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question:Alex, a STEM student who is highly skeptical of philosophy and believes in the supremacy of science and reason, is conducting an experiment to measure the time it takes for different objects to fall from the same height. Alex drops three objects: a metal ball, a wooden cube, and a plastic disc. The metal ball takes 2 seconds to reach the ground, the wooden cube takes 3 seconds, and the plastic disc takes 4 seconds. Alex wants to calculate the average time it took for the objects to fall, as well as the total time spent observing the falls. Calculate the average time it took for the three objects to fall and find the total time Alex spent observing the falls.
answer:To solve the problem, we need to calculate two things: the average time it took for the objects to fall and the total time spent observing the falls.Step-by-step solution:1. Calculate the average time it took for the objects to fall: The average time is calculated by summing up the individual times each object took to fall and then dividing by the number of objects. Let ( t_1 = 2 ) seconds (time for metal ball), ( t_2 = 3 ) seconds (time for wooden cube), ( t_3 = 4 ) seconds (time for plastic disc). The average time ( bar{t} ) is given by: [ bar{t} = frac{t_1 + t_2 + t_3}{3} ] Substituting the given values: [ bar{t} = frac{2 + 3 + 4}{3} = frac{9}{3} = 3 text{ seconds} ]2. Calculate the total time Alex spent observing the falls: The total time ( T ) is simply the sum of the times it took for each object to fall: [ T = t_1 + t_2 + t_3 ] Substituting the given values: [ T = 2 + 3 + 4 = 9 text{ seconds} ]#Final Answer:Average time: 3 secondsTotal time: 9 seconds
question:Jamie is a die-hard Fortnite player and spends 3 hours every day playing the game. On weekends, Jamie hosts a special Fortnite marathon where they play for twice as long each day as they do on weekdays. If Jamie plays Fortnite every day for a week, how many hours in total does Jamie spend playing Fortnite in that week?
answer:To solve the problem, we need to calculate the total number of hours Jamie spends playing Fortnite in a week.Step 1: Calculate the number of hours Jamie plays on weekdays.- Jamie plays 3 hours every day on weekdays.- There are 5 weekdays in a week.[text{Total weekday hours} = 3 text{ hours/day} times 5 text{ days} = 15 text{ hours}]Step 2: Calculate the number of hours Jamie plays on weekends.- On weekends, Jamie plays for twice as long each day compared to weekdays.- Therefore, on weekends, Jamie plays (3 times 2 = 6) hours per day.- There are 2 weekend days (Saturday and Sunday).[text{Total weekend hours} = 6 text{ hours/day} times 2 text{ days} = 12 text{ hours}]Step 3: Calculate the total number of hours Jamie plays in the entire week.- Add the total hours played on weekdays and weekends:[text{Total weekly hours} = text{Total weekday hours} + text{Total weekend hours} = 15 text{ hours} + 12 text{ hours} = 27 text{ hours}]# 27
question:Jamie owns a boutique store in the mall. Currently, her store receives about 150 visitors per day. She is planning a special weekend sale to increase foot traffic. She estimates that the sale will bring in 20% more visitors each day over the weekend. If the sale runs for two days, how many total visitors does Jamie expect to have in her store over the entire weekend?
answer:To solve the problem, we need to calculate the estimated total number of visitors for each day during the weekend sale and then sum those amounts for the entire weekend. Here’s a step-by-step solution:1. Current Daily Visitors: Jamie's store currently receives 150 visitors per day.2. Percentage Increase: The sale is expected to increase the number of visitors by 20%.3. Calculate the Increase in Visitors: The increase in visitors per day due to the sale is calculated as follows: [ text{Increase in visitors} = 150 times 0.20 = 30 ]4. Total Visitors Per Day During Sale: With the increase, the total number of visitors per day during the sale is: [ text{Total visitors per day} = 150 + 30 = 180 ]5. Calculate Total Visitors Over the Two-Day Sale: Since the sale lasts for two days (the entire weekend), the total number of visitors over the weekend is: [ text{Total visitors over two days} = 180 times 2 = 360 ]The expected number of total visitors Jamie expects to have in her store over the entire weekend is 360.# 360
question:A local journalist from Mandi Bahauddin is preparing a report on the number of articles published in different sections of the newspaper over a week. On Monday, the journalist wrote 3 articles for the local news section, 2 articles for the sports section, and 1 article for the lifestyle section. On Tuesday, the journalist wrote 4 articles in total: 2 for the local news and 2 for the sports section. On Wednesday, the journalist managed to write 5 articles: 3 for the lifestyle section and 2 for the local news. If the journalist continues this pattern for the rest of the week, how many articles will the journalist have written in total by Sunday?
answer:To solve this problem, we need to establish the pattern of articles written by the journalist each day and then calculate the total number of articles written from Monday to Sunday. Step-by-step Solution:1. Identify the Pattern: - Monday: 3 articles for local news, 2 for sports, 1 for lifestyle. Total = 3 + 2 + 1 = 6 articles. - Tuesday: 2 articles for local news, 2 for sports. Total = 2 + 2 = 4 articles. - Wednesday: 3 articles for lifestyle, 2 for local news. Total = 3 + 2 = 5 articles.2. Continue the Pattern for the Week: - Thursday: Based on the pattern, Thursday will have the same distribution as Monday: 3 local news, 2 sports, 1 lifestyle. Total = 6 articles. - Friday: Follows Tuesday's pattern: 2 local news, 2 sports. Total = 4 articles. - Saturday: Follows Wednesday’s pattern: 3 lifestyle, 2 local news. Total = 5 articles. - Sunday: Repeats Monday's pattern again: 3 local news, 2 sports, 1 lifestyle. Total = 6 articles.3. Calculate the Total Number of Articles for the Week: - Monday: 6 articles - Tuesday: 4 articles - Wednesday: 5 articles - Thursday: 6 articles - Friday: 4 articles - Saturday: 5 articles - Sunday: 6 articles Total articles = 6 + 4 + 5 + 6 + 4 + 5 + 64. Perform the Addition: - 6 + 4 = 10 - 10 + 5 = 15 - 15 + 6 = 21 - 21 + 4 = 25 - 25 + 5 = 30 - 30 + 6 = 36Therefore, the journalist will have written a total of 36 articles by the end of Sunday.# 36
question:A skilled artisan is working with a conservator to repair and reconstruct a damaged medieval painting. The painting is divided into a grid of 20 equal sections, and each section takes 2 hours to repair. The artisan can work on 4 sections per day, while the conservator can handle 2 sections per day. If they both work together for 3 days, how many sections of the painting will still need repair?
answer:To solve this problem, we'll determine how many sections the artisan and the conservator can repair together in the given time, and then subtract this from the total number of sections to find out how many sections are still in need of repair.1. Total sections of the painting: The painting is divided into 20 sections.2. Work rate of the artisan: The artisan can work on 4 sections per day.3. Work rate of the conservator: The conservator can work on 2 sections per day.4. Combined work rate: Together, the artisan and the conservator can work on: [ 4 text{ sections/day (artisan)} + 2 text{ sections/day (conservator)} = 6 text{ sections/day} ]5. Number of days working together: They work together for 3 days.6. Total sections repaired together in 3 days: [ 6 text{ sections/day} times 3 text{ days} = 18 text{ sections} ]7. Sections still needing repair: Subtract the number of sections repaired from the total number of sections. [ 20 text{ total sections} - 18 text{ sections repaired} = 2 text{ sections still need repair} ]Final answer: # 2
question:Farmer Jane specializes in growing allergy-friendly crops on her small farm. This week, she harvested 120 pounds of millet, 75 pounds of quinoa, and 105 pounds of amaranth. She sells millet for 2 per pound, quinoa for 3 per pound, and amaranth for 1.50 per pound. How much total revenue will Farmer Jane earn from selling all her harvested crops this week?
answer:To determine Farmer Jane's total revenue from selling her crops, we need to calculate the revenue from each type of crop separately and then sum these amounts.1. Calculate Revenue from Millet: - Farmer Jane harvested 120 pounds of millet. - The selling price for millet is 2 per pound. - Revenue from millet = Number of pounds of millet × Price per pound [ text{Revenue from millet} = 120 , text{pounds} times 2 , text{dollars/pound} = 240 , text{dollars} ]2. Calculate Revenue from Quinoa: - Farmer Jane harvested 75 pounds of quinoa. - The selling price for quinoa is 3 per pound. - Revenue from quinoa = Number of pounds of quinoa × Price per pound [ text{Revenue from quinoa} = 75 , text{pounds} times 3 , text{dollars/pound} = 225 , text{dollars} ]3. Calculate Revenue from Amaranth: - Farmer Jane harvested 105 pounds of amaranth. - The selling price for amaranth is 1.50 per pound. - Revenue from amaranth = Number of pounds of amaranth × Price per pound [ text{Revenue from amaranth} = 105 , text{pounds} times 1.5 , text{dollars/pound} = 157.5 , text{dollars} ]4. Calculate Total Revenue: - Total revenue is the sum of the revenue from millet, quinoa, and amaranth. [ text{Total revenue} = text{Revenue from millet} + text{Revenue from quinoa} + text{Revenue from amaranth} ] [ text{Total revenue} = 240 + 225 + 157.5 = 622.5 , text{dollars} ]Therefore, Farmer Jane's total revenue from selling all her harvested crops this week is:[boxed{622.5}]# 622.5