answer:To solve this problem, we need to calculate the remaining number of unique species on each island after 5 years, taking into account the annual percentage decrease.Island A:- Initial number of unique species: 150- Annual decrease rate: 2%The formula for the remaining quantity after a percentage decrease over a number of years is given by:[ text{Final amount} = text{Initial amount} times (1 - text{decrease rate})^{text{number of years}} ]For Island A:[ text{Final species count after 5 years} = 150 times (1 - 0.02)^5 ]Calculate step-by-step:1. Calculate the annual retention rate: ( 1 - 0.02 = 0.98 )2. Raise this retention rate to the power of 5 (for 5 years): ( 0.98^5 ) [ 0.98^5 approx 0.9039207968 ]3. Multiply this value by the initial number of species: [ 150 times 0.9039207968 approx 135.58811952 ]Round to the nearest whole number:- Island A will have approximately 136 unique species left after 5 years.Island B:- Initial number of unique species: 200- Annual decrease rate: 1%For Island B:[ text{Final species count after 5 years} = 200 times (1 - 0.01)^5 ]Calculate step-by-step:1. Calculate the annual retention rate: ( 1 - 0.01 = 0.99 )2. Raise this retention rate to the power of 5 (for 5 years): ( 0.99^5 ) [ 0.99^5 approx 0.9509900499 ]3. Multiply this value by the initial number of species: [ 200 times 0.9509900499 approx 190.19800998 ]Round to the nearest whole number:- Island B will have approximately 190 unique species left after 5 years.# 136 species on Island A, 190 species on Island B

answer:To solve this problem, we need to calculate how much of the CAD 10,000 budget the filmmaker has already spent and then subtract that total from the original budget to find out how much is left.1. Calculate the amount spent on camera equipment: [ text{Camera equipment cost} = 30% text{ of CAD 10,000} = 0.30 times 10,000 = text{CAD 3,000} ]2. Calculate the amount spent on lighting: [ text{Lighting cost} = 25% text{ of CAD 10,000} = 0.25 times 10,000 = text{CAD 2,500} ]3. Calculate the amount spent on sound equipment: [ text{Sound equipment cost} = 15% text{ of CAD 10,000} = 0.15 times 10,000 = text{CAD 1,500} ]4. Calculate the amount spent on editing software: [ text{Editing software cost} = 10% text{ of CAD 10,000} = 0.10 times 10,000 = text{CAD 1,000} ]5. Calculate the total amount spent: [ text{Total spent} = text{CAD 3,000} + text{CAD 2,500} + text{CAD 1,500} + text{CAD 1,000} = text{CAD 8,000} ]6. Calculate the remaining budget: [ text{Remaining budget} = text{Original budget} - text{Total spent} = text{CAD 10,000} - text{CAD 8,000} = text{CAD 2,000} ]The amount of money the filmmaker has left to spend on other aspects of the film is CAD 2,000.# CAD 2,000

answer:To solve the problem, we need to determine how many total episodes Jamie will watch each weekend and how many weekends are required to watch all 20 episodes.1. Calculate the total episodes watched per weekend: - Jamie plans to watch 3 episodes on Saturday and 4 episodes on Sunday. - Total episodes per weekend = 3 (Saturday) + 4 (Sunday) = 7 episodes.2. Determine the number of weekends needed: - We need to find out how many weekends are needed to watch all 20 episodes with a pace of 7 episodes each weekend.3. Divide the total number of episodes by episodes per weekend: - Total number of episodes in the series = 20 - Episodes watched per weekend = 7 - Number of weekends needed = Total episodes / Episodes per weekend = 20 / 7.4. Calculate the division: - 20 divided by 7 gives approximately 2.857.5. Determine the number of complete weekends: - Since Jamie cannot watch a fraction of a weekend, they will need to round up to ensure they complete watching the series. - Rounding up 2.857 gives us 3 weekends.Therefore, Jamie will need 3 weekends to finish watching the entire series.# 3

answer:To solve this problem, we need to determine how many unique sets of 4 books can be selected from a collection of 60 books. This is a typical combination problem, which can be expressed using the combination formula:[C(n, k) = frac{n!}{k!(n-k)!}]where ( n ) is the total number of items to choose from, ( k ) is the number of items to choose, and ( ! ) denotes factorial, which is the product of all positive integers up to that number.In this case, ( n = 60 ) (the total number of books) and ( k = 4 ) (the number of books selected each week). So, we need to calculate:[C(60, 4) = frac{60!}{4!(60-4)!} = frac{60!}{4! times 56!}]The factorial ( 60! ) is the product of all positive integers from 1 to 60, but in this combination calculation, it simplifies considerably because the ( 56! ) in the denominator cancels out most of the terms in ( 60! ). Therefore, we only need to compute:[frac{60 times 59 times 58 times 57}{4 times 3 times 2 times 1}]Let's calculate the numerator:[60 times 59 times 58 times 57]First, compute ( 60 times 59 ):[60 times 59 = 3540]Next, compute ( 3540 times 58 ):[3540 times 58 = 205320]Finally, compute ( 205320 times 57 ):[205320 times 57 = 11703640]Now, calculate the denominator:[4 times 3 times 2 times 1 = 24]Finally, divide the numerator by the denominator to find the number of combinations:[frac{11703640}{24} = 487635]Thus, Jamie can provide unique recommendations for 487635 weeks before needing to repeat any book suggestion.# 487635

answer:To solve this problem, we need to calculate the total amount of funding Professor Green will have over the two years if they receive both the new grants. Follow these steps:1. Identify the amount of funding received last year: - Last year's grant: 150,0002. Identify the amounts of the two new grants applied for this year: - First new grant: 85,000 - Second new grant: 120,0003. Calculate the total amount of funding for this year if both grants are received: - Total for this year = First new grant + Second new grant - Total for this year = 85,000 + 120,000 = 205,0004. Calculate the total funding over the two years: - Total funding = Last year's grant + Total for this year - Total funding = 150,000 + 205,000 = 355,000Therefore, if Professor Green receives both new grants, the total funding over the two years will be 355,000.# 355,000

answer:To find out what time Veronica and Betty will finish watching all 4 seasons, let's go through the problem step by step:1. Calculate the Total Number of Episodes: - 4 seasons × 20 episodes per season = 80 episodes total.2. Calculate Total Watching Time Without Breaks: - Each episode is 42 minutes long. - Total watching time = 80 episodes × 42 minutes = 3360 minutes.3. Determine the Number of Breaks: - They take a break after every 5 episodes. - Number of breaks = ( leftlfloor frac{80}{5} rightrfloor ) = 16 breaks. - Note that they don't need a break after the last set of episodes if they finish exactly after a break.4. Calculate Total Break Time: - Each break is 15 minutes long. - Total break time = 16 breaks × 15 minutes = 240 minutes.5. Calculate Total Time Including Breaks: - Total time = Total watching time + Total break time = 3360 minutes + 240 minutes = 3600 minutes.6. Convert Total Time to Hours and Minutes: - 3600 minutes = 3600 ÷ 60 = 60 hours.7. Determine the Finish Time: - They start at 9:00 AM on Saturday. - 60 hours later would be: - 24 hours takes them to 9:00 AM on Sunday. - Another 24 hours takes them to 9:00 AM on Monday. - The remaining 12 hours takes them to 9:00 PM on Monday.Therefore, Veronica and Betty will finish watching all 4 seasons at:# 9:00 PM on Monday