Asurvey of 1,107 tourists visiting orlando was taken. of those surveyed:
268 tourists had visited the magic kingdom
258 tourists had visited universal studios
68 tourists had visited both the magic kingdom and legoland
79 tourists had visited both the magic kingdom and universal studios
72 tourists had visited both legoland and universal studios
36 tourists had visited all three theme parks
58 tourists did not visit any of these theme parks
how many tourists only visited the legoland (of these three)?

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.

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region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true