The number of trays that contain both a cup and a plate = 11.
<h3>What are sets?</h3>
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind
To find the elements in the sets A and B, we refer to the formula:
n(A) + n(B) - n(A∪B) = n(A∩B),
where,
- n(A) = number of elements in set A,
- n(B) = number of elements in set B,
- n(A∪B) = number of elements that are either in set A or B,
- n(A∩B) = number of elements that are in both the sets A and B.
Given:
- Number of trays on a table: 25
- Each tray has either:
- only a cup
- only a plate
- both cup and plate
- Trays containing cups = 15
- Trays containing plates = 21
To find: number of trays containing both cup and plate.
Finding:
Let the number of trays containing cups be C and those containing plate be P.
Then, n(C) = number of tray containing only cups = 15
n(P) = number of tray containing only plates = 21
n(C∩P) = ?
Since, each plate contains at least a cup or a plate, n(U) = total number of trays = n(C∪P) = number of trays containing either a cup or a plate
=> n(C∪P) = 25
By the formula of sets: n(A) + n(B) - n(A∪B) = n(A∩B),
We get: n(C∩P) = 15 + 21 - 25 = 15 - 4 = 11
Hence, the number of trays that contain both a cup and a plate = 11.
To learn more about sets, refer to the link: brainly.com/question/13458417
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Answer:
Step-by-step explanation:
- Let the speed of raft (current) - r
- Speed of motorboat - 12 km/h
- The distance between villages - 44 km
- Let the time spent by Aniskin - t
- The time the thief was in travel = 2 hr 40 min + t = 2 40/60 + t = 3/8 + t
- The distance the thief traveled = 44 - 27 = 17 km
<u>We have following equations:</u>
- r(8/3 + t) = 17
- (12 - r)t = 27
<u>Simplify the equations:</u>
- r(8/3 + t) = 17 ⇒ rt + 8/3r = 17
- (12 - r)t = 27 ⇒ 12t - rt = 27
<u>Add up the equations and solve for r:</u>
- rt + 8/3r + 12t - rt = 44
- 8/3r + 12t = 44
- r = 16.5 - 4.5t
<u>Substitute r into second equation:</u>
- (12 - 16.5 + 4.5t)t = 27
- 4.5t² - 4.5t = 27
- 9t² - 9t - 54 = 0
<u>Solving we get</u>
<u>Find r:</u>
- r = 16.5 - 4.5*3 = 3 km/h
I think it’s 4x^2 and 3y2 you divide it all:)
Answer: Plan A is cheaper, because the cost of a 2-minute call and a 4-minute call is less than the cost of a 2-minute call and a 4-minute of Plan B call.
Step-by-step explanation:
1. You have the following information of Plan A:
- A 2 minute call costs .54 cents.
- A 4 minutes call costs $1.08.
2. For Plan B, you know that the cost of is given by the equation:
3. Therefore, you can compare both plans by finding the cost of a call of 2 minutes and a call of 4 minutes of Plan B. You can calculate this by giving these values to :
4. Substitute the values into the equation:
(This is more expensive)
(This is more expensive)
5. Therefore, Plan A is cheaper, because the cost of a 2-minute call and a 4-minute call is less than the cost of a 2-minute call and a 4-minute of Plan B call.
Answer:
Amaia walked 28 meters
Step-by-step explanation:
So first we know that the side x+3 is equal to the side 3x+1
subtract 1 and x from both sides to get x=1
then we plug in the 1 to the equation x+9 and we know that side equals 10, meaning the parallel side is also 10.
plug in 1 to one of the original equations to get 4
4+4+10+10=28