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question:John is the traditional breadwinner for his family, and he values his wife Mary's role in raising their three children. Every month, John earns 4,500 from his job. Mary manages the household expenses, which include 1,200 for groceries, 800 for utilities, 500 for the children's educational needs, and 200 for miscellaneous expenses. One month, the family also decides to put aside 300 for a family vacation. How much money does John have left after covering all these monthly expenses?
answer:To solve this problem, we need to calculate the total monthly expenses and subtract this from John's monthly income to determine how much money is left.1. Calculate the total monthly expenses: - Groceries: 1,200 - Utilities: 800 - Children's educational needs: 500 - Miscellaneous expenses: 200 - Family vacation savings: 300 Add these expenses together to get the total monthly expenses: [ 1,200 + 800 + 500 + 200 + 300 = 3,000 ]2. Subtract the total expenses from John's monthly income: John's monthly income is 4,500. To find out how much money is left after expenses, subtract the total expenses from his income: [ 4,500 - 3,000 = 1,500 ]Therefore, after covering all the monthly expenses, John has 1,500 left.# 1500
question:Detective Riley, a renowned crime fiction author, is known for crafting intricate plots and unexpected twists. To outdo their rival, another crime fiction author named Alex, Riley decides to write a series of suspenseful short stories. Riley plans to write 5 stories, each with 12 chapters, while Alex is writing a novel with 40 chapters. Each chapter in Riley's stories contains 8 scenes, and each scene takes Riley 3 hours to write. Meanwhile, Alex writes at a steady pace of 4 chapters per week. How many more total hours will it take Riley to complete all the scenes in their stories compared to the number of weeks it will take Alex to complete their novel?
answer:To solve this problem, let's break down the tasks for both Riley and Alex. Step 1: Calculate the total number of scenes Riley needs to write.Riley plans to write 5 stories, each with 12 chapters. Each chapter contains 8 scenes. Therefore, the total number of scenes Riley needs to write is:[5 text{ stories} times 12 text{ chapters/story} times 8 text{ scenes/chapter} = 480 text{ scenes}] Step 2: Calculate the total time it takes Riley to write all the scenes.Each scene takes Riley 3 hours to write. Therefore, the total time Riley spends writing all the scenes is:[480 text{ scenes} times 3 text{ hours/scene} = 1440 text{ hours}] Step 3: Calculate the total number of chapters Alex needs to write.Alex is writing a novel with 40 chapters. Step 4: Calculate the total number of weeks it takes Alex to complete their novel.Alex writes at a steady pace of 4 chapters per week. Therefore, the total number of weeks Alex takes to complete the novel is:[frac{40 text{ chapters}}{4 text{ chapters/week}} = 10 text{ weeks}] Step 5: Determine how many more total hours it takes Riley compared to Alex's weeks.We need to compare Riley's total writing hours to the number of weeks Alex takes, noting that each week has 168 hours (7 days/week * 24 hours/day).First, calculate the total hours Alex takes in weeks:[10 text{ weeks} times 168 text{ hours/week} = 1680 text{ hours}]Next, compare the hours:Riley's total hours: 1440 hours Alex's total hours: 1680 hoursRiley spends 1440 hours, which is less than Alex's time measured in hours. Therefore, the difference is:[1680 text{ hours} - 1440 text{ hours} = 240 text{ hours}]Thus, Riley takes 240 fewer hours to complete their work compared to the total hours Alex's work would take if measured in the same unit. Final Answer:# 240
question:As a government accountability officer, you are tasked with ensuring that public funds are spent efficiently. You are reviewing the budget for a new community park project. The initial budget for the park was 250,000. After auditing the expenses, you found that 45,000 was used for landscaping, 30,000 for playground equipment, and 55,000 on construction materials. Additionally, 10,000 was allocated for administrative costs, and 20,000 was set aside for unexpected expenses, which were not used. Calculate how much of the initial budget remains unspent after covering all the costs.
answer:To solve the problem, we need to determine how much of the initial budget remains unspent after accounting for all the costs.Let's go through the expenses one by one and add them up:1. Landscaping: 45,0002. Playground equipment: 30,0003. Construction materials: 55,0004. Administrative costs: 10,0005. Unexpected expenses: 20,000 (although allocated, it was not used, so we shouldn't count it as spent)Now, calculate the total amount spent:[text{Total spent} = text{Landscaping} + text{Playground equipment} + text{Construction materials} + text{Administrative costs}][text{Total spent} = 45,000 + 30,000 + 55,000 + 10,000 = 140,000]Next, subtract the total amount spent from the initial budget to find the unspent amount:[text{Unspent amount} = text{Initial budget} - text{Total spent}][text{Unspent amount} = 250,000 - 140,000 = 110,000]Thus, the amount of the initial budget that remains unspent is 110,000.# 110,000
question:Alex is a ham radio operator who loves sharing real-time weather updates with fellow radio enthusiasts. Every hour, Alex collects weather data and reports it over the radio. During a particularly busy day, Alex reports the temperature, humidity, and wind speed over the course of 5 hours. Hour 1: Temperature is 72°F, humidity is 60%, and wind speed is 5 mph.Hour 2: Temperature increases by 3°F, humidity decreases by 5%, and wind speed increases by 2 mph.Hour 3: Temperature increases by 2°F, humidity decreases by 10%, and wind speed remains the same.Hour 4: Temperature decreases by 5°F, humidity increases by 8%, and wind speed decreases by 1 mph.Hour 5: Temperature stays the same, humidity increases by 2%, and wind speed increases by 3 mph.What are the final temperature, humidity, and wind speed Alex reports at the end of the 5 hours?
answer:To solve the problem, let's track the changes in temperature, humidity, and wind speed over each hour and compute the final values.Initial conditions (Hour 1):- Temperature: 72°F- Humidity: 60%- Wind speed: 5 mphHour 2:- Temperature increases by 3°F: [ 72 + 3 = 75°F ]- Humidity decreases by 5%: [ 60 - 5 = 55% ]- Wind speed increases by 2 mph: [ 5 + 2 = 7 text{ mph} ]Hour 3:- Temperature increases by 2°F: [ 75 + 2 = 77°F ]- Humidity decreases by 10%: [ 55 - 10 = 45% ]- Wind speed remains the same: [ 7 text{ mph} ]Hour 4:- Temperature decreases by 5°F: [ 77 - 5 = 72°F ]- Humidity increases by 8%: [ 45 + 8 = 53% ]- Wind speed decreases by 1 mph: [ 7 - 1 = 6 text{ mph} ]Hour 5:- Temperature stays the same: [ 72°F ]- Humidity increases by 2%: [ 53 + 2 = 55% ]- Wind speed increases by 3 mph: [ 6 + 3 = 9 text{ mph} ]The final values after 5 hours are:- Temperature: 72°F- Humidity: 55%- Wind speed: 9 mph#Final Answer:Temperature: 72°F, Humidity: 55%, Wind Speed: 9 mph
question:A historian fascinated by the developments in Tianjin city is studying the growth of its population over several decades. In 1950, the population of Tianjin was approximately 2 million people. By 1980, the population had grown to around 5 million people. If the population continued to grow at this same rate, what would be the estimated population in 2010?
answer:To solve the problem of estimating the population of Tianjin in 2010, we can assume a constant rate of growth over the periods given. We will use linear interpolation to estimate the population growth over time. Step-by-Step Solution:1. Determine the time intervals: - The population data is given for 1950 and 1980. - The time interval from 1950 to 1980 is 30 years. - We want to estimate the population for the year 2010, which is 60 years from 1950.2. Calculate the rate of population growth: - Initial population in 1950 = 2 million - Population in 1980 = 5 million - Increase in population from 1950 to 1980 = (5 , text{million} - 2 , text{million} = 3 , text{million}) - Growth rate per year = (frac{3 , text{million}}{30 , text{years}} = 0.1 , text{million per year})3. Estimate the population in 2010: - 2010 is 30 years beyond 1980. - Population increase from 1980 to 2010 = (0.1 , text{million per year} times 30 , text{years} = 3 , text{million}) - Estimated population in 2010 = Population in 1980 + Increase from 1980 to 2010 - Estimated population in 2010 = (5 , text{million} + 3 , text{million} = 8 , text{million})Thus, using the assumption of constant rate growth, the estimated population of Tianjin in 2010 would be 8 million people.# 8 million
question:The aspiring novelist, who loves crafting whimsical stories about animals, is writing a new book about a magical forest where each animal has a unique talent. In this forest, there are 12 rabbits who can paint, 8 squirrels who can sing, and 10 turtles who can dance. Each rabbit paints 3 pictures per day, each squirrel sings 2 songs per day, and each turtle performs 1 dance per day. If the novelist wants to write about the total number of paintings, songs, and dances that happen in the forest over 5 days, how many of each activity will she include in her story?
answer:To solve this problem, we need to calculate the total number of paintings, songs, and dances produced by the animals in the forest over the course of 5 days. We will do this by calculating each activity separately:Step 1: Calculate the total number of paintings.- Each rabbit paints 3 pictures per day.- There are 12 rabbits.- Therefore, in one day, the total number of paintings is: [ 12 text{ rabbits} times 3 text{ pictures per rabbit} = 36 text{ pictures} ]- Over 5 days, the total number of paintings is: [ 36 text{ pictures per day} times 5 text{ days} = 180 text{ pictures} ]Step 2: Calculate the total number of songs.- Each squirrel sings 2 songs per day.- There are 8 squirrels.- Therefore, in one day, the total number of songs is: [ 8 text{ squirrels} times 2 text{ songs per squirrel} = 16 text{ songs} ]- Over 5 days, the total number of songs is: [ 16 text{ songs per day} times 5 text{ days} = 80 text{ songs} ]Step 3: Calculate the total number of dances.- Each turtle performs 1 dance per day.- There are 10 turtles.- Therefore, in one day, the total number of dances is: [ 10 text{ turtles} times 1 text{ dance per turtle} = 10 text{ dances} ]- Over 5 days, the total number of dances is: [ 10 text{ dances per day} times 5 text{ days} = 50 text{ dances} ]Thus, the total number of activities over 5 days is:- 180 paintings- 80 songs- 50 dances# 180 paintings, 80 songs, 50 dances