There are 125 people in a sport centre. 59 people use the gym. 70 people use the swimming pool. 55 people use the track. 25 peop
le use the gym and the pool. 30 people use the pool and the track. 17 people use the gym and the track. 6 people use all three facilities. Given that a randomly selected person uses the gym and the track, what is the probability they do not use the swimming pool?
1 answer:
Answer:
Step-by-step explanation:
As illustrated in the Venn diagram,
We let
U=[The total number of people at the sport center]
This implies that,
n(U)=125
G=[Those who use the gym]
This implies that,
n(G)=59
P=[Those who use the pool]
This implies that,
n(P)=70
T=[Those who use the track]
This implies that,
n(T)=55
a=[Those who use the gym only]
This implies that,
n(a)=59-(6+11+19)=59-36=23
b=[Those who use the pool only]
This implies that,
n(b)=70-(6+19+24)=70-49=21
c=[Those who use the track only]
This implies that,
n(c)=55-(6+24+11)=55-31=14
As shown in the diagram, 7 people do not use any of the facilities
Also, number of people who use gym and track=11+23+19+6+14+24=97
Hence P(a randomly selected person uses the gym and the track,but does not use the swimming pool)
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Answer:
602 tourists visited only the LEGOLAND.
Step-by-step explanation:
To solve this problem, we must build the Venn's Diagram of this set.
I am going to say that:
-The set A represents the tourists that visited LEGOLAND
-The set B represents the tourists that visited Universal Studios
-The set C represents the tourists that visited Magic Kingdown.
-The value d is the number of tourists that did not visit any of these parks, so:
We have that:
In which a is the number of tourists that only visited LEGOLAND, is the number of tourists that visited both LEGOLAND and Universal Studies,
is the number of tourists that visited both LEGOLAND and the Magic Kingdom. and
is the number of students that visited all these parks.
By the same logic, we have:
This diagram has the following subsets:
There were 1,107 tourists suveyed. This means that:
We start finding the values from the intersection of three sets.
The problem states that:
36 tourists had visited all three theme parks. So:
72 tourists had visited both LEGOLAND and Universal Studios. So:
79 tourists had visited both the Magic Kingdom and Universal Studios
68 tourists had visited both the Magic Kingdom and LEGOLAND
258 tourists had visited Universal Studios:
268 tourists had visited the Magic Kingdom:
How many tourists only visited the LEGOLAND (of these three)?
We have to find the value of a, and we can do this by the following equation:
602 tourists visited only the LEGOLAND.
The number of solutions in each equation are as follows:
- 1 solution: 4^x = 2^{-x}
- 2 solution: 3/2x + 2 = 2^{x} + 1 and 3x + 1 = 2^{-x}.
- No solution: 4^x + 2 = 3^x - 1 and 2x - 5 = 3^{x} + 2.
In order to determine the number of solutions, we would split the single equation to two different equations and then plot a graph, so as to reveal their solutions.
This ultimately implies that, the number of solutions is equal to the point of intersection between the lines of the equations plotted on a graph.
In conclusion, the number of solutions in each equation are as follows:
- 1 solution: 4^x = 2^{-x}
- 2 solution: 3/2x + 2 = 2^{x} + 1 and 3x + 1 = 2^{-x}.
- No solution: 4^x + 2 = 3^x - 1 and 2x - 5 = 3^{x} + 2.
Read more on number of solutions here: brainly.com/question/12558210
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