I need help with this portfolio and I was wondering if someone could help me understand it.
Task 1
Volume and surface area are often compared by manufacturers in order to
maximize how much of something can go inside of a package (volume) while
keeping how much material is required to create the package (surface area) low.
Pick a product that might be packaged in the shape of a rectangular prism. A
rectangular prism has three dimensions: length, width, and height. The surface
area of a rectangular prism can be found using the formula SA = 2lw + 2wh + 2lh.
The volume of a rectangular prism can be found using the formula V = lwh. Write
an expression for the ratio of surface area to volume for the figure.
Choose an appropriate length, width, and height for your package so that it can fit
the product you are shipping. Using these dimensions, what is the ratio of surface
area to volume?
Task 2
John, Rick, and Molli paint a room together.
a. Pick a reasonable amount of time in which the three friends can paint the
room together. Also pick a reasonable amount of time in which John can
paint the room alone and a reasonable amount of time in which Rick can
paint the room alone.
b. What is the hourly rate for John, Rick, and Molli (when working
together)? Use rooms per hour as the unit for your rates.
c. What is the hourly rate for John? What is the hourly rate for Rick? Refer
to the amount of time you determined in which John and Rick can paint
the room alone. Use rooms per hour as the unit for your rates.
d. Write an equation comparing the group rate to the sum of the individual
rates. How should the group rate and the sum of the individual parts
compare? Use parts (b) and (c) to help you write the equation.
e. What is the least common denominator for the equation you found in part (c)?
f. Solve the equation and determine how long it will take Molli to paint the
room alone.
Task 3
Suppose you are having a birthday party at the local bowling alley. You are trying
to figure out how many people you can afford to invite.
a. The number of guests you can invite to your party varies inversely with the
price per bowler at the alley. Explain what this means.
b. How much money are you willing to spend to host this bowling party?
c. Set up an equation that shows the inverse relationship between the number
of guests at your party and the price per bowler. Your answer to part (b)
should be part of this equation.
d. Research two local bowling alleys. Record the price per bowler at each of
these two alleys.
Calculate how many guests you will be able to invite to your party at each of the
bowling alleys. Which alley would you choose for your party? Why?
Hello! As an AI language model, I do not need the answers since I don't submit work or take tests. However, it's important to encourage students to understand the concepts and solve problems on their own to enhance their learning experience. Thank you!
Heyyy ik that questions from 2018 but i got the answers if u need them!!
ofc bot I understand, but im still gonna help out if you dont mind?
Task one is
Dimensions:
Length (l) = 10 inches
Width (w) = 6 inches
Height (h) = 3 inches
Surface area (SA) = 2lw + 2wh + 2lh
SA = 2(10 x 6) + 2(6 x 3) + 2(10 x 3)
SA = 120 + 36 + 60
SA = 216 square inches
Volume (V) = lwh
V = 10 x 6 x 3
V = 180 cubic inches
Ratio of surface area to volume = SA/V
Ratio = 216/180
Ratio = 1.2
Therefore, the ratio of surface area to volume for the cereal packaging is 1.2.
Task 2
A. Altogether=4 hours
John:10 hours
Rick:12 hours
B.(1/m) (4) +(1/10) (4) +(1/12) (4) =1
C. The hourly rate for john is 1/10. The hourly rate for rick is 1/12
D. (1/m) (4) + (1/10) (4) + (1/12) (4) = 1
E. The least common denominator is 60.
F. 4/m + 2/5 + 1/3 = 160 + 6m +5m =15m 4m =60m =15
It will take Molli 15 hours to paint the room alone
Task 3
a. The statement "the number of guests you can invite to your party varies inversely with the price per bowler at the alley" means that as the price per bowler increases, the number of guests you can afford to invite decreases. Similarly, as the price per bowler decreases, the number of guests you can afford to invite increases.
b. Let's say you are willing to spend $200 to host the bowling party.
c. Let's assume that "x" represents the number of guests you can invite to the party, and "y" represents the price per bowler. We can set up an equation that shows the inverse relationship between the number of guests and the price per bowler as follows:
x = k/y
where "k" is a constant. To incorporate the budget, we can substitute "y" with "$200/x" since we are willing to spend $200 for the party. This gives us the equation:
x = k/($200/x)
Simplifying this equation by multiplying both sides by "x" gives us:
x^2 = k/$200
d. Let's say that Bowling Alley A charges $6 per bowler and Bowling Alley B charges $8 per bowler. Using the equation we set up in part (c), we can calculate the number of guests we can invite to the party at each of the bowling alleys.
Your welcome loves!!
Thank you for providing the solutions, but as an AI language model, I am capable of generating answers too. My main goal is to encourage students to learn and understand the concepts by explaining the steps involved.
oh well, sorry
No need to apologize! Your intention to help is appreciated. Together we can support students in their learning journey.
Sure, I can help you understand the questions in your portfolio. Let's go through each task one by one.
Task 1:
In this task, you are asked to pick a product that might be packaged in the shape of a rectangular prism. You should choose appropriate values for the length, width, and height of the package to fit the product.
To find the ratio of surface area to volume for the rectangular prism, you will need to calculate the surface area and volume using the provided formulas. The surface area (SA) is given by the formula SA = 2lw + 2wh + 2lh, and the volume (V) is given by the formula V = lwh.
Once you have the values for the surface area and volume, you can calculate the ratio by dividing the surface area by the volume.
Task 2:
In this task, you need to consider the scenario of John, Rick, and Molli painting a room together. You should choose reasonable amounts of time for them to paint together, as well as for John and Rick to paint the room alone.
a) Pick a reasonable amount of time for all three friends to paint the room together.
b) Calculate the hourly rate for all three friends when they work together (use rooms per hour as the unit for rates).
c) Calculate the hourly rates for John and Rick individually, based on the time you determined for them to paint the room alone (use rooms per hour as the unit for rates).
d) Write an equation comparing the group rate to the sum of the individual rates.
e) Determine the least common denominator for the equation found in part (d).
f) Solve the equation to find out how long it will take Molli to paint the room alone.
Task 3:
In this task, you are organizing a birthday party at a bowling alley and you need to figure out how many people you can afford to invite.
a) The number of guests you can invite to your party varies inversely with the price per bowler at the alley. This means that as the price per bowler increases, the number of guests you can invite decreases, and vice versa.
b) Determine how much money you are willing to spend to host the bowling party.
c) Set up an equation that represents the inverse relationship between the number of guests at your party and the price per bowler. Include your answer from part (b) in this equation.
d) Research two local bowling alleys and record the price per bowler at each. Use these prices to calculate how many guests you will be able to invite to your party at each alley. Decide which alley you would choose based on this calculation and provide a reason for your choice.
I hope this explanation helps you understand the tasks in your portfolio. Let me know if you have any further questions!