answer:To solve the problem, we need to calculate the total number of hours Alex spends preparing all three series for the exhibition. Let's break it down step-by-step:1. Number of Photographs per Series: - Alex plans to showcase a total of 48 photographs. - He divides the photographs into 3 equal series. - Therefore, the number of photographs per series is: [ frac{48}{3} = 16 text{ photographs per series.} ]2. Time Spent Shooting the Photographs: - For each series, Alex spends 3 hours shooting. - There are 3 series, so the total time spent shooting is: [ 3 text{ hours/series} times 3 text{ series} = 9 text{ hours.} ]3. Time Spent Editing the Photographs: - For each series, Alex spends 2 hours editing. - There are 3 series, so the total time spent editing is: [ 2 text{ hours/series} times 3 text{ series} = 6 text{ hours.} ]4. Time Spent Setting Up Each Series: - For each series, Alex spends 1 hour setting it up. - There are 3 series, so the total time spent setting up is: [ 1 text{ hour/series} times 3 text{ series} = 3 text{ hours.} ]5. Total Time Spent Preparing the Exhibition: - Add all the hours spent on shooting, editing, and setting up: [ 9 text{ hours (shooting)} + 6 text{ hours (editing)} + 3 text{ hours (setting up)} = 18 text{ hours.} ]Thus, Alex spends a total of 18 hours preparing all three series for the exhibition.# 18

answer:To solve the problem, we will break it down into parts: Step 1: Calculate the total number of people watching the movie.John sets up 8 rows of chairs with 6 chairs in each row. Therefore, the total number of chairs is:[ 8 text{ rows} times 6 text{ chairs per row} = 48 text{ chairs} ]Since all rows are fully occupied and John also sits down to watch the movie, the total number of people watching is:[ 48 text{ people} + 1 text{ (John)} = 49 text{ people} ] Step 2: Calculate the popcorn availability.John buys 5 large popcorn tubs. Each tub can be shared by 4 people, so the total number of people who can have popcorn is:[ 5 text{ tubs} times 4 text{ people per tub} = 20 text{ people} ] Step 3: Calculate the soda availability.John buys 3 large soda bottles. Each soda bottle can serve 6 people, so the total number of people who can have soda is:[ 3 text{ bottles} times 6 text{ people per bottle} = 18 text{ people} ] Step 4: Determine if there is enough popcorn and soda for everyone.- Popcorn: 49 people are watching the movie, but only 20 people can have popcorn. Thus, there is not enough popcorn for everyone. - Soda: 49 people are watching the movie, but only 18 people can have soda. Thus, there is not enough soda for everyone. Conclusion:1. Total number of people watching the movie: 492. Popcorn and soda availability: John does not have enough popcorn tubs and soda bottles to ensure every person watching the movie can have some popcorn and soda.Therefore, the answers to the questions are:1. 49 people2. No, John does not have enough popcorn and soda for everyone.# 49, No

answer:To solve this problem, we need to determine the total amount of each ingredient required for a batch of 10 vegan burger patties, where each patty weighs 200 grams and contains specified percentages of quinoa, black beans, and sweet potatoes.Step 1: Calculate the weight of each ingredient per patty.Each patty weighs 200 grams, and the composition is as follows:- Quinoa: 50% of the patty- Black beans: 30% of the patty- Sweet potatoes: 20% of the pattyCalculate the weight of each ingredient in one patty:- Weight of quinoa per patty = 50% of 200 grams = 0.50 * 200 = 100 grams- Weight of black beans per patty = 30% of 200 grams = 0.30 * 200 = 60 grams- Weight of sweet potatoes per patty = 20% of 200 grams = 0.20 * 200 = 40 gramsStep 2: Calculate the total weight of each ingredient for 10 patties.Since there are 10 patties in the batch, we multiply the weight of each ingredient per patty by 10 to get the total amount needed for the batch:- Total weight of quinoa for 10 patties = 100 grams/patty * 10 patties = 1000 grams- Total weight of black beans for 10 patties = 60 grams/patty * 10 patties = 600 grams- Total weight of sweet potatoes for 10 patties = 40 grams/patty * 10 patties = 400 gramsFinal Answer:Total grams needed:- Quinoa: 1000 grams- Black beans: 600 grams- Sweet potatoes: 400 grams#Total grams of quinoa: 1000 gramsTotal grams of black beans: 600 gramsTotal grams of sweet potatoes: 400 grams

answer:To solve this problem, we need to determine how many weeks it will take for Alex to accumulate at least 120 hours of volunteer work.1. Determine the volunteer hours per week: - Alex volunteers for 8 hours each Saturday. - Alex volunteers for 4 hours each Wednesday. - Total hours volunteered per week = 8 hours (Saturday) + 4 hours (Wednesday) = 12 hours per week.2. Calculate the number of weeks needed: - We need a total of at least 120 hours. - Since Alex volunteers 12 hours each week, we can set up the equation: [ 12 times text{weeks} = 120 ] - Solving for weeks, we divide both sides by 12: [ text{weeks} = frac{120}{12} = 10 ]3. Conclusion: - It will take Alex 10 weeks to complete the required 120 hours of volunteer work.# 10

answer:To determine the total number of unique outfit combinations Alex can create for all three clients, we will calculate the combinations for each client individually and then sum them up.Client 1:- Tops: 3 options- Pants: 2 options- Accessories: 2 optionsFor each outfit combination, Alex must choose one top, one pair of pants, and one accessory. Therefore, the total number of combinations for the first client is calculated by multiplying the number of choices for each item:[3 text{ (tops)} times 2 text{ (pants)} times 2 text{ (accessories)} = 12 text{ combinations}]Client 2:- Dresses: 4 options- Accessories: 3 optionsFor each outfit combination, Alex must choose one dress and one accessory. Therefore, the total number of combinations for the second client is:[4 text{ (dresses)} times 3 text{ (accessories)} = 12 text{ combinations}]Client 3:- Suits: 2 options- Shirts: 3 options- Ties: 2 optionsFor each outfit combination, Alex must choose one suit, one shirt, and one tie. Therefore, the total number of combinations for the third client is:[2 text{ (suits)} times 3 text{ (shirts)} times 2 text{ (ties)} = 12 text{ combinations}]Total Combinations for All Clients:Finally, sum the combinations for all three clients to find the total number of unique outfit combinations Alex can create:[12 text{ (Client 1)} + 12 text{ (Client 2)} + 12 text{ (Client 3)} = 36 text{ total combinations}]# 36

answer:To solve the problem, we need to determine how many games will be played in the tournament, and then calculate the total number of hours required for all the games.1. Determine the number of teams: There are 4 teams in total.2. Calculate the number of games: Each team plays against every other team exactly once. This is a classic example of a combination problem where we need to select 2 teams from 4 to form a game. The number of ways to choose 2 teams out of 4 is given by the combination formula: [ binom{n}{r} = frac{n!}{r!(n-r)!} ] where ( n ) is the total number of teams, and ( r ) is the number of teams to choose for each game. Substituting the values, we get: [ binom{4}{2} = frac{4!}{2!(4-2)!} = frac{4 times 3}{2 times 1} = 6 ] So, there are 6 games in total.3. Calculate the total time for the games: Each game takes 2 hours. Therefore, the total time for all the games is: [ 6 text{ games} times 2 text{ hours per game} = 12 text{ hours} ]Thus, the tournament will take a total of 12 hours.# 12