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question:A potential client is moving to Llanelli and needs residential conveyancing services for their new home. They found a house in Llanelli that costs £250,000. The conveyancing service charges a flat fee of £1,200 plus 0.5% of the house's purchase price. How much will the client pay in total for the conveyancing services?
answer:To find out how much the client will pay in total for the conveyancing services, we need to calculate both parts of the conveyancing fee and then add them together.1. Flat Fee: The conveyancing service charges a flat fee of £1,200. 2. Percentage of the House's Purchase Price: The conveyancing service also charges 0.5% of the house's purchase price. - First, convert the percentage to a decimal: 0.5% = 0.005. - Multiply the house price by this decimal to find the percentage fee: [ 0.005 times £250,000 = £1,250 ]3. Total Conveyancing Fee: Add the flat fee to the percentage fee to find the total conveyancing fee: [ £1,200 + £1,250 = £2,450 ]The total amount the client will pay for the conveyancing services is £2,450.# £2,450
question:The reclusive musician has agreed to give an exclusive interview to a journalist. The musician has composed a total of 24 albums over his career. In preparation for the interview, the journalist plans to listen to 3 albums per day. If the journalist starts listening to the albums on a Monday, on which day of the week will the journalist finish listening to all the albums?
answer:To solve the problem, we need to determine how many days it will take for the journalist to listen to all 24 albums, given that they listen to 3 albums per day.1. Calculate the number of days needed: - The journalist listens to 3 albums per day. - Total number of albums = 24. - Number of days needed = Total albums / Albums per day = 24 / 3 = 8 days.2. Determine the starting day: - The journalist starts listening on a Monday.3. Find the ending day: - We add 8 days to Monday to find out on which day the journalist will finish listening to all the albums. - Days of the week cycle every 7 days, so we need to consider the modulo operation to find the day of the week after 8 days. - Starting from Monday, we count forward 8 days: - 1st day: Monday - 2nd day: Tuesday - 3rd day: Wednesday - 4th day: Thursday - 5th day: Friday - 6th day: Saturday - 7th day: Sunday - 8th day: MondayThus, the journalist will finish listening to all the albums on a Monday.# Monday
question:Professor Taylor, a literature professor who believes in the timeless value of literature, has a collection of 180 classic novels and 120 modern technology-related books. She wants to set up a display that highlights the balance between literature and technology by creating pairs of one classic novel and one technology-related book. 1. How many complete pairs can Professor Taylor create with her collection?2. After creating as many pairs as possible, how many books of each type will be left without a pair?
answer:To solve this problem, we need to determine how many complete pairs of one classic novel and one technology-related book Professor Taylor can create, and how many books of each type will remain unpaired.1. Determine the Number of Complete Pairs: A complete pair consists of one classic novel and one technology-related book. Professor Taylor has: - 180 classic novels - 120 technology-related books To find the number of complete pairs, we compare the two quantities because each pair uses one book from each category. The limiting factor for the number of pairs is the smaller quantity, which is the number of technology-related books. Therefore, the number of complete pairs is the smaller of the two quantities: [ text{Number of complete pairs} = min(180, 120) = 120 ]2. Determine the Number of Unpaired Books: - Classic Novels: After forming 120 pairs, we subtract the number of pairs from the total number of classic novels: [ text{Unpaired classic novels} = 180 - 120 = 60 ] - Technology-related Books: After forming 120 pairs, all technology-related books are used up, since there were only 120 to begin with: [ text{Unpaired technology-related books} = 120 - 120 = 0 ]Now we have the complete solution. #Final Answer: 120 complete pairs; 60 unpaired classic novels, 0 unpaired technology-related books.
question:A statistics analyst is compiling comprehensive records of a retired cricketer's career. The analyst finds that the cricketer played 150 test matches and scored an average of 45 runs per match. In one of his best series, he scored 120, 85, and 97 runs in three consecutive matches. However, due to an error in previous recordings, 5 runs were added to each of these scores. The analyst needs to correct the error and calculate the cricketer's accurate average runs over the entire 150 test matches. What is the cricketer's correct average runs per match after adjusting for the error in those three matches?
answer:To solve this problem, we need to find the cricketer's correct total runs and then calculate the corrected average runs per match.1. Initial Calculation of Total Runs: The cricketer played 150 test matches with an average of 45 runs per match. So, the initial total runs recorded are: [ text{Total Runs} = text{Average Runs} times text{Number of Matches} = 45 times 150 = 6750 ]2. Identify the Error in the Specific Matches: The scores in three specific matches were incorrectly recorded due to an addition of 5 runs to each actual score. The recorded scores were 120, 85, and 97.3. Determine the Actual Scores: To find the actual scores, subtract 5 from each recorded score: - Actual score in the first match: (120 - 5 = 115) - Actual score in the second match: (85 - 5 = 80) - Actual score in the third match: (97 - 5 = 92)4. Calculate the Total Runs for These Matches: - Total recorded runs for these three matches: (120 + 85 + 97 = 302) - Total actual runs for these three matches: (115 + 80 + 92 = 287)5. Adjust the Total Runs: The error in total runs for these matches is: [ 302 - 287 = 15 ] So, the corrected total runs for all matches is: [ 6750 - 15 = 6735 ]6. Calculate the Correct Average Runs: With the corrected total runs, the average runs per match over 150 matches is: [ text{Correct Average} = frac{6735}{150} = 44.9 ]#44.9
question:Alex, a prolific writer, has published 8 collections of short stories. Each collection consists of 15 stories. Alex has recently taken an interest in local news and decided to write 2 new short stories inspired by each of the 5 local news topics they read about last month. If Alex combines all these new stories with their existing collections, how many short stories does Alex have in total?
answer:To solve this problem, we need to calculate the total number of short stories Alex has by considering both the existing collections and the new stories inspired by local news topics.Step-by-Step Solution:1. Calculate the number of stories in the existing collections: - Alex has published 8 collections. - Each collection contains 15 stories. - Therefore, the total number of stories in the existing collections is: [ 8 text{ collections} times 15 text{ stories per collection} = 120 text{ stories} ]2. Calculate the number of new stories inspired by local news topics: - Alex was inspired by 5 local news topics. - For each topic, they wrote 2 new short stories. - Therefore, the total number of new stories inspired by these topics is: [ 5 text{ topics} times 2 text{ stories per topic} = 10 text{ stories} ]3. Calculate the total number of short stories Alex has: - Sum the stories from the existing collections and the new stories: [ 120 text{ stories from collections} + 10 text{ new stories} = 130 text{ stories} ]Thus, the total number of short stories Alex has is 130.# 130
question:A program officer is reviewing grant applications for research in biomaterials and tissue engineering. She has received a total of 45 applications. She decides to fund 1/3 of them. Out of the funded applications, 4 are focused on developing new types of biomaterials, and the rest are focused on tissue engineering. How many applications focused on tissue engineering does she decide to fund?
answer:To solve the problem, let's follow these steps:1. Determine the number of applications to be funded: - The program officer received a total of 45 applications. - She decides to fund 1/3 of these applications. - Calculate the number of applications to be funded: [ text{Number of funded applications} = frac{1}{3} times 45 = 15 ]2. Determine the number of funded applications focused on biomaterials: - Out of the 15 funded applications, 4 are focused on developing new types of biomaterials.3. Determine the number of funded applications focused on tissue engineering: - The remaining funded applications are focused on tissue engineering. - Calculate the number of applications focused on tissue engineering: [ text{Number of tissue engineering applications} = 15 - 4 = 11 ]Thus, the program officer decides to fund 11 applications focused on tissue engineering.Final answer:# 11