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question:Samantha is a dance instructor who loves John Travolta's iconic role in 'Saturday Night Fever' and often incorporates routines inspired by the movie in her dance classes. She decides to teach a special dance sequence that includes 8 different moves. Each move takes approximately 2 minutes to teach and practice. Samantha has 5 classes scheduled this week, and she plans to dedicate 30 minutes of each class to this special sequence. If Samantha wants to teach the entire sequence to all her classes this week, how many additional minutes will she need to borrow from other parts of her classes to cover the full duration of teaching all 8 moves?
answer:To solve this problem, we need to determine the total time required to teach all 8 moves and compare it to the time Samantha has allocated in her classes.Step 1: Calculate the total time required to teach all 8 moves.Each move takes approximately 2 minutes to teach and practice. Therefore, the total time required for all 8 moves is:[ 8 text{ moves} times 2 text{ minutes per move} = 16 text{ minutes} ]Step 2: Calculate the total time Samantha has allocated for the sequence in one class.Samantha has dedicated 30 minutes of each class to the special sequence.Step 3: Determine if the allocated time in one class is sufficient.Since each class offers 30 minutes for the sequence, and the sequence requires only 16 minutes, Samantha has more than enough time in each class to teach the entire sequence without needing additional minutes.Step 4: Calculate the total time allocated across all 5 classes.Samantha has 5 classes, each with 30 minutes allocated. Thus, the total allocated time is:[ 5 text{ classes} times 30 text{ minutes per class} = 150 text{ minutes} ]Step 5: Determine the total time needed for all classes.To teach the entire sequence to all 5 classes, Samantha would need:[ 5 text{ classes} times 16 text{ minutes per class} = 80 text{ minutes} ]Step 6: Calculate whether Samantha needs additional time.Compare the total allocated time with the total needed time:- Total allocated time: 150 minutes- Total needed time: 80 minutesSince 150 minutes (total allocated time) is greater than 80 minutes (total needed time), Samantha does not need any additional time.# 0
question:A wildlife biologist is studying a forest area that has been affected by landmines. She has observed that each landmine leaves a circular barren patch of land with a radius of 2 meters. In a section of the forest, she found 15 such barren patches. If the total area of this section of the forest is 1,000 square meters, how much of the forest area remains unbarren (not affected by landmines)?
answer:To solve the problem, we need to calculate the total area of the barren patches and then subtract this from the total area of the forest section to find the unbarren area.Step 1: Calculate the area of one barren patch.Each barren patch is circular with a radius of 2 meters. The area ( A ) of a circle is given by the formula:[A = pi r^2]where ( r ) is the radius. Substituting the given radius:[A = pi (2)^2 = 4pi text{ square meters}]Step 2: Calculate the total area of all barren patches.There are 15 barren patches. Therefore, the total barren area is:[text{Total barren area} = 15 times 4pi = 60pi text{ square meters}]Step 3: Calculate the unbarren area of the forest.The total area of the forest section is 1,000 square meters. To find the unbarren area, subtract the total barren area from the total forest area:[text{Unbarren area} = 1000 - 60pi]Step 4: Numerical approximation (if needed).To find a numerical approximation, use an approximate value for (pi), such as (pi approx 3.14159):[60pi approx 60 times 3.14159 = 188.4954]Thus, the approximate unbarren area is:[1000 - 188.4954 approx 811.5046]Therefore, the approximate unbarren area of the forest is 811.5046 square meters.# 811.5046
question:Dr. Mina is a physicist who loves using topology, a branch of mathematics, to study the fascinating world of subatomic particles. One day, she is examining a group of particles which she has grouped into different shapes. She has 8 groups of particles, and each group forms a different geometrical shape. For her experiment, she needs to calculate the total number of particles in all the groups combined. Here is the number of particles in each group:1. The group shaped like a triangle has 15 particles.2. The group shaped like a square has 20 particles.3. The group shaped like a pentagon has 25 particles.4. The group shaped like a hexagon has 18 particles.5. The group shaped like a heptagon has 22 particles.6. The group shaped like an octagon has 30 particles.7. The group shaped like a nonagon has 27 particles.8. The group shaped like a decagon has 40 particles.How many particles are there in total across all the groups?
answer:To find the total number of particles across all the groups, we need to sum the number of particles in each group. Here is the step-by-step calculation:1. The triangle group has 15 particles.2. The square group has 20 particles.3. The pentagon group has 25 particles.4. The hexagon group has 18 particles.5. The heptagon group has 22 particles.6. The octagon group has 30 particles.7. The nonagon group has 27 particles.8. The decagon group has 40 particles.Now, we add these numbers together:[15 + 20 + 25 + 18 + 22 + 30 + 27 + 40]Let's perform the addition step-by-step:- First, add the first two numbers: (15 + 20 = 35).- Add the next number: (35 + 25 = 60).- Add the next number: (60 + 18 = 78).- Add the next number: (78 + 22 = 100).- Add the next number: (100 + 30 = 130).- Add the next number: (130 + 27 = 157).- Add the last number: (157 + 40 = 197).Thus, the total number of particles is (197).# 197
question:The elected official has successfully secured additional funding to improve neighborhood security by installing new street lights and surveillance cameras. The official plans to install 120 new street lights and 80 surveillance cameras across 4 neighborhoods. The cost of installing one street light is 300, and the cost of installing one surveillance camera is 500. If the official decides to distribute the installations equally among the 4 neighborhoods, what will be the total cost of installations for one neighborhood?
answer:To determine the total cost of installations for one neighborhood, we can follow these steps:1. Calculate the number of street lights and cameras per neighborhood: The official plans to distribute the installations equally among 4 neighborhoods. - Total street lights to be installed = 120 - Total surveillance cameras to be installed = 80 Number of street lights per neighborhood: [ frac{120 text{ street lights}}{4 text{ neighborhoods}} = 30 text{ street lights per neighborhood} ] Number of surveillance cameras per neighborhood: [ frac{80 text{ cameras}}{4 text{ neighborhoods}} = 20 text{ cameras per neighborhood} ]2. Calculate the cost per installation for each type of equipment: - Cost of one street light = 300 - Cost of one surveillance camera = 5003. Calculate the total cost for installations in one neighborhood: Total cost for street lights in one neighborhood: [ 30 text{ street lights} times 300/text{street light} = 9,000 ] Total cost for surveillance cameras in one neighborhood: [ 20 text{ cameras} times 500/text{camera} = 10,000 ]4. Calculate the total cost for all installations in one neighborhood: [ 9,000 text{ (street lights)} + 10,000 text{ (cameras)} = 19,000 ]Thus, the total cost of installations for one neighborhood is:# 19,000
question:Jamie is a hard-core fan of McKinley Dixon, and she is excited to attend his upcoming concert. She wants to buy some merchandise at the concert. She has saved 150 for the event. A McKinley Dixon T-shirt costs 25, a poster is 10, and a CD is 15. Jamie wants to buy 2 T-shirts, 3 posters, and 1 CD. How much money will Jamie have left after buying these items?
answer:To determine how much money Jamie will have left after buying the merchandise, we need to calculate the total cost of the items she wants to purchase and then subtract that from the amount she has saved.1. Calculate the cost of the T-shirts: - Jamie wants to buy 2 T-shirts. - Each T-shirt costs 25. - Total cost for T-shirts = 2 T-shirts × 25/T-shirt = 50.2. Calculate the cost of the posters: - Jamie wants to buy 3 posters. - Each poster costs 10. - Total cost for posters = 3 posters × 10/poster = 30.3. Calculate the cost of the CD: - Jamie wants to buy 1 CD. - Each CD costs 15. - Total cost for the CD = 1 CD × 15/CD = 15.4. Calculate the total cost of all items: - Total cost = Total cost for T-shirts + Total cost for posters + Total cost for the CD - Total cost = 50 (T-shirts) + 30 (posters) + 15 (CD) = 95.5. Calculate how much money Jamie will have left: - Jamie has saved 150 for the event. - Money left = Amount saved - Total cost - Money left = 150 - 95 = 55.Jamie will have 55 left after buying the merchandise.# 55
question:A technology director hired IT consultants to improve the company's efficiency and reduce costs. Before the consultants were hired, the company was spending 2,000 each month on outdated software maintenance and 3,000 on server downtime issues. After the consultants implemented new systems, the software maintenance costs dropped to 1,200 per month, and server downtime costs were reduced to 1,500 per month. If the consultants charge a one-time fee of 5,000 for their services, how much money does the company save in total after three months, considering both the new costs and the consultant fee?
answer:To determine the total savings for the company after three months, we will follow these steps:1. Calculate the initial total monthly costs before hiring the consultants: - Software maintenance costs: 2,000 per month - Server downtime costs: 3,000 per month Total initial monthly costs = 2,000 + 3,000 = 5,0002. Calculate the total monthly costs after the consultants implemented the new systems: - New software maintenance costs: 1,200 per month - New server downtime costs: 1,500 per month Total new monthly costs = 1,200 + 1,500 = 2,7003. Determine the monthly savings: Monthly savings = Initial total monthly costs - New total monthly costs = 5,000 - 2,700 = 2,3004. Calculate the total savings over three months: Total savings over three months = Monthly savings × 3 = 2,300 × 3 = 6,9005. Subtract the one-time consultant fee from the savings: Net savings after consultant fee = Total savings over three months - Consultant fee = 6,900 - 5,000 = 1,900#1,900