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question:María is a senior Spanish screenwriter who has been part of the television industry for decades. Over her 40-year career, she has worked on a total of 25 different television shows. On average, each show has 3 seasons, and each season contains 10 episodes. If María writes an average of 2 scripts per episode, how many scripts has she written throughout her career?
answer:To solve the problem, we need to determine the total number of scripts María has written throughout her career. Let's break it down step-by-step:1. Determine the Total Number of Shows: María has worked on a total of 25 different television shows.2. Calculate the Total Number of Seasons: On average, each show has 3 seasons. Therefore, the total number of seasons María has worked on is: [ 25 text{ shows} times 3 text{ seasons per show} = 75 text{ seasons} ]3. Calculate the Total Number of Episodes: Each season contains 10 episodes. Thus, the total number of episodes María has worked on is: [ 75 text{ seasons} times 10 text{ episodes per season} = 750 text{ episodes} ]4. Calculate the Total Number of Scripts: María writes an average of 2 scripts per episode. Therefore, the total number of scripts she has written is: [ 750 text{ episodes} times 2 text{ scripts per episode} = 1500 text{ scripts} ]Therefore, the total number of scripts María has written throughout her career is:# 1500
question:Jamie is a marketing specialist who promotes and manages the sales of ShieldGuard Antivirus software. Last month, Jamie organized a successful marketing campaign that increased sales by 25%. Before the campaign, ShieldGuard was selling 480 copies of the antivirus software each month. After the campaign, for every 3 copies of ShieldGuard sold, 2 copies of ShieldGuard Plus, an upgraded version, were also sold. If ShieldGuard Plus costs twice as much as the regular ShieldGuard, and the price of a ShieldGuard copy is 40, how much total revenue did Jamie generate from ShieldGuard and ShieldGuard Plus sales in the month following the campaign?
answer:To solve the problem, we'll break it down step-by-step:1. Determine the number of ShieldGuard copies sold after the campaign: - Sales increased by 25%. - Before the campaign, 480 copies were sold each month. - Increase in sales = 25% of 480 = 0.25 × 480 = 120 copies. - Therefore, after the campaign, the total number of ShieldGuard copies sold is 480 + 120 = 600.2. Determine the relationship between ShieldGuard and ShieldGuard Plus sales: - For every 3 copies of ShieldGuard sold, 2 copies of ShieldGuard Plus are sold. - The ratio of ShieldGuard to ShieldGuard Plus sales is 3:2.3. Calculate the number of ShieldGuard Plus copies sold: - Let the number of ShieldGuard Plus copies sold be ( x ). - According to the ratio, for every 3 ShieldGuard, 2 ShieldGuard Plus are sold. - (frac{x}{600} = frac{2}{3}) - Solve for ( x ): ( x = frac{2}{3} times 600 = 400 ).4. Determine the revenue from ShieldGuard sales: - Price per ShieldGuard copy = 40. - Number of ShieldGuard copies sold = 600. - Revenue from ShieldGuard = 600 × 40 = 24,000.5. Determine the revenue from ShieldGuard Plus sales: - ShieldGuard Plus costs twice as much as ShieldGuard. - Price per ShieldGuard Plus copy = 2 × 40 = 80. - Number of ShieldGuard Plus copies sold = 400. - Revenue from ShieldGuard Plus = 400 × 80 = 32,000.6. Calculate the total revenue from both ShieldGuard and ShieldGuard Plus: - Total revenue = Revenue from ShieldGuard + Revenue from ShieldGuard Plus. - Total revenue = 24,000 + 32,000 = 56,000.#The total revenue generated from ShieldGuard and ShieldGuard Plus sales in the month following the campaign is 56,000.
question:Sally loves to chat and share news with her friends. One day, she starts talking to her friend Alex and shares 3 pieces of gossip. Alex becomes interested and tells 2 friends each of those 3 pieces of gossip. Each of those friends then shares the gossip with 2 more friends of theirs. How many people, including Sally, have heard the gossip by the end of the day?
answer:To solve this problem, we will track the spread of each piece of gossip separately and then combine the results to find the total number of people who have heard any gossip.1. Initial Sharing by Sally: - Sally shares 3 pieces of gossip. She tells Alex, so initially, 2 people (Sally and Alex) have heard each piece of gossip.2. Spread by Alex: - Alex tells 2 friends each piece of gossip. So, for each piece of gossip, 2 more people hear it. - Therefore, for each piece of gossip, the number of people who have heard it increases by 2, making a total of 4 people who have heard each piece of gossip (Sally, Alex, and 2 of Alex's friends).3. Spread by Alex's Friends: - Each of the 2 friends that Alex told, shares each piece of gossip with 2 more friends each. - This means each friend tells 2 others, adding 2 × 2 = 4 more people per piece of gossip. - Thus, for each piece of gossip, there are now 4 (those who already heard from Alex) + 4 (new people hearing from Alex's friends) = 8 people who have heard it.4. Total People who have heard any gossip: - Since this process is the same for each of the 3 pieces of gossip and considering the same people might hear more than one piece, let's find the unique count: - Initially, Sally is counted once. - Alex is counted once. - The 2 friends Alex tells each piece are unique per gossip piece, but since they each hear 2 gossip pieces, let's consider them generically as 2 unique people across all pieces. - The 4 new people for each piece of gossip from Alex's friends' sharing are unique per gossip piece.5. Uniqueness Calculation: - Sally (1 person) - Alex (1 person) - The 2 friends Alex tells (2 people, they are unique per gossip piece so they are not shared between pieces) - The 4 new people per gossip piece from the sharing by Alex's friends, each unique, thus for 3 pieces: 3 × 4 = 12 unique people.6. Final Total Calculation: - Total unique people = 1 (Sally) + 1 (Alex) + 2 (friends Alex directly told) + 12 (from Alex's friends' sharing) = 16 people.# 16
question:A concerned mother wants to help her child understand the value of aligning their future major with their true passions. She decides to use a simple math exercise to illustrate the importance of balance. The mother lists three subjects her child is interested in: Art, Science, and History. Over a month, the child spends 12 hours on Art, 20 hours on Science, and 8 hours on History.To help her child find balance, the mother suggests that the child should try to spend the same amount of time on each subject next month. How many total hours should the child spend on each subject next month to achieve this equal balance, while keeping the total hours spent the same as this month?
answer:To solve the problem, we need to determine how many hours the child should spend on each subject next month, while keeping the total hours spent the same and distributing them equally across the three subjects.Step 1: Calculate the total hours spent this month.The child spends:- 12 hours on Art,- 20 hours on Science, and- 8 hours on History.Total hours spent = 12 + 20 + 8 = 40 hours.Step 2: Determine how many hours should be spent on each subject next month.Next month, the child should spend the same total number of hours (40 hours) but distribute them equally across the three subjects: Art, Science, and History.Since there are 3 subjects, we divide the total hours by 3 to find the equal number of hours for each subject:[ text{Hours per subject} = frac{text{Total hours}}{text{Number of subjects}} = frac{40}{3} approx 13.33 ]The child should spend approximately 13.33 hours on each subject next month to achieve equal balance. Since exact fractional hours might not be practical, the child can aim to spend approximately 13 hours and 20 minutes on each subject, recognizing that slight adjustments might be needed in practice.#13.33
question:Dr. Smith has been a dedicated physician in Indiana for over 30 years. On average, Dr. Smith sees 20 patients a day, and she works 5 days a week. How many patients does Dr. Smith see in a typical year, assuming she works 50 weeks each year?
answer:To find how many patients Dr. Smith sees in a typical year, we can follow these steps:1. Determine the number of patients Dr. Smith sees in a week: [ text{Patients per day} times text{Days per week} = 20 times 5 = 100 ] So, Dr. Smith sees 100 patients each week.2. Calculate the number of patients Dr. Smith sees in a year: [ text{Patients per week} times text{Weeks per year} = 100 times 50 = 5000 ] Therefore, Dr. Smith sees 5000 patients in a typical year.# 5000
question:Dr. Gene works as a DNA analyst and has to analyze samples from different cases. In one case, she needs to compare DNA sequences from 4 different samples. Each DNA sequence consists of 150 nucleotides. Dr. Gene can analyze 30 nucleotides per hour. If she works for 5 hours each day, how many days will it take her to analyze all 4 DNA samples completely?
answer:To solve this problem, we need to determine the total amount of time Dr. Gene will need to analyze all 4 DNA samples, given her analysis speed and work schedule.Step 1: Calculate the total number of nucleotides Dr. Gene needs to analyze.- Each DNA sequence consists of 150 nucleotides.- There are 4 DNA samples.So, the total number of nucleotides = 150 nucleotides/sample × 4 samples = 600 nucleotides.Step 2: Determine how many nucleotides Dr. Gene can analyze in one hour.- Dr. Gene can analyze 30 nucleotides per hour.Step 3: Calculate the total number of hours required to analyze all nucleotides.- Total number of nucleotides to analyze = 600.- Nucleotides analyzed per hour = 30.Total hours required = Total nucleotides / Nucleotides per hour= 600 nucleotides / 30 nucleotides per hour= 20 hours.Step 4: Determine how many hours Dr. Gene works per day.- Dr. Gene works 5 hours each day.Step 5: Calculate the total number of days required to complete the analysis.- Total hours required = 20 hours.- Hours worked per day = 5 hours.Total days required = Total hours required / Hours per day= 20 hours / 5 hours per day= 4 days.Thus, it will take Dr. Gene 4 days to analyze all 4 DNA samples completely.# 4