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question：Alex is a mechanic who specializes in vintage car restoration. He is currently working on restoring a 1950s classic car and needs to replace the old vinyl on the car seats. He recommends a reliable supplier that sells high-quality vinyl material. The supplier charges 12 per square yard of vinyl. The car seats require a total of 15 square yards of vinyl. In addition, Alex needs to factor in an extra 10% for any potential mistakes during installation. How much will Alex spend on the vinyl material for the car seats, including the extra allowance?Calculate the total cost of vinyl material that Alex needs to purchase.
answer：First, I need to determine the total amount of vinyl Alex requires, including the extra 10% for potential mistakes.Alex initially needs 15 square yards of vinyl. Adding 10% to this amount ensures there is enough material to cover any errors during installation.Calculating 10% of 15 square yards gives 1.5 square yards. Adding this to the initial 15 square yards results in a total requirement of 16.5 square yards.Next, I'll calculate the cost of 16.5 square yards of vinyl at the supplier's rate of 12 per square yard. Multiplying 16.5 by 12 gives the total cost.
question：Alex is a data analyst who enjoys working with numbers in silence and prefers spending time alone rather than discussing celebrity gossip. One quiet afternoon, Alex decided to analyze the number of hours they worked over the past week. On Monday, Alex worked 4 hours without any distractions. On Tuesday, they worked 6 hours. Wednesday was a particularly focused day, and Alex managed to work 8 hours. On Thursday, Alex worked 5 hours, and on Friday, they wrapped up the week with another 7 hours of work.To better understand their work pattern, Alex wants to calculate the total number of hours worked over the week and the average number of hours worked per day. What is the total number of hours Alex worked during the week, and what is the average number of hours worked per day?
answer：To determine the total number of hours Alex worked during the week, I will add up the hours worked each day.First, I will list the hours worked each day:- Monday: 4 hours- Tuesday: 6 hours- Wednesday: 8 hours- Thursday: 5 hours- Friday: 7 hoursNext, I will add these numbers together to find the total hours:4 + 6 = 1010 + 8 = 1818 + 5 = 2323 + 7 = 30So, the total number of hours worked during the week is 30 hours.To find the average number of hours worked per day, I will divide the total hours by the number of days worked. Alex worked from Monday to Friday, which is 5 days.30 hours ÷ 5 days = 6 hours per dayTherefore, the average number of hours worked per day is 6 hours.
question：A group of executives is responsible for overseeing the operations of a data center. The data center has 120 servers, and each server can handle 75 terabytes of data. During a routine check, the executives discover that 20% of the servers are under maintenance and cannot be used. The remaining servers are operating at full capacity. How many terabytes of data can the operating servers collectively handle?
answer：First, determine the total number of servers in the data center, which is 120.Next, calculate 20% of the servers to find out how many are under maintenance. 20% of 120 is 24 servers.Subtract the number of servers under maintenance from the total number of servers to find out how many are operating. 120 minus 24 equals 96 servers.Each operating server can handle 75 terabytes of data. Multiply the number of operating servers by the capacity of each server to find the total data capacity. 96 multiplied by 75 equals 7,200 terabytes.Therefore, the operating servers can collectively handle 7,200 terabytes of data.
question：A brilliant mathematician, inspired by the captain's logical approach to problem-solving, decides to organize a treasure hunt puzzle for their students. The treasure is hidden in a series of locked boxes, each requiring a number code to open. The mathematician creates a series of clues based on logical reasoning and arithmetic operations.The first clue directs the students to a map with 5 locations marked, labeled A through E. The students must solve a series of math problems to find the correct order to visit these locations. The mathematician provides the following instructions:1. Start at location A and add 8 to the number of letters in the name of the location (A has 1 letter).2. Move to location B, which has 1 more letter than location A. Multiply this number by 3.3. At location C, which has 1 more letter than location B, subtract 2 from the result.4. Go to location D, which has 1 more letter than location C, and divide the result by 4.5. Finally, at location E, which has 1 more letter than location D, add 12 to the result.What is the final number code the students need to unlock the last box and find the treasure?
answer：First, I'll identify the number of letters in each location's name:- A has 1 letter.- B has 2 letters.- C has 3 letters.- D has 4 letters.- E has 5 letters.Next, I'll follow the mathematician's instructions step by step:1. Start at location A and add 8 to the number of letters: 1 + 8 = 9.2. Move to location B and multiply the result by 3: 9 × 3 = 27.3. At location C, subtract 2 from the result: 27 - 2 = 25.4. Go to location D and divide the result by 4: 25 ÷ 4 = 6.25.5. Finally, at location E, add 12 to the result: 6.25 + 12 = 18.25.The final number code needed to unlock the last box is 18.25.
question：A customs supervisor from the Southern region is visiting another customs supervisor in the Northern region to discuss best practices and strategies. During their meeting, they decide to compare the number of shipments they each process weekly. The Southern region supervisor processes 23 shipments per day, while the Northern region supervisor processes 17 shipments per day. If both supervisors work 5 days a week, how many more shipments does the Southern region supervisor process than the Northern region supervisor in one week?
answer：First, I need to determine the number of shipments each supervisor processes in one week.The Southern region supervisor processes 23 shipments per day and works 5 days a week. So, I'll multiply 23 by 5 to find the weekly total.Similarly, the Northern region supervisor processes 17 shipments per day and also works 5 days a week. I'll multiply 17 by 5 to find their weekly total.After calculating both totals, I'll subtract the Northern supervisor's total from the Southern supervisor's total to find out how many more shipments the Southern supervisor processes in one week.
question：Alex is a motorcycle enthusiast who customizes their bike to perfection. Last weekend, Alex decided to take a thrilling ride on their favorite mountain trail. Before starting, Alex checked their bike and saw that the fuel tank was full, holding 15 liters of gasoline. Their custom bike uses 0.5 liters of gasoline per 10 kilometers. Alex plans to ride to a scenic point 60 kilometers away and then return home along the same route. How many liters of gasoline will Alex have left in the tank after completing the round trip?
answer：First, I need to determine the total distance of Alex's round trip. Since the scenic point is 60 kilometers away and Alex plans to return home along the same route, the total distance will be 60 km multiplied by 2, which equals 120 kilometers.Next, I'll calculate the total amount of gasoline required for the trip. The bike consumes 0.5 liters of gasoline for every 10 kilometers. To find out how many 10-kilometer segments are in the 120-kilometer trip, I'll divide 120 by 10, resulting in 12 segments. Multiplying the number of segments by the gasoline consumption per segment (0.5 liters) gives a total gasoline usage of 6 liters.Finally, I'll determine how much gasoline will remain in the tank after the trip. Alex started with a full tank of 15 liters. Subtracting the 6 liters used during the trip from the initial 15 liters leaves 9 liters of gasoline remaining in the tank.