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question:During a dance showcase, a talented dancer known for improvisation and creating beautiful duets was scheduled to perform three different duets. In the first duet, the dancer improvised 16 unique moves. In the second duet, the dancer used 10 more moves than in the first duet. For the third duet, the dancer decided to improvise twice as many moves as in the second duet. How many unique moves did the dancer improvise across all three duets?
answer:To solve the problem, let's denote the number of unique moves in each duet as follows:- Let ( m_1 ) be the number of unique moves in the first duet.- Let ( m_2 ) be the number of unique moves in the second duet.- Let ( m_3 ) be the number of unique moves in the third duet.According to the information given in the problem:1. In the first duet, the dancer improvised 16 unique moves, so: [ m_1 = 16 ]2. In the second duet, the dancer used 10 more moves than in the first duet, so: [ m_2 = m_1 + 10 = 16 + 10 = 26 ]3. In the third duet, the dancer improvised twice as many moves as in the second duet, so: [ m_3 = 2 times m_2 = 2 times 26 = 52 ]To find the total number of unique moves the dancer improvised across all three duets, we sum up the unique moves for each duet:[text{Total moves} = m_1 + m_2 + m_3 = 16 + 26 + 52]Now, calculate the sum:[16 + 26 = 42][42 + 52 = 94]Therefore, the dancer improvised a total of 94 unique moves across all three duets.# 94
question:Maria is a film director who has visited 5 different countries to judge beauty pageants this year. In each country, she visited, there were 3 rounds of judging: evening wear, talent, and interview. During the evening wear round, Maria scored 10 contestants and awarded each contestant 8 points. In the talent round, she scored 12 contestants and awarded each contestant 7 points. Finally, in the interview round, she scored 15 contestants and awarded each contestant 9 points. What is the total number of points Maria awarded across all the rounds in all 5 countries?
answer:To solve this problem, we need to calculate the total points Maria awarded in each round and then sum those points across all five countries.1. Evening Wear Round: - In each country, Maria scored 10 contestants. - She awarded each contestant 8 points. - Points per country for evening wear = 10 contestants * 8 points/contestant = 80 points. - Since Maria visited 5 countries, total points for evening wear across all countries = 5 countries * 80 points/country = 400 points.2. Talent Round: - In each country, Maria scored 12 contestants. - She awarded each contestant 7 points. - Points per country for talent = 12 contestants * 7 points/contestant = 84 points. - Total points for talent across all countries = 5 countries * 84 points/country = 420 points.3. Interview Round: - In each country, Maria scored 15 contestants. - She awarded each contestant 9 points. - Points per country for interview = 15 contestants * 9 points/contestant = 135 points. - Total points for interview across all countries = 5 countries * 135 points/country = 675 points.4. Total Points Across All Rounds: - Total points from evening wear = 400 points. - Total points from talent = 420 points. - Total points from interview = 675 points. - Sum of all points = 400 + 420 + 675 = 1495 points.Therefore, the total number of points Maria awarded across all the rounds in all 5 countries is:# 1495
question:Dr. Stone, a geologist, is exploring a cave system known for its stunning stalactites and stalagmites. She discovers that one section of the cave has 15 stalactites hanging from the ceiling and 20 stalagmites growing from the ground. Each stalactite drips water once every 3 minutes, and each stalagmite absorbs a drop of water every 5 minutes. If Dr. Stone spends one hour observing this section of the cave, how many total drops of water will drip from the stalactites, and how many drops will the stalagmites absorb during her observation?
answer:To solve this problem, we'll break it down into two parts: the number of drops from stalactites and the number of drops absorbed by stalagmites. Part 1: Drops from Stalactites1. Number of stalactites: There are 15 stalactites.2. Drip rate of each stalactite: Each stalactite drips once every 3 minutes.3. Total observation time: Dr. Stone spends 1 hour observing the cave, which is 60 minutes.Calculate the total number of drips from one stalactite:- Each stalactite drips once every 3 minutes.- In 60 minutes, the number of drips from one stalactite is: [ frac{60 text{ minutes}}{3 text{ minutes/drop}} = 20 text{ drops} ]Calculate the total number of drips from all stalactites:- There are 15 stalactites, so the total number of drips from all stalactites is: [ 15 text{ stalactites} times 20 text{ drops/stalactite} = 300 text{ drops} ] Part 2: Drops Absorbed by Stalagmites1. Number of stalagmites: There are 20 stalagmites.2. Absorption rate of each stalagmite: Each stalagmite absorbs a drop every 5 minutes.3. Total observation time: Dr. Stone spends 1 hour observing the cave, which is 60 minutes.Calculate the total number of drops absorbed by one stalagmite:- Each stalagmite absorbs a drop every 5 minutes.- In 60 minutes, the number of drops absorbed by one stalagmite is: [ frac{60 text{ minutes}}{5 text{ minutes/drop}} = 12 text{ drops} ]Calculate the total number of drops absorbed by all stalagmites:- There are 20 stalagmites, so the total number of drops absorbed by all stalagmites is: [ 20 text{ stalagmites} times 12 text{ drops/stalagmite} = 240 text{ drops} ] Final AnswerThe total number of drops of water that will drip from the stalactites is 300, and the total number of drops absorbed by the stalagmites is 240.# 300 drops from stalactites, 240 drops absorbed by stalagmites
question:Mr. Johnson, a retired war veteran, has a remarkable collection of 240 photographs and 80 memoirs from his time in service. He wants to organize these items into albums. Each album can hold either 12 photographs or 10 memoirs. If Mr. Johnson uses the maximum number of albums possible for his photographs and then uses the remaining albums for his memoirs, how many albums will he need in total?
answer:To solve the problem, we need to determine how Mr. Johnson can organize his collection of photographs and memoirs into albums, given the capacity constraints.1. Determine the number of albums needed for photographs: Mr. Johnson has 240 photographs, and each album can hold 12 photographs. [ text{Number of albums for photographs} = frac{240 text{ photographs}}{12 text{ photographs/album}} = 20 text{ albums} ] Therefore, Mr. Johnson will use 20 albums for his photographs.2. Determine the number of albums needed for memoirs: Mr. Johnson has 80 memoirs remaining, and each album can hold 10 memoirs. [ text{Number of albums for memoirs} = frac{80 text{ memoirs}}{10 text{ memoirs/album}} = 8 text{ albums} ] Therefore, Mr. Johnson will use 8 albums for his memoirs.3. Calculate the total number of albums needed: [ text{Total number of albums} = text{Number of albums for photographs} + text{Number of albums for memoirs} = 20 + 8 = 28 ]Thus, Mr. Johnson will need a total of 28 albums in order to organize his photographs and memoirs.# 28
question:Nurse Maria is a public health nurse responsible for conducting disease surveillance and monitoring in a small town with a population of 10,000 people. Last month, she conducted a survey to track the number of flu cases and found that 120 people were diagnosed with the flu. This month, she observed a 25% increase in flu cases compared to last month. How many people were diagnosed with the flu this month?
answer:To solve this problem, we need to calculate the number of flu cases this month based on last month's cases and the percentage increase observed this month.Step 1: Identify the number of flu cases last month.Last month, 120 people were diagnosed with the flu.Step 2: Determine the percentage increase in flu cases this month.This month, there is a 25% increase in flu cases.Step 3: Calculate the increase in the number of flu cases.To find the increase, we multiply the number of cases last month by the percentage increase (expressed as a decimal):[ text{Increase in cases} = 120 times 0.25 = 30 ]Step 4: Calculate the total number of flu cases this month.Add the increase in cases to last month's cases to find the total number of cases this month:[ text{Total cases this month} = 120 + 30 = 150 ]Therefore, the number of people diagnosed with the flu this month is 150.# 150
question:An Italian postgraduate anthropology student specializing in Asian studies is planning a research trip across three countries in Asia: Japan, South Korea, and China. The student has set aside a budget for purchasing anthropology books from each country. In Japan, they plan to buy 5 books, each costing 3,000 yen. In South Korea, they will purchase 4 books, each priced at 15,000 won. Finally, in China, they intend to buy 6 books, each costing 80 yuan. If the current exchange rates are 1 yen = 0.007 USD, 1 won = 0.00075 USD, and 1 yuan = 0.14 USD, what is the total cost of all the books in USD?
answer:To solve this problem, we need to calculate the total cost of the books in each country in their local currency, then convert those amounts to USD using the given exchange rates. Finally, we sum these converted amounts to find the total cost in USD.Step 1: Calculate the total cost in Japan in yen.- Number of books in Japan: 5- Cost per book in Japan: 3,000 yen- Total cost in Japan = Number of books × Cost per book- Total cost in Japan = 5 × 3,000 = 15,000 yenStep 2: Convert the total cost in Japan from yen to USD.- Exchange rate: 1 yen = 0.007 USD- Total cost in Japan in USD = 15,000 yen × 0.007 USD/yen- Total cost in Japan in USD = 105 USDStep 3: Calculate the total cost in South Korea in won.- Number of books in South Korea: 4- Cost per book in South Korea: 15,000 won- Total cost in South Korea = Number of books × Cost per book- Total cost in South Korea = 4 × 15,000 = 60,000 wonStep 4: Convert the total cost in South Korea from won to USD.- Exchange rate: 1 won = 0.00075 USD- Total cost in South Korea in USD = 60,000 won × 0.00075 USD/won- Total cost in South Korea in USD = 45 USDStep 5: Calculate the total cost in China in yuan.- Number of books in China: 6- Cost per book in China: 80 yuan- Total cost in China = Number of books × Cost per book- Total cost in China = 6 × 80 = 480 yuanStep 6: Convert the total cost in China from yuan to USD.- Exchange rate: 1 yuan = 0.14 USD- Total cost in China in USD = 480 yuan × 0.14 USD/yuan- Total cost in China in USD = 67.2 USDStep 7: Calculate the total cost of all the books in USD.- Total cost in USD = Total cost in Japan in USD + Total cost in South Korea in USD + Total cost in China in USD- Total cost in USD = 105 USD + 45 USD + 67.2 USD- Total cost in USD = 217.2 USD#The total cost of all the books in USD is 217.2 USD.