John surveyed 25 of his classmates about their music preferences7 students said they like hip-hop, 13 students said they pop, and 8 students said they liked neither hip-hop nor pop musicJohn made a Venn diagram to find the number of students who like both hip-hop and pop music Evaluate John's work Did he use the Venn diagram accurately to arrive at a correct solution?

The venn diagram is not included in the question, but il try to answer it in a general way.

We have a sample of 25 persons.

7 of them like hiphop.

13 of them like pop

8 of them do not like neither.

So in our Venn diagarm we will have two circles, one for the students that like pop and other for the students that like hip-hop.

in the pop circle we have 13 students, in the circle of hiphop we have 7 students, and outside both circles we have 8 stundents.

Now, if we add it all we get:

13 + 7 + 8 = 28,

But we have 25 students, this means that 3 of the students like both genres, hip hop and pop.

Then the circles of hip hop and pop must have an intersection, and in the intersection we must have 3 students.

geometry: triangles

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lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584