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question:A young dancer from Brazil is practicing a new dance routine inspired by a South Korean dancer's unique style. The routine consists of 4 different dance moves. The first move takes 3 minutes to practice, the second move takes twice as long as the first, the third move takes 5 minutes longer than the second move, and the fourth move takes 6 minutes less than the third. How many total minutes does the Brazilian dancer spend practicing the entire routine?
answer:To solve the problem, let's define the time taken for each dance move based on the information provided:1. First Move: The first move takes 3 minutes to practice.2. Second Move: The second move takes twice as long as the first move. - Since the first move takes 3 minutes, the second move takes (2 times 3 = 6) minutes.3. Third Move: The third move takes 5 minutes longer than the second move. - Since the second move takes 6 minutes, the third move takes (6 + 5 = 11) minutes.4. Fourth Move: The fourth move takes 6 minutes less than the third move. - Since the third move takes 11 minutes, the fourth move takes (11 - 6 = 5) minutes.Now, to find the total practice time, we add up the times for all four moves:- First Move: 3 minutes- Second Move: 6 minutes- Third Move: 11 minutes- Fourth Move: 5 minutesTotal minutes spent practicing:[ 3 + 6 + 11 + 5 = 25 ]# 25
question:Nurse Alex is a psychiatric nurse who works closely with Dr. Smith, a psychologist, to help patients on their treatment plans. In one week, Alex sees 5 patients per day on Monday, Wednesday, and Friday, and 3 patients per day on Tuesday and Thursday. Each patient requires 45 minutes of evaluation and treatment plan discussion. How many hours does Nurse Alex spend with patients in total during that week?
answer:To solve this problem, we need to calculate the total time Nurse Alex spends with patients over the week, given the schedule provided.1. Determine the number of patients Nurse Alex sees each day: - Monday: 5 patients - Tuesday: 3 patients - Wednesday: 5 patients - Thursday: 3 patients - Friday: 5 patients2. Calculate the total number of patients Nurse Alex sees in a week: [ text{Total patients} = 5 (text{Monday}) + 3 (text{Tuesday}) + 5 (text{Wednesday}) + 3 (text{Thursday}) + 5 (text{Friday}) ] [ text{Total patients} = 5 + 3 + 5 + 3 + 5 = 21 ]3. Determine how much time Nurse Alex spends with each patient: - Each patient requires 45 minutes.4. Calculate the total time spent on all patients in minutes: [ text{Total time in minutes} = 21 text{ patients} times 45 text{ minutes per patient} = 945 text{ minutes} ]5. Convert the total time from minutes to hours: - There are 60 minutes in an hour. [ text{Total time in hours} = frac{945 text{ minutes}}{60 text{ minutes per hour}} = 15.75 text{ hours} ]Therefore, Nurse Alex spends a total of 15.75 hours with patients in that week.# 15.75
question:The editor of a leading physics journal is eagerly awaiting the senior physicist's latest paper on quantum entanglement. The journal typically publishes 12 issues a year, and each issue contains 5 papers. This year, the editor plans to dedicate 3 issues specifically to quantum physics, with 4 papers in each of these issues focused on quantum topics.If the editor wants to feature 2 papers on quantum entanglement in each of these dedicated issues, how many papers on quantum entanglement will be published in total this year?
answer:To solve the problem, we will follow these steps:1. Identify the total number of dedicated issues and papers per issue: - The editor plans to dedicate 3 issues specifically to quantum physics. - Each of these dedicated issues will contain 4 papers focused on quantum topics.2. Determine how many papers on quantum entanglement are featured in each dedicated issue: - The editor wants to feature 2 papers on quantum entanglement in each of these dedicated issues.3. Calculate the total number of papers on quantum entanglement: - Since there are 3 dedicated issues and each contains 2 papers on quantum entanglement, the total number of quantum entanglement papers is: [ 3 text{ issues} times 2 text{ papers/issue} = 6 text{ papers} ]Thus, the total number of papers on quantum entanglement that will be published in the journal this year is 6.# 6
question:Dr. Smith is a lecturer at a low-tier technical university. He often feels jealous of his friend, Dr. Johnson, who teaches at a prestigious institution. Dr. Smith recently discovered that Dr. Johnson's class has 3 times as many students as his own. If Dr. Smith has 25 students in his class, how many students does Dr. Johnson have? Additionally, Dr. Smith learns that Dr. Johnson's students scored an average of 12 points higher on their exams than his own students, who scored an average of 68 points. What is the average exam score of Dr. Johnson's students?
answer:To solve the problem, we need to determine two things: the number of students in Dr. Johnson's class and the average exam score of Dr. Johnson's students. Step 1: Determine the number of students in Dr. Johnson's class1. We are given that Dr. Johnson's class has 3 times as many students as Dr. Smith's class.2. Dr. Smith has 25 students in his class.3. Therefore, the number of students in Dr. Johnson's class is: [ 3 times 25 = 75 ] Step 2: Determine the average exam score of Dr. Johnson's students1. Dr. Smith's students scored an average of 68 points.2. Dr. Johnson's students scored an average of 12 points higher than Dr. Smith's students.3. Therefore, the average score of Dr. Johnson's students is: [ 68 + 12 = 80 ] Final AnswersNumber of students in Dr. Johnson's class: 75Average exam score of Dr. Johnson's students: 80# 75, 80
question:Emily, an editor, is reviewing the relationship between authors and their readers. She is working with two authors, Author A and Author B. Author A has written 5 books, and each book has an average of 120 readers. Author B has written 3 books, and each book has an average of 200 readers. Emily wants to find out how many more readers Author B has in total compared to Author A. How many more readers does Author B have than Author A?
answer:To solve this problem, we need to calculate the total number of readers for both Author A and Author B and then find the difference between them.Step 1: Calculate the total number of readers for Author A.- Author A has written 5 books, with each book having an average of 120 readers.- To find the total readers for Author A, multiply the number of books by the average number of readers per book: [ text{Total readers for Author A} = 5 times 120 = 600 ]Step 2: Calculate the total number of readers for Author B.- Author B has written 3 books, with each book having an average of 200 readers.- To find the total readers for Author B, multiply the number of books by the average number of readers per book: [ text{Total readers for Author B} = 3 times 200 = 600 ]Step 3: Find the difference in the total number of readers between Author B and Author A.- Since both authors have the same total number of readers, we subtract the total readers of Author A from Author B: [ text{Difference} = 600 - 600 = 0 ]Therefore, Author B has the same number of readers as Author A, resulting in no additional readers.# 0
question:Dr. Smith, a historian specializing in religious and mission history, is researching the spread of missions in the 18th century. She discovers that in the year 1750, there were 20 missions established. Each subsequent decade, the number of missions increased by 30% from the previous decade. How many missions were established by the year 1800?
answer:To solve the problem, we need to determine how many missions were established by the year 1800, given that the number of missions increases by 30% each decade starting from 1750 with 20 missions.1. Initial number of missions in 1750: ( M_{1750} = 20 )2. Rate of increase per decade: The number of missions increases by 30% each decade. Therefore, the factor of increase per decade is ( 1 + 0.30 = 1.30 ).3. Calculate the number of missions for each subsequent decade: - 1760: ( M_{1760} = M_{1750} times 1.30 = 20 times 1.30 = 26 ) - 1770: ( M_{1770} = M_{1760} times 1.30 = 26 times 1.30 = 33.8 ) - 1780: ( M_{1780} = M_{1770} times 1.30 = 33.8 times 1.30 = 43.94 ) - 1790: ( M_{1790} = M_{1780} times 1.30 = 43.94 times 1.30 = 57.122 ) - 1800: ( M_{1800} = M_{1790} times 1.30 = 57.122 times 1.30 = 74.2586 )4. Final Answer: We round the number of missions in 1800 to the nearest whole number, since you can't have a fraction of a mission.# 74