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question：Dr. Lise Meitner, an Austrian-Swedish physicist, was a prominent scientist in the early 20th century. She is known for her work on nuclear fission, which she conducted with her collaborator Otto Hahn. Suppose you are writing a paper on lesser-known scientists like Meitner and you want to include some interesting numbers related to her life and work.Dr. Meitner was born in 1878 and she began collaborating with Otto Hahn in 1907. They worked together for 31 years until she had to flee Germany in 1938. During the next 20 years, she continued to contribute to scientific research and published an average of 3 papers per year until she retired.Calculate the total number of years Dr. Meitner was actively working in science, the number of years she collaborated with Otto Hahn, and the total number of papers she published after fleeing Germany. Then, find the sum of these three numbers to get a final interesting number related to her career.
answer：First, I need to calculate the total number of years Dr. Meitner was actively working in science. She started her career in 1907 and continued until she retired. Since she retired after 20 years of publishing papers post-1938, her retirement year would be 1958. Therefore, the total active years are from 1907 to 1958, which is 51 years.Next, the number of years she collaborated with Otto Hahn is given as 31 years, from 1907 to 1938.Lastly, to find the total number of papers she published after fleeing Germany, I multiply the number of years she published (20 years) by the average number of papers per year (3 papers). This gives a total of 60 papers.Finally, I sum these three numbers: 51 years of active work, 31 years of collaboration, and 60 papers, resulting in a final interesting number of 142.
question：An archaeology student, inspired by Sylvia Hallam's work on prehistoric settlements, is conducting a survey on a newly discovered site. The student aims to map out the area to understand how ancient people might have lived. The site is rectangular and measures 150 meters in length and 100 meters in width. The student decides to divide the site into smaller, square plots for detailed study, with each plot having a side length of 10 meters. How many square plots will the student be able to create from the entire site?
answer：First, I need to determine the area of the entire archaeological site. The site is rectangular, so its area can be calculated by multiplying its length by its width.Next, I'll calculate the area of one square plot. Since each plot has a side length of 10 meters, the area of one plot is 10 meters multiplied by 10 meters.Finally, to find out how many square plots can be created from the entire site, I'll divide the total area of the site by the area of one square plot. This will give me the total number of plots.
question：Alex is a developer who is working on optimizing an online trading platform to execute trades faster. Before optimization, the platform was able to process 120 trades in one minute. After Alex improved the system, the platform can now process trades 25% faster. If each trade represents a transaction fee of 0.50 for the platform, calculate the increase in transaction fees per minute after Alex's optimization.
answer：First, I need to determine the original number of trades processed per minute, which is 120.Next, since the system is now 25% faster, I'll calculate the new processing speed. A 25% increase means multiplying the original number by 1.25, resulting in 150 trades per minute.Then, I'll find out how many additional trades are being processed each minute by subtracting the original number from the new number: 150 - 120 = 30 extra trades per minute.Each trade generates a transaction fee of 0.50, so the increase in transaction fees per minute is 30 trades multiplied by 0.50, which equals 15.
question：Jamie is a competitive cyclist known for setting record times in local triathlon events. In one triathlon, Jamie completed the cycling portion in 1 hour and 12 minutes. This was 15 minutes faster than Jamie's previous record time for the cycling portion of the same event. If the swimming and running portions together took Jamie 2 hours and 8 minutes to complete, what was Jamie's total time for the entire triathlon in hours and minutes?
answer：First, I need to determine the total time Jamie spent on the triathlon by adding the time taken for each portion: swimming, cycling, and running.Jamie completed the cycling portion in 1 hour and 12 minutes. The swimming and running portions together took 2 hours and 8 minutes.To find the total time, I'll add the cycling time to the combined swimming and running time.1 hour and 12 minutes plus 2 hours and 8 minutes equals 3 hours and 20 minutes.Therefore, Jamie's total time for the entire triathlon is 3 hours and 20 minutes.
question：An Alaskan native wants to honor Buzzy Peltola by organizing a community event to celebrate his contributions. They plan to bake traditional salmon pies and distribute them to 4 villages in the area. Each village will receive the same number of pies. They have enough ingredients to bake 32 salmon pies in total. Additionally, they need 3 extra pies to be served at the event itself. If they bake a total of 35 pies, how many pies will each village receive?
answer：First, I need to determine the total number of salmon pies baked, which is 35.Out of these, 3 pies are reserved to be served at the event itself.This leaves 35 minus 3, which equals 32 pies to be distributed to the villages.There are 4 villages that will each receive the same number of pies.To find out how many pies each village gets, I divide the remaining 32 pies by 4.32 divided by 4 equals 8.Therefore, each village will receive 8 pies.
question：A jazz bassist is practicing for an upcoming concert. They have a setlist of 12 songs, and each song lasts about 5 minutes. For each song, the bassist performs a solo that lasts an additional 2 minutes. How many total minutes will the bassist spend practicing all the songs and solos together?
answer：First, I need to determine the total duration of the songs. There are 12 songs, each lasting 5 minutes. So, the total time for the songs is 12 multiplied by 5, which equals 60 minutes.Next, I'll calculate the total duration of the solos. The bassist performs a solo for each song, and each solo lasts 2 minutes. Therefore, the total time for the solos is 12 multiplied by 2, which equals 24 minutes.Finally, to find the total practice time, I'll add the total song duration and the total solo duration together. Adding 60 minutes and 24 minutes gives a total of 84 minutes.