answer:To solve this problem, we need to determine how long it will take for Alex's tool to analyze a total of 960 keywords when the tool analyzes 120 keywords per hour.Let's break down the steps:1. Identify the given information: - The tool analyzes 120 keywords per hour. - The total number of keywords to be analyzed is 960.2. Set up the equation: - We want to find the number of hours (let's call it ( h )) it takes to analyze 960 keywords. - Since the tool analyzes 120 keywords per hour, the total number of keywords analyzed in ( h ) hours is given by the equation: [ 120 times h = 960 ]3. Solve for ( h ): - To find ( h ), divide both sides of the equation by 120: [ h = frac{960}{120} ]4. Perform the division: - Calculate ( frac{960}{120} ): [ h = 8 ]Thus, it will take 8 hours for the tool to analyze 960 keywords.# 8

answer:To solve this problem, we need to determine the total time of all the performances and compare it to the total duration of the festival to find the leftover time.Step 1: Calculate the total duration of the festival.- The festival runs from 3:00 PM to 11:00 PM.- Start time: 3:00 PM- End time: 11:00 PM- Total duration = End time - Start time = 11:00 PM - 3:00 PM = 8 hoursConvert the total duration into minutes:[ 8 text{ hours} times 60 text{ minutes/hour} = 480 text{ minutes} ]Step 2: Calculate the total performance time for the bands.- There are 5 local bands.- Each band performs for 45 minutes.- Total performance time for bands = Number of bands × Performance time per band[ = 5 times 45 text{ minutes} = 225 text{ minutes} ]Step 3: Calculate the total performance time for the solo artists.- There are 3 solo artists.- Each solo artist performs for 30 minutes.- Total performance time for solo artists = Number of solo artists × Performance time per solo artist[ = 3 times 30 text{ minutes} = 90 text{ minutes} ]Step 4: Calculate the total performance time for all performances.- Total performance time = Total performance time for bands + Total performance time for solo artists[ = 225 text{ minutes} + 90 text{ minutes} = 315 text{ minutes} ]Step 5: Calculate the leftover time after all performances.- Total festival duration = 480 minutes- Total performance time = 315 minutes- Leftover time = Total festival duration - Total performance time[ = 480 text{ minutes} - 315 text{ minutes} = 165 text{ minutes} ]# 165 minutes

answer:To solve this problem, let's go through the steps:1. Determine the total number of matches Jamie needs to watch: Jamie wants to watch all 18 of Chris Evert's Grand Slam singles victories. Therefore, Jamie needs to watch 18 matches in total.2. Determine how many matches Jamie plans to watch each weekend: Jamie plans to watch 3 matches each weekend.3. Calculate the number of weekends needed: To find how many weekends it will take, divide the total number of matches by the number of matches Jamie plans to watch each weekend. [ text{Number of weekends} = frac{text{Total matches}}{text{Matches per weekend}} = frac{18}{3} = 6 ]Jamie will need 6 weekends to watch all 18 of Chris Evert's Grand Slam victories.# 6

answer:To solve the problem, we need to calculate the total annual cost of both the travel and home insurance policies for Jake's photography equipment. We will consider the different periods when Jake is traveling and when he is not traveling.1. Identify the policies and their costs: - Travel insurance policy costs 15 per month. - Home insurance policy costs 10 per month.2. Determine the duration for each policy: - Jake travels for 3 months each year, so he needs the travel insurance policy for 3 months. - Jake is not traveling for the other 9 months of the year, so he needs the home insurance policy for these 9 months.3. Calculate the total cost for the travel insurance: - Travel insurance is used for 3 months. - Total cost for travel insurance = 3 months × 15/month = 45.4. Calculate the total cost for the home insurance: - Home insurance is used for 9 months. - Total cost for home insurance = 9 months × 10/month = 90.5. Add the costs of both policies to find the total annual cost: - Total annual cost = Cost of travel insurance + Cost of home insurance. - Total annual cost = 45 + 90 = 135.Therefore, the total annual cost of both insurance policies for Jake's photography equipment is 135.# 135

answer:To solve the problem, we need to calculate the total amount Alex spends on museum visits and academic expenses over the course of the semester.Step 1: Calculate the cost of museum visits.- Alex plans to visit 5 different museums.- Each museum visit costs 12.The total cost for museum visits is:[ text{Total cost for museum visits} = 5 text{ visits} times 12 text{ dollars/visit} = 60 text{ dollars} ]Step 2: Calculate the monthly academic expenses.- Each month, Alex spends 80 on textbooks and 40 on stationery.The total monthly academic expenses are:[ text{Monthly academic expenses} = 80 text{ dollars} + 40 text{ dollars} = 120 text{ dollars} ]Step 3: Calculate the total academic expenses for the semester.- The semester lasts 4 months.The total academic expenses for the semester are:[ text{Total academic expenses for the semester} = 120 text{ dollars/month} times 4 text{ months} = 480 text{ dollars} ]Step 4: Calculate the total expenses for museum visits and academic expenses.- Total cost for museum visits: 60- Total academic expenses for the semester: 480The total amount spent by Alex by the end of the semester is:[ text{Total expenses} = 60 text{ dollars} + 480 text{ dollars} = 540 text{ dollars} ]#[ 540 ]

answer:To solve the problem, we need to calculate the number of solar panels SunPower Inc. will produce each month with the increased production and then find the total production over six months.1. Current Monthly Production: SunPower Inc. currently produces 500 solar panels each month.2. Increased Production Rate: With government support, they can increase their production by 40%. The increased production can be calculated as follows: [ text{Increased Production} = text{Current Production} + 0.40 times text{Current Production} ] [ text{Increased Production} = 500 + 0.40 times 500 = 500 + 200 = 700 text{ solar panels} ]3. Total Production Over Six Months: Since they maintain this increased production for six months, we multiply the increased production by six: [ text{Total Production in Six Months} = 700 times 6 = 4200 text{ solar panels} ]Therefore, with government support, SunPower Inc. will produce a total of 4200 solar panels over the six-month period.# 4200