes per plant, Plot C produces 20 tomatoes per plant, and Plot D produces 22 tomatoes per plant. What is the total number of tomatoes produced by all the plants in Dr. Green's experiment?
answer:To solve the problem, we need to determine the total number of tomatoes produced by all the plants in Dr. Green's experiment. Here are the steps:1. Determine the number of plants in each plot: - Dr. Green has 120 tomato plants divided equally into 4 plots. - Therefore, the number of plants in each plot is ( frac{120}{4} = 30 ) plants.2. Calculate the total yield for each plot: - Plot A: Each plant produces 15 tomatoes, and there are 30 plants. Thus, the total yield for Plot A is: [ 30 times 15 = 450 text{ tomatoes} ] - Plot B: Each plant produces 18 tomatoes, and there are 30 plants. Thus, the total yield for Plot B is: [ 30 times 18 = 540 text{ tomatoes} ] - Plot C: Each plant produces 20 tomatoes, and there are 30 plants. Thus, the total yield for Plot C is: [ 30 times 20 = 600 text{ tomatoes} ] - Plot D: Each plant produces 22 tomatoes, and there are 30 plants. Thus, the total yield for Plot D is: [ 30 times 22 = 660 text{ tomatoes} ]3. Sum the yields from all plots to find the total number of tomatoes produced: [ 450 + 540 + 600 + 660 = 2250 text{ tomatoes} ]Hence, the total number of tomatoes produced by all the plants in Dr. Green's experiment is 2250.# 2250