Mathematics, 14.09.2019 04:30 dcardenas2005

a survey of 1,168 tourists visiting orlando was taken. of those surveyed:
266 tourists had visited legoland
295 tourists had visited universal studios
87 tourists had visited both the magic kingdom and legoland
68 tourists had visited both the magic kingdom and universal studios
91 tourists had visited both legoland and universal studios
16 tourists had visited all three theme parks
74 tourists did not visit any of these theme parks
how many tourists only visited the magic kingdom (of these three)?

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Answer from: irlShadow

624 tourists only visited the Magic Kindgom.

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: d = 74

We have that:

$A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)$

In which a is the number of tourists that only visited LEGOLAND, $A \cap B$ is the number of tourists that visited both LEGOLAND and Universal Studies, $A \cap C$ is the number of tourists that visited both LEGOLAND and the Magic Kingdom. and $A \cap B \cap C$ is the number of students that visited all these parks.

By the same logic, we have:

$B = b + (B \cap C) + (A \cap B) + (A \cap B \cap C)$

$C = c + (A \cap C) + (B \cap C) + (A \cap B \cap C)$

This diagram has the following subsets:

$a,b,c,d,(A \cap B), (A \cap C), (B \cap C), (A \cap B \cap C)$

There were 1,168 tourists suveyed. This means that:

$a + b + c + d + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 1,168$

We start finding the values from the intersection of three sets.

The problem states that:

16 tourists had visited all three theme parks. So:

$A \cap B \cap C = 16$

91 tourists had visited both LEGOLAND and Universal Studios. So:

$(A \cap B) + (A \cap B \cap C) = 91$

$(A \cap B) = 91-16$

$(A \cap B) = 75$

68 tourists had visited both the Magic Kingdom and Universal Studios. So

$(B \cap C) + (A \cap B \cap C) = 68$

$(B \cap C) = 68-16$

$(B \cap C) = 52$

87 tourists had visited both the Magic Kingdom and LEGOLAND

$(A \cap C) + (A \cap B \cap C) = 87$

$(A \cap C) = 87-16$

$(A \cap C) = 71$

295 tourists had visited Universal Studios

B = 295

$B = b + (B \cap C) + (A \cap B) + (A \cap B \cap C)$

295 = b + 52 + 75 + 16

b + 143 = 295

b = 152

266 tourists had visited LEGOLAND

A = 266

$A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)$

266 = a + 75 + 71 + 16

a + 162 = 266

a = 104

How many tourists only visited the Magic Kingdom (of these three)?

This is the value of c, the we can find in the following equation:

$a + b + c + d + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 1,168$

104 + 152 + c + 74 + 75 + 71 + 52 + 16 = 1,168

c + 544 = 1,168

c = 624

624 tourists only visited the Magic Kindgom.

Answer from: Quest

c. 16 units

step-by-step explanation:

mark brainliest and have a great day!

Answer from: Quest

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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