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question:Samantha, a dancer turned fitness enthusiast, loves to create workout routines inspired by dance steps. In her latest class, she combines dance moves with fitness exercises. She plans a routine where each segment lasts the same amount of time. Samantha starts with a 5-minute warm-up, followed by 4 segments of dance-inspired exercises. Each segment consists of 8 minutes of dance cardio, 6 minutes of strength training, and 4 minutes of stretching. After completing all the segments, she finishes with a 10-minute cool-down. How long, in minutes, is Samantha's entire workout routine?
answer:To find the total duration of Samantha's workout routine, we need to calculate the time spent in each part of the routine and then sum them up. Here's the step-by-step breakdown:1. Warm-up: The routine starts with a 5-minute warm-up.2. Each Segment Duration: Each segment consists of: - 8 minutes of dance cardio - 6 minutes of strength training - 4 minutes of stretching So, the duration of one segment is: [ 8 text{ minutes} + 6 text{ minutes} + 4 text{ minutes} = 18 text{ minutes} ]3. Total Duration of All Segments: Samantha has 4 segments in her routine. Therefore, the total time for all segments is: [ 4 times 18 text{ minutes} = 72 text{ minutes} ]4. Cool-down: The routine ends with a 10-minute cool-down.5. Total Workout Duration: Add up the time for the warm-up, all segments, and the cool-down: [ 5 text{ minutes (warm-up)} + 72 text{ minutes (segments)} + 10 text{ minutes (cool-down)} = 87 text{ minutes} ]Thus, the total duration of Samantha's entire workout routine is 87 minutes.# 87
question:Professor Smith, a political science professor specializing in electoral systems, has been studying the voting patterns in Wisconsin for decades. In a recent election, Wisconsin had 72 counties. Professor Smith noticed that 40% of the counties favored Candidate A, while the remaining counties favored Candidate B. After analyzing the data, Professor Smith found that, on average, 25,000 people voted in each county that favored Candidate A, and 30,000 people voted in each county that favored Candidate B. How many total votes did both candidates receive combined in this election?
answer:To solve this problem, we need to perform the following steps:1. Determine the number of counties favoring each candidate: - The total number of counties in Wisconsin is 72. - 40% of the counties favored Candidate A. Therefore, the number of counties favoring Candidate A is (0.40 times 72 = 28.8). Since we cannot have a fraction of a county, we interpret this as 28 counties favoring Candidate A. - The remaining counties favored Candidate B. Therefore, the number of counties favoring Candidate B is (72 - 28 = 44).2. Calculate the total number of votes for each candidate: - For counties favoring Candidate A, the average number of voters per county is 25,000. Therefore, the total number of votes from counties favoring Candidate A is (28 times 25,000 = 700,000). - For counties favoring Candidate B, the average number of voters per county is 30,000. Therefore, the total number of votes from counties favoring Candidate B is (44 times 30,000 = 1,320,000).3. Calculate the combined total votes for both candidates: - To find the total number of votes in the election, we add the votes for Candidate A and Candidate B: [ 700,000 + 1,320,000 = 2,020,000 ]Thus, the total number of votes received by both candidates combined is:# 2,020,000
question:A religious scholar who specializes in Mariology is visiting a region with a rich tradition of honoring the Virgin Mary through local folklore. In this region, there are 12 villages, and each village has its own unique festival dedicated to the Virgin Mary. The scholar decides to attend as many festivals as possible during a 30-day research trip. Each festival lasts 2 days, and the scholar needs 1 day of rest after attending each festival. How many festivals can the scholar attend during the 30-day trip, given the schedule of each festival does not overlap?
answer:To solve this problem, we need to consider the constraints and optimize the number of festivals the scholar can attend during the 30-day trip. Here are the steps to find the solution:1. Understand the Schedule: - Each festival lasts 2 days. - After attending a festival, the scholar requires 1 day of rest. - This means attending one festival takes up a total of 3 days (2 days for the festival + 1 day of rest).2. Calculate Total Time Required Per Festival: - If the scholar attends one festival, they use up 3 days total. - Therefore, in a 30-day period, the scholar can attend a maximum number of festivals given by the integer division of 30 by 3.3. Perform the Calculation: - Number of festivals = Total days available / Days per festival - Number of festivals = 30 days / 3 days per festival - Number of festivals = 104. Conclusion: - The scholar can attend 10 festivals during the 30-day trip, as each festival and rest cycle consumes 3 days, allowing for exactly 10 such cycles in 30 days.Thus, the final answer is:# 10
question:Agent Taylor, a rising star in the FBI, is working on a case to protect the nation from a group planning a major heist. The group is planning to steal from 5 different locations across the city, and each location has a different amount of money. The amounts are: 120,000, 150,000, 180,000, 200,000, and 250,000. Agent Taylor needs to find the total amount of money the group is planning to steal. Additionally, if Agent Taylor can recover 3/5 of the total amount, how much money will Agent Taylor successfully recover?
answer:To solve the problem, we need to perform the following steps:1. Calculate the total amount of money planned to be stolen: We add up all the amounts from the different locations: [ 120,000 + 150,000 + 180,000 + 200,000 + 250,000 ] Let's do the addition step-by-step: [ 120,000 + 150,000 = 270,000 ] [ 270,000 + 180,000 = 450,000 ] [ 450,000 + 200,000 = 650,000 ] [ 650,000 + 250,000 = 900,000 ] So, the total amount of money the group is planning to steal is 900,000.2. Calculate the amount of money Agent Taylor can recover: Agent Taylor can recover (frac{3}{5}) of the total amount. To find this, we calculate: [ frac{3}{5} times 900,000 ] First, calculate (frac{3}{5} times 900,000): [ frac{3}{5} times 900,000 = 3 times frac{900,000}{5} ] Calculate (frac{900,000}{5}): [ frac{900,000}{5} = 180,000 ] Multiply by 3: [ 3 times 180,000 = 540,000 ] Therefore, Agent Taylor can successfully recover 540,000.Now, output the final answer.# 540,000
question:A veteran role coach is training 5 trainees for a play. Each trainee has to learn 3 different lines before the first rehearsal. The coach wants to ensure that each line is memorized with the correct emotion, so he spends 20 minutes per line with each trainee. Additionally, the coach spends 10 extra minutes with each trainee to check their adaptability to different situations. How much total time does the coach spend with all the trainees combined?
answer:To solve the problem, we need to calculate the total time the coach spends with all 5 trainees.Step-by-step solution:1. Determine the time spent per trainee for learning lines: - Each trainee has to learn 3 different lines. - The coach spends 20 minutes per line with each trainee. - Therefore, the time spent per trainee on lines is: [ 3 , text{lines} times 20 , text{minutes/line} = 60 , text{minutes per trainee} ]2. Determine the time spent per trainee for adaptability check: - The coach spends an additional 10 minutes with each trainee for checking adaptability. - Therefore, the total time spent per trainee (including lines and adaptability check) is: [ 60 , text{minutes (lines)} + 10 , text{minutes (adaptability)} = 70 , text{minutes per trainee} ]3. Calculate the total time spent for all trainees: - There are 5 trainees. - The total time spent with all trainees is: [ 5 , text{trainees} times 70 , text{minutes/trainee} = 350 , text{minutes} ]The total time the coach spends with all the trainees combined is 350 minutes.# 350
question:A Serbian historian is researching the number of important World War II events that took place in the former Yugoslavia. She finds that in the year 1941, there were 18 significant events. In 1942, the number of events increased by 25%, and in 1943, there was an additional increase of 10 events compared to 1942. In 1944, the number of events decreased by 20% from the previous year, and in 1945, the number of events was half of what it was in 1944. How many significant events took place in total from 1941 to 1945 in the former Yugoslavia?
answer:To solve the problem, we need to calculate the number of significant events for each year from 1941 to 1945, and then sum these numbers.1. 1941: - Number of events = 182. 1942: - The number of events increased by 25% compared to 1941. - Increase = 25% of 18 = 0.25 × 18 = 4.5 - Number of events in 1942 = 18 + 4.5 = 22.53. 1943: - The number of events increased by 10 compared to 1942. - Number of events in 1943 = 22.5 + 10 = 32.54. 1944: - The number of events decreased by 20% compared to 1943. - Decrease = 20% of 32.5 = 0.20 × 32.5 = 6.5 - Number of events in 1944 = 32.5 - 6.5 = 265. 1945: - The number of events was half of what it was in 1944. - Number of events in 1945 = 26 / 2 = 136. Total number of significant events from 1941 to 1945: - Total = 18 + 22.5 + 32.5 + 26 + 13 = 112Therefore, the total number of significant events from 1941 to 1945 is:# 112