Appearance
question:Alex's family lives off the grid and uses solar panels to generate electricity for their home. On a sunny day, the solar panels produce 5 kilowatt-hours (kWh) of electricity per hour. However, on cloudy days, the production drops to just 2 kWh per hour. Last week, there were 4 sunny days and 3 cloudy days. If each day the solar panels operate for 8 hours, how many total kilowatt-hours of electricity did Alex's family generate last week?
answer:To solve this problem, we need to calculate the total electricity generated on sunny days and on cloudy days separately, and then sum these amounts.Step 1: Calculate the electricity generated on sunny days.- On a sunny day, the solar panels produce 5 kWh per hour.- The panels operate for 8 hours each sunny day.- There were 4 sunny days last week.Electricity generated on one sunny day:[ 5 , text{kWh/hour} times 8 , text{hours} = 40 , text{kWh} ]Electricity generated on 4 sunny days:[ 40 , text{kWh/day} times 4 , text{days} = 160 , text{kWh} ]Step 2: Calculate the electricity generated on cloudy days.- On a cloudy day, the solar panels produce 2 kWh per hour.- The panels operate for 8 hours each cloudy day.- There were 3 cloudy days last week.Electricity generated on one cloudy day:[ 2 , text{kWh/hour} times 8 , text{hours} = 16 , text{kWh} ]Electricity generated on 3 cloudy days:[ 16 , text{kWh/day} times 3 , text{days} = 48 , text{kWh} ]Step 3: Calculate the total electricity generated last week.Total electricity generated:[ 160 , text{kWh (sunny days)} + 48 , text{kWh (cloudy days)} = 208 , text{kWh} ]# 208
question:A retired meteorologist who knew Vernon Dvorak is organizing his collection of weather data from past hurricanes. He decides to use the Dvorak technique, which Vernon developed, to estimate the intensity of hurricanes based on satellite imagery. He has data from 3 hurricanes. For the first hurricane, he records a Dvorak number of 4.0, for the second hurricane, a Dvorak number of 5.5, and for the third hurricane, a Dvorak number of 3.5. Each increase of 1.0 in the Dvorak number corresponds to an increase of 20 knots in wind speed. Calculate the total wind speed for all three hurricanes based on their Dvorak numbers.
answer:To solve this problem, we need to calculate the wind speed for each hurricane based on the given Dvorak numbers and then find the total wind speed for all three hurricanes.Step 1: Calculate the wind speed for each hurricane1. First Hurricane: - Dvorak number = 4.0 - Wind speed = (Dvorak number) × 20 knots - Wind speed = 4.0 × 20 knots = 80 knots2. Second Hurricane: - Dvorak number = 5.5 - Wind speed = (Dvorak number) × 20 knots - Wind speed = 5.5 × 20 knots = 110 knots3. Third Hurricane: - Dvorak number = 3.5 - Wind speed = (Dvorak number) × 20 knots - Wind speed = 3.5 × 20 knots = 70 knotsStep 2: Calculate the total wind speed for all three hurricanes- Total wind speed = Wind speed of first hurricane + Wind speed of second hurricane + Wind speed of third hurricane- Total wind speed = 80 knots + 110 knots + 70 knots = 260 knotsThe total wind speed for all three hurricanes is 260 knots.#260 knots
question:The Johnson family wants to ensure they have a balanced diet while sticking to their budget of 50 for a week's worth of groceries. They decide to buy three types of food items: whole grain bread, fresh vegetables, and beans. The cost of whole grain bread is 2.50 per loaf, and they plan to buy 4 loaves. Fresh vegetables cost 0.75 per pound, and they want to buy 10 pounds. A can of beans costs 1.20, and they plan to buy 8 cans. How much money will the Johnson family have left after buying these groceries?
answer:To find out how much money the Johnson family will have left after buying their groceries, we need to calculate the total cost of the items they plan to buy and subtract this amount from their budget.Step 1: Calculate the cost of whole grain bread- The cost per loaf of whole grain bread is 2.50. - They plan to buy 4 loaves.- Total cost for bread = Cost per loaf × Number of loaves = 2.50 × 4 = 10.00Step 2: Calculate the cost of fresh vegetables- The cost per pound of fresh vegetables is 0.75.- They plan to buy 10 pounds.- Total cost for vegetables = Cost per pound × Number of pounds = 0.75 × 10 = 7.50Step 3: Calculate the cost of beans- The cost per can of beans is 1.20.- They plan to buy 8 cans.- Total cost for beans = Cost per can × Number of cans = 1.20 × 8 = 9.60Step 4: Calculate the total cost of groceries- Total cost = Cost of bread + Cost of vegetables + Cost of beans- Total cost = 10.00 + 7.50 + 9.60 = 27.10Step 5: Calculate the remaining budget- Initial budget is 50.00.- Remaining budget = Initial budget - Total cost- Remaining budget = 50.00 - 27.10 = 22.90# 22.90
question:Nigel, a seasoned expat with an ironic sense of humor, decided to throw a "Welcome to the New World" party to celebrate his 20th year of living abroad. He sent out 60 invitations but, in a humorous twist, the invitation stated that only 75% of the invitees were actually welcome to show up. On the day of the party, 10% of those invited showed up unannounced, ignoring the ironic instruction. How many guests actually attended Nigel's party?
answer:To solve the problem, we need to determine how many guests attended Nigel's party. We proceed step-by-step:1. Identify the number of invitees: Nigel sent out 60 invitations.2. Determine how many were actually welcome: According to the invitation, only 75% of the invitees were welcome to show up. Calculate 75% of 60: [ 0.75 times 60 = 45 ] So, 45 people were welcome to attend.3. Determine how many showed up unannounced: It is stated that 10% of those invited showed up, ignoring the invitation's instruction. Calculate 10% of 60: [ 0.10 times 60 = 6 ] Therefore, 6 people showed up unannounced.4. Determine the total number of attendees: Since the 6 unannounced attendees are part of the original 60 invitees, and they are additional to the 45 who were welcome, they all attend irrespective of the invitation's instruction. Therefore, the total number of guests is the number welcome plus those who showed up unannounced: [ 45 + 6 = 51 ]Thus, the total number of guests who actually attended Nigel's party is 51.# 51
question:Jordan is a star athlete who spends 6 hours a week training for upcoming competitions and initially doubts the effectiveness of counseling. However, after attending counseling sessions for 4 weeks, Jordan notices a positive change in focus and performance. During each of these weeks, Jordan attends 2 counseling sessions, each lasting 1.5 hours. After these 4 weeks, Jordan decides to reduce training time by 1 hour per week to allow for rest and reflection, while continuing the same number of weekly counseling sessions. How many total hours does Jordan spend on training and counseling combined in the 4th week?
answer:To solve this problem, we need to determine the total number of hours Jordan spends on both training and counseling during the 4th week.1. Determine training hours in the 4th week: Initially, Jordan trains for 6 hours per week. However, after 4 weeks of counseling, Jordan decides to reduce training by 1 hour per week. Therefore, in the 4th week, Jordan's training time is: [ 6 , text{hours/week} - 1 , text{hour} = 5 , text{hours/week} ]2. Calculate counseling hours per week: Jordan attends 2 counseling sessions each week, with each session lasting 1.5 hours. Therefore, the total counseling time per week is: [ 2 , text{sessions/week} times 1.5 , text{hours/session} = 3 , text{hours/week} ]3. Determine total hours spent on training and counseling in the 4th week: Together, training and counseling hours in the 4th week add up to: [ 5 , text{hours (training)} + 3 , text{hours (counseling)} = 8 , text{hours} ]Thus, the total number of hours Jordan spends on training and counseling combined in the 4th week is:# 8
question:Alex, a mid-career attorney, is considering opening a solo practice. Currently, Alex earns 120,000 per year working at a law firm. To set up the solo practice, Alex estimates the following initial costs: 15,000 for office rent, 8,000 for office furniture, 10,000 for a computer and software setup, and 5,000 for marketing. Additionally, Alex expects monthly operating expenses to be 3,000.If Alex wants to ensure that the first year's revenue from the solo practice will at least match the current annual salary, how much revenue does Alex need to generate each month to meet this goal? Assume there are no other income sources and that the practice operates for 12 months in the first year.
answer:To solve this problem, we need to calculate the total costs Alex will incur in the first year of operating the solo practice, including both initial setup costs and ongoing operating expenses. Then, we determine the monthly revenue required to match Alex's current annual salary of 120,000.Step 1: Calculate the Initial Setup CostsAlex's initial costs are as follows:- Office rent: 15,000- Office furniture: 8,000- Computer and software setup: 10,000- Marketing: 5,000Total initial setup costs = 15,000 + 8,000 + 10,000 + 5,000 Total initial setup costs = 38,000Step 2: Calculate the Annual Operating ExpensesMonthly operating expenses are 3,000. Therefore, the annual operating expenses will be:[ text{Annual Operating Expenses} = 3,000 times 12 = 36,000 ]Step 3: Calculate the Total Costs for the First YearThe total costs for the first year include both the initial setup costs and the annual operating expenses:[ text{Total First Year Costs} = text{Initial Setup Costs} + text{Annual Operating Expenses} ][ text{Total First Year Costs} = 38,000 + 36,000 = 74,000 ]Step 4: Calculate the Required Revenue to Match Current SalaryTo match Alex's current annual salary, the practice needs to generate at least 120,000 in revenue. Therefore, the required revenue from the solo practice in the first year is:[ text{Required Revenue} = text{Current Salary} + text{Total First Year Costs} ][ text{Required Revenue} = 120,000 + 74,000 = 194,000 ]Step 5: Calculate the Monthly Revenue NeededTo find the monthly revenue needed to meet the first year's revenue goal, divide the total required revenue by 12 months:[ text{Monthly Revenue Needed} = frac{text{Required Revenue}}{12} ][ text{Monthly Revenue Needed} = frac{194,000}{12} ][ text{Monthly Revenue Needed} approx 16,166.67 ]Therefore, Alex needs to generate approximately 16,166.67 in revenue each month to meet the goal of matching his current salary while covering the costs of setting up and running the solo practice.# 16,166.67