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question:Ms. Nkosi is a business owner in South Africa who values privacy. She has a small secret garden behind her office where she often retreats to enjoy some peaceful moments. Her garden is in the shape of a rectangle. The length of the garden is 12 meters, and the width is 8 meters. She decides to plant a border of lavender plants around the edge of the garden. If each lavender plant requires 1 meter of space, how many lavender plants will Ms. Nkosi need to plant around the entire perimeter of her garden?
answer:To determine how many lavender plants Ms. Nkosi will need to plant around the perimeter of her garden, we will follow these steps:1. Calculate the perimeter of the rectangular garden. The formula to calculate the perimeter ( P ) of a rectangle is: [ P = 2 times (text{length} + text{width}) ] Given: - Length = 12 meters - Width = 8 meters Plug these values into the formula: [ P = 2 times (12 + 8) ] [ P = 2 times 20 ] [ P = 40 text{ meters} ]2. Determine how many lavender plants are needed. Each lavender plant requires 1 meter of space. Therefore, the number of lavender plants needed is equal to the perimeter of the garden, since each 1-meter segment along the perimeter can accommodate one plant. Thus, Ms. Nkosi will need: [ 40 text{ lavender plants} ]The final solution is:# 40
question:The vineyard owner, Maria, produces bottles of wine each season. She has 250 grapevines, and each vine produces about 4 bunches of grapes. Each bunch of grapes can make 1 bottle of wine. Maria wants to minimize the use of additives, so she decides to only use additives in 20% of the bottles for added flavor. If Maria decides to use additives in the wine, how many bottles will have additives, and how many bottles will be additive-free?
answer:To solve this problem, we need to follow these steps:1. Calculate the total number of bottles produced: - Maria has 250 grapevines. - Each vine produces about 4 bunches of grapes. - Each bunch of grapes can make 1 bottle of wine. Therefore, the total number of bottles produced is: [ 250 , text{vines} times 4 , text{bunches per vine} = 1000 , text{bottles} ]2. Determine the number of bottles with additives: - Maria decides to use additives in 20% of the bottles. Thus, the number of bottles with additives is: [ 0.20 times 1000 , text{bottles} = 200 , text{bottles} ]3. Calculate the number of additive-free bottles: - Subtract the number of bottles with additives from the total number of bottles to find the number of additive-free bottles. Thus, the number of additive-free bottles is: [ 1000 , text{bottles} - 200 , text{bottles} = 800 , text{bottles} ]Now, let's present the final answer.# 200 bottles with additives, 800 bottles additive-free
question:Emily is an aspiring young author who writes a short story every week inspired by her favorite author, Lara Prescott. She plans to write a total of 50 short stories this year. If she has already written 18 stories, how many more stories does she need to write to reach her goal? After reaching her goal, Emily plans to compile her stories into collections, with each collection containing 5 stories. How many collections will she be able to make once she has completed all 50 stories?
answer:To solve this problem, we need to figure out two things: how many more stories Emily needs to write to reach her goal of 50 stories, and how many collections of 5 stories each she can make once she has completed all 50 stories.Step 1: Determine how many more stories Emily needs to write.1. Emily has a goal of writing 50 stories.2. She has already written 18 stories.3. To find out how many more stories she needs to write, subtract the number of stories she has already written from her goal: [ 50 - 18 = 32 ] So, Emily needs to write 32 more stories to reach her goal of 50 stories.Step 2: Determine how many collections of 5 stories each she can make.1. Once Emily reaches her goal, she will have 50 stories.2. Each collection will contain 5 stories.3. To find out how many collections Emily can make, divide the total number of stories by the number of stories per collection: [ frac{50}{5} = 10 ] Therefore, Emily can make 10 collections of stories.Final Answer:# 10
question:Alex, a computer science student, has created an interactive website to help explain algorithm complexity to beginners. To illustrate the concept of time complexity, Alex has designed a series of interactive exercises. One of these exercises involves sorting various numbers and comparing the time it takes using different algorithms.In one of the exercises, Alex asks the users to sort a list of numbers using both a simple sorting algorithm and a more efficient one. The simple algorithm takes 5 seconds to sort 10 numbers. For every additional 5 numbers, it takes an additional 3 seconds. The more efficient algorithm takes 2 seconds to sort 10 numbers and an additional 1 second for every additional 5 numbers.If a user has a list of 25 numbers to sort, how much faster in seconds is the more efficient algorithm compared to the simple one?
answer:To solve this problem, we need to calculate the time taken by both the simple sorting algorithm and the more efficient algorithm to sort a list of 25 numbers, and then find the difference in time.Step 1: Calculate the time taken by the simple algorithm.- According to the problem, the simple algorithm takes 5 seconds to sort 10 numbers.- For every additional 5 numbers, it takes an additional 3 seconds.Let's break it down:1. For the first 10 numbers, it takes 5 seconds.2. For the next 5 numbers (making 15 in total), it takes an additional 3 seconds (5 + 3 = 8 seconds).3. For the next 5 numbers (making 20 in total), it takes another 3 seconds (8 + 3 = 11 seconds).4. For the next 5 numbers (making 25 in total), it takes another 3 seconds (11 + 3 = 14 seconds).Thus, the total time taken by the simple algorithm to sort 25 numbers is 14 seconds.Step 2: Calculate the time taken by the more efficient algorithm.- According to the problem, the more efficient algorithm takes 2 seconds to sort 10 numbers.- For every additional 5 numbers, it takes an additional 1 second.Let's break it down:1. For the first 10 numbers, it takes 2 seconds.2. For the next 5 numbers (making 15 in total), it takes an additional 1 second (2 + 1 = 3 seconds).3. For the next 5 numbers (making 20 in total), it takes another 1 second (3 + 1 = 4 seconds).4. For the next 5 numbers (making 25 in total), it takes another 1 second (4 + 1 = 5 seconds).Thus, the total time taken by the more efficient algorithm to sort 25 numbers is 5 seconds.Step 3: Calculate the difference in time between the two algorithms.- Time taken by the simple algorithm: 14 seconds.- Time taken by the more efficient algorithm: 5 seconds.To find how much faster the more efficient algorithm is, we subtract the time taken by the more efficient algorithm from the time taken by the simple algorithm:[ 14 , text{seconds} - 5 , text{seconds} = 9 , text{seconds} ]The more efficient algorithm is 9 seconds faster than the simple algorithm.# 9
question:Mr. Lewis, a high school history teacher in Montserrat, is planning a field trip for his students to visit the Montserrat National Museum. He needs to arrange transportation for the 24 students in his class. Each bus can hold 8 students. If the cost to rent one bus is 50, how much will it cost Mr. Lewis to rent enough buses for the entire class?
answer:To determine how much it will cost Mr. Lewis to rent enough buses for his class, we need to follow these steps:1. Calculate the number of buses needed: - Each bus can hold 8 students. - Mr. Lewis has 24 students in his class. - To find the number of buses needed, divide the total number of students by the capacity of one bus: [ text{Number of buses needed} = frac{24}{8} = 3 ] So, Mr. Lewis needs 3 buses.2. Calculate the total cost of renting the buses: - The cost to rent one bus is 50. - Since Mr. Lewis needs 3 buses, the total cost will be: [ text{Total cost} = 3 times 50 = 150 ]Therefore, the total cost for Mr. Lewis to rent enough buses for the entire class is 150.#150
question:A representative from the Ministry of Culture is organizing a series of workshops to promote cross-disciplinary projects between anthropology and technology. Each workshop will have 5 anthropologists and 3 technologists collaborating on projects. If the representative plans to hold 8 workshops, how many anthropologists and technologists in total will participate in these workshops?
answer:To determine the total number of anthropologists and technologists participating in the workshops, we'll follow these steps:1. Calculate the total number of anthropologists for all workshops: - Each workshop includes 5 anthropologists. - There are 8 workshops. - Therefore, the total number of anthropologists is: [ 5 text{ anthropologists/workshop} times 8 text{ workshops} = 40 text{ anthropologists} ]2. Calculate the total number of technologists for all workshops: - Each workshop includes 3 technologists. - There are 8 workshops. - Therefore, the total number of technologists is: [ 3 text{ technologists/workshop} times 8 text{ workshops} = 24 text{ technologists} ]3. Calculate the total number of participants: - Add the total number of anthropologists and technologists: [ 40 text{ anthropologists} + 24 text{ technologists} = 64 text{ participants} ]The total number of participants in all workshops is:# 64