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question:A government official is responsible for ensuring financial compliance in the video game sector. This year, she is reviewing the finances of three major video game companies: GameTech, PlayZone, and DigiWorld. Each company must pay a compliance fee based on their annual revenue. - GameTech has an annual revenue of 2,000,000 and needs to pay 5% of this as a compliance fee.- PlayZone has an annual revenue of 3,500,000 and needs to pay 4% of this as a compliance fee.- DigiWorld has an annual revenue of 4,800,000 and needs to pay 3% of this as a compliance fee.Calculate the total amount of compliance fees collected from all three companies.
answer:To solve this problem, we will calculate the compliance fee for each company based on their annual revenue and the specified percentage. Then, we will sum the fees to find the total amount collected.1. Calculate the compliance fee for GameTech: - Annual revenue: 2,000,000 - Compliance fee rate: 5% - Compliance fee for GameTech = 5% of 2,000,000 - Compliance fee for GameTech = (0.05 times 2,000,000 = 100,000)2. Calculate the compliance fee for PlayZone: - Annual revenue: 3,500,000 - Compliance fee rate: 4% - Compliance fee for PlayZone = 4% of 3,500,000 - Compliance fee for PlayZone = (0.04 times 3,500,000 = 140,000)3. Calculate the compliance fee for DigiWorld: - Annual revenue: 4,800,000 - Compliance fee rate: 3% - Compliance fee for DigiWorld = 3% of 4,800,000 - Compliance fee for DigiWorld = (0.03 times 4,800,000 = 144,000)4. Calculate the total compliance fees collected: - Total compliance fees = Compliance fee for GameTech + Compliance fee for PlayZone + Compliance fee for DigiWorld - Total compliance fees = 100,000 + 140,000 + 144,000 - Total compliance fees = 384,000# 384,000
question:A local historian from St. Louis is organizing a walking tour of historical landmarks in the city. The tour includes 5 stops: the Gateway Arch, the Old Courthouse, the Anheuser-Busch Brewery, the Missouri History Museum, and the Cathedral Basilica of St. Louis. The tour starts at the Gateway Arch and covers a total distance of 12 miles. If the distance between the Gateway Arch and the Old Courthouse is 1.5 miles, the distance between the Old Courthouse and the Anheuser-Busch Brewery is 2.5 miles, the distance between the Anheuser-Busch Brewery and the Missouri History Museum is 3.5 miles, and the distance between the Missouri History Museum and the Cathedral Basilica of St. Louis is 2 miles, how far is the final walk from the Cathedral Basilica back to the Gateway Arch?
answer:To solve the problem, we need to find the final distance from the Cathedral Basilica of St. Louis back to the starting point, the Gateway Arch. We will do this by first adding up the known distances between the stops and then subtracting this sum from the total tour distance of 12 miles to find the remaining distance back to the Gateway Arch.1. List the known distances between stops: - Gateway Arch to Old Courthouse: 1.5 miles - Old Courthouse to Anheuser-Busch Brewery: 2.5 miles - Anheuser-Busch Brewery to Missouri History Museum: 3.5 miles - Missouri History Museum to Cathedral Basilica of St. Louis: 2 miles2. Calculate the sum of the known distances: [ text{Total Known Distance} = 1.5 text{ miles} + 2.5 text{ miles} + 3.5 text{ miles} + 2 text{ miles} ] [ = 1.5 + 2.5 + 3.5 + 2 = 9.5 text{ miles} ]3. Calculate the remaining distance from the Cathedral Basilica back to the Gateway Arch: [ text{Remaining Distance} = text{Total Tour Distance} - text{Total Known Distance} ] [ = 12 text{ miles} - 9.5 text{ miles} = 2.5 text{ miles} ]Therefore, the distance from the Cathedral Basilica of St. Louis back to the Gateway Arch is 2.5 miles.# 2.5 miles
question:A retired professional football player has joined the local high school wrestling team as a coach. To improve the team’s stamina and discipline, the coach plans a special training session. He decides to include 3 exercises: push-ups, squats, and sprints. Each wrestler will do 20 push-ups, 30 squats, and 10 sprints. There are 12 wrestlers on the team. After the first week, the coach notices that each wrestler improved their performance by doing 5 more push-ups, 10 more squats, and 2 more sprints in each session.How many total push-ups, squats, and sprints will the team complete by the end of the second week if they train 3 times a week?
answer:To solve this problem, we need to calculate the total number of exercises completed by the team by the end of the second week. We'll approach this by calculating the total for each exercise separately and then summing them up. Step 1: Initial Exercises per SessionEach wrestler initially performs:- 20 push-ups- 30 squats- 10 sprintsSince there are 12 wrestlers, the total number of exercises per session is:- Push-ups: ( 20 times 12 = 240 )- Squats: ( 30 times 12 = 360 )- Sprints: ( 10 times 12 = 120 ) Step 2: Improved Exercises per SessionAfter the first week, each wrestler increases their exercises to:- Push-ups: ( 20 + 5 = 25 )- Squats: ( 30 + 10 = 40 )- Sprints: ( 10 + 2 = 12 )The total number of exercises per session after improvement is:- Push-ups: ( 25 times 12 = 300 )- Squats: ( 40 times 12 = 480 )- Sprints: ( 12 times 12 = 144 ) Step 3: Total Exercises for the Second WeekThe team trains 3 times a week. Thus, for the second week, the total number of exercises is:- Push-ups: ( 300 times 3 = 900 )- Squats: ( 480 times 3 = 1440 )- Sprints: ( 144 times 3 = 432 ) Step 4: Final Total CountNow, add the total numbers to find the overall exercises completed by the end of the second week:- Total exercises = Push-ups + Squats + Sprints- Total exercises = ( 900 + 1440 + 432 )Now, calculate this sum:[ 900 + 1440 + 432 = 2772 ]# 2772
question:Dr. Ada is a computer scientist working on a project to develop algorithms that assist in logical proof verification. She needs to determine the efficiency of her algorithms by calculating the average time they take to verify proofs. One day, Dr. Ada tests her algorithm on 4 logical proofs. The first proof takes 12 minutes to verify, the second takes 15 minutes, the third takes 9 minutes, and the fourth takes 14 minutes.To further enhance her algorithm, Dr. Ada decides to implement an optimization that she predicts will reduce the verification time by 20% for each proof. Calculate the new average verification time per proof after applying the optimization to all four proofs.
answer:To solve this problem, we need to calculate the average verification time per proof after applying a 20% reduction to the original times of each proof. Let's go through the steps:1. Calculate the original total time: - First proof: 12 minutes - Second proof: 15 minutes - Third proof: 9 minutes - Fourth proof: 14 minutes Sum the times: [ 12 + 15 + 9 + 14 = 50 text{ minutes} ]2. Calculate the reduced time for each proof: Since the reduction is 20%, each proof will take 80% of its original time. - First proof: (12 times 0.8 = 9.6) minutes - Second proof: (15 times 0.8 = 12) minutes - Third proof: (9 times 0.8 = 7.2) minutes - Fourth proof: (14 times 0.8 = 11.2) minutes3. Calculate the total reduced time: Sum the reduced times: [ 9.6 + 12 + 7.2 + 11.2 = 40 text{ minutes} ]4. Calculate the new average verification time: Divide the total reduced time by the number of proofs: [ frac{40}{4} = 10 text{ minutes} ]Thus, the new average verification time per proof after applying the optimization is (10) minutes.# 10
question:Alex, a young polymath pursuing dual degrees in English Literature and Computer Science, is organizing her bookshelf. She has 120 books, with 3/5 of them being literature books and the rest being computer science books. Alex wants to arrange her literature books in stacks of 8 and her computer science books in stacks of 5. How many stacks of each type of book will Alex have?
answer:To solve the problem, we need to determine how many literature books and how many computer science books Alex has, and then find out how many stacks of each type she can make.Step 1: Calculate the number of literature books.- Alex has 120 books in total.- 3/5 of her books are literature books.[text{Number of literature books} = frac{3}{5} times 120 = 72]Step 2: Calculate the number of computer science books.- The rest of the books are computer science books.[text{Number of computer science books} = 120 - 72 = 48]Step 3: Determine the number of stacks for literature books.- Literature books are arranged in stacks of 8.[text{Number of stacks of literature books} = frac{72}{8} = 9]Step 4: Determine the number of stacks for computer science books.- Computer science books are arranged in stacks of 5.[text{Number of stacks of computer science books} = frac{48}{5} = 9.6]Since Alex wants full stacks, she can only make 9 full stacks with 3 books left over (since (48 div 5 = 9 text{ R } 3)).Therefore, Alex will have:- 9 stacks of literature books- 9 full stacks of computer science books# 9 stacks of literature books and 9 full stacks of computer science books
question:Jamie is a young fashion student who loves discovering unique fabrics at local thrift stores. On Saturday, Jamie found a vintage floral fabric for 4 per yard and bought 3 yards. Later, Jamie found a rare geometric print fabric for 5 per yard and purchased 2 yards. On Sunday, Jamie visited another thrift store and found a beautiful striped fabric for 3 per yard and bought 4 yards. How much did Jamie spend in total on fabric over the weekend?
answer:To find out how much Jamie spent in total on fabric over the weekend, we need to calculate the cost for each fabric purchase and then add them all together.Step 1: Calculate the cost of the vintage floral fabric.Jamie bought 3 yards of vintage floral fabric at 4 per yard. Cost of vintage floral fabric = Number of yards × Price per yard = 3 yards × 4/yard = 12Step 2: Calculate the cost of the geometric print fabric.Jamie bought 2 yards of geometric print fabric at 5 per yard. Cost of geometric print fabric = Number of yards × Price per yard = 2 yards × 5/yard = 10Step 3: Calculate the cost of the striped fabric.Jamie bought 4 yards of striped fabric at 3 per yard. Cost of striped fabric = Number of yards × Price per yard = 4 yards × 3/yard = 12Step 4: Calculate the total cost.Now, add up the costs of all the fabrics Jamie purchased. Total cost = Cost of vintage floral fabric + Cost of geometric print fabric + Cost of striped fabric = 12 + 10 + 12 = 34# 34