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question:As a pit crew chief with years of experience in NASCAR racing, you know the importance of quick and efficient pit stops. During a race, your team is responsible for completing tasks like refueling the car and changing the tires. On average, your pit crew can change a set of 4 tires in 12 seconds and refuel the car in 8 seconds. If your driver needs 3 pit stops during a race and each pit stop requires both a tire change and a refuel, how many total seconds will your crew spend working during the race?
answer:To solve the problem, we need to calculate the total time spent by the pit crew on each pit stop and then multiply it by the number of pit stops.Step 1: Determine the time spent on one pit stop.- Time to change 4 tires = 12 seconds- Time to refuel the car = 8 seconds- Total time for one pit stop = time to change tires + time to refuel [ text{Total time for one pit stop} = 12 text{ seconds} + 8 text{ seconds} = 20 text{ seconds} ]Step 2: Determine the total time for all pit stops.- Number of pit stops = 3- Total time for 3 pit stops = number of pit stops (times) time per pit stop [ text{Total time for 3 pit stops} = 3 times 20 text{ seconds} = 60 text{ seconds} ]Thus, the total time your crew will spend working during the race is 60 seconds.# 60
question:A philosopher from a distant country spends 3 hours each day meditating and teaching Eastern philosophy. On Monday, she meditated for 2 hours and taught philosophy for 1 hour. On Tuesday, she meditated for 1 hour and taught philosophy for 2 hours. On Wednesday, she meditated for 1.5 hours and taught philosophy for 1.5 hours. Calculate the total number of hours she spent meditating and teaching philosophy over these three days.
answer:To solve the problem, we need to find the total number of hours the philosopher spent meditating and teaching philosophy over the three days: Monday, Tuesday, and Wednesday.Step-by-step solution:1. Calculate total hours for Monday: - Meditating: 2 hours - Teaching philosophy: 1 hour - Total for Monday = 2 + 1 = 3 hours2. Calculate total hours for Tuesday: - Meditating: 1 hour - Teaching philosophy: 2 hours - Total for Tuesday = 1 + 2 = 3 hours3. Calculate total hours for Wednesday: - Meditating: 1.5 hours - Teaching philosophy: 1.5 hours - Total for Wednesday = 1.5 + 1.5 = 3 hours4. Sum the total hours across all three days: - Total hours for Monday = 3 hours - Total hours for Tuesday = 3 hours - Total hours for Wednesday = 3 hours - Total over the three days = 3 + 3 + 3 = 9 hoursThus, the philosopher spent a total of 9 hours meditating and teaching philosophy over the three days.# 9
question:A winemaker has three vineyards, each with its own unique characteristics. The first vineyard produces 250 bottles of wine from every acre, the second vineyard produces 300 bottles from every acre, and the third vineyard produces 350 bottles from every acre. The winemaker has a special blend that requires combining the wine from all three vineyards.This year, the winemaker harvested grapes from 5 acres of the first vineyard, 4 acres of the second vineyard, and 3 acres of the third vineyard. How many bottles of wine in total did the winemaker produce this year from all three vineyards?
answer:To solve this problem, we need to calculate the total number of bottles of wine produced from each vineyard and then sum these amounts.Step 1: Calculate the number of bottles produced from the first vineyard.The first vineyard produces 250 bottles per acre. The winemaker harvested grapes from 5 acres of this vineyard.[text{Bottles from first vineyard} = 250 , text{bottles/acre} times 5 , text{acres} = 1250 , text{bottles}]Step 2: Calculate the number of bottles produced from the second vineyard.The second vineyard produces 300 bottles per acre. The winemaker harvested grapes from 4 acres of this vineyard.[text{Bottles from second vineyard} = 300 , text{bottles/acre} times 4 , text{acres} = 1200 , text{bottles}]Step 3: Calculate the number of bottles produced from the third vineyard.The third vineyard produces 350 bottles per acre. The winemaker harvested grapes from 3 acres of this vineyard.[text{Bottles from third vineyard} = 350 , text{bottles/acre} times 3 , text{acres} = 1050 , text{bottles}]Step 4: Calculate the total number of bottles produced.Add the bottles produced from each vineyard to find the total number of bottles:[text{Total bottles} = 1250 , text{bottles} + 1200 , text{bottles} + 1050 , text{bottles} = 3500 , text{bottles}]Therefore, the total number of bottles of wine produced this year from all three vineyards is:# 3500
question:Dr. Sam, a biology PhD student, is studying the spread of disease using agent-based models. In one of their simulations, they are observing a population of 100 virtual animals. Initially, 5 of these animals are infected with a disease. Every day, each infected animal has a chance to spread the disease to 2 more healthy animals. If Dr. Sam runs the simulation for 3 days, how many animals will be infected by the end of the third day, assuming no animal recovers or dies during this time?
answer:To solve this problem, we need to track the spread of the disease over the course of 3 days, given the initial conditions and spread dynamics.Day 0 (Initial Condition):- Total animals = 100- Initially infected animals = 5Day 1:- Each infected animal spreads the disease to 2 more healthy animals.- Number of new infections = 5 infected animals * 2 new infections per animal = 10 new infections- Total infected animals by the end of Day 1 = Initial infected (5) + New infections (10) = 15Day 2:- Now, 15 animals are infected.- Each of these infected animals spreads the disease to 2 more healthy animals.- Number of new infections on Day 2 = 15 infected animals * 2 new infections per animal = 30 new infections- Total infected animals by the end of Day 2 = Previously infected (15) + New infections (30) = 45Day 3:- Now, 45 animals are infected.- Each of these infected animals spreads the disease to 2 more healthy animals.- Number of new infections on Day 3 = 45 infected animals * 2 new infections per animal = 90 new infections- However, there are only 100 total animals, so let's calculate the maximum number of animals that can be infected.- Before Day 3, 45 animals are already infected.- Maximum possible additional infections = Total animals (100) - Already infected (45) = 55- Since the number of new infections (90) exceeds the number of remaining healthy animals (55), only 55 new infections can occur.- Total infected animals by the end of Day 3 = Previously infected (45) + Additional possible infections (55) = 100By the end of the third day, all animals will be infected.# 100
question:Mr. Johnson is a credit union manager who provides microloans to help small businesses in his community grow. This month, he approved microloans for 5 different enterprises. Each enterprise received a loan of 2,000. In addition, Mr. Johnson also approved a loan of 1,500 for a local bakery and 1,200 for a community gardening project. How much money in total did Mr. Johnson distribute in microloans this month?
answer:To find the total amount of money Mr. Johnson distributed in microloans this month, we need to add up all the loans he approved. Let's break it down step-by-step:1. Calculate the total amount for the 5 enterprises: Each of the 5 enterprises received a loan of 2,000. [ text{Total for enterprises} = 5 times 2,000 = 10,000 ]2. Add the amount for the local bakery: The local bakery received a loan of 1,500. [ text{Total for enterprises and bakery} = 10,000 + 1,500 = 11,500 ]3. Add the amount for the community gardening project: The community gardening project received a loan of 1,200. [ text{Total distributed} = 11,500 + 1,200 = 12,700 ]Therefore, the total amount of money Mr. Johnson distributed in microloans this month is 12,700.# 12,700
question:The local radio talk show host in Indiana, who loves discussing state politics, plans to dedicate a special week of shows to cover the upcoming state elections. Each day from Monday to Friday, they feature a different political topic. On Monday, they have 5 callers discussing education policies. On Tuesday, 8 callers share their views on healthcare. Wednesday sees 6 callers debating environmental issues. Thursday, 7 callers discuss transportation policies, and Friday wraps up with 9 callers talking about economic development.If each caller spends an average of 3 minutes on air, how many total minutes of airtime does the host dedicate to callers over the entire week?
answer:To find the total minutes of airtime dedicated to callers over the entire week, we need to calculate the total number of callers and multiply that by the average time each caller spends on air.1. Calculate the number of callers each day: - Monday: 5 callers - Tuesday: 8 callers - Wednesday: 6 callers - Thursday: 7 callers - Friday: 9 callers2. Calculate the total number of callers for the week: [ text{Total callers} = 5 + 8 + 6 + 7 + 9 ]3. Perform the addition: [ 5 + 8 = 13 ] [ 13 + 6 = 19 ] [ 19 + 7 = 26 ] [ 26 + 9 = 35 ] So, there are 35 callers in total.4. Each caller spends an average of 3 minutes on air. Calculate the total airtime: [ text{Total airtime} = 35 text{ callers} times 3 text{ minutes per caller} ]5. Perform the multiplication: [ 35 times 3 = 105 ]The host dedicates a total of 105 minutes of airtime to callers over the entire week.# 105