Students preferred dubstep, 25 % of the students liked trance music, and 20 % wanted to hear only house music. Fifteen percent of the respondents selected both dubstep and trance. The proportion of students that like either dubstep or trance is:

proportion of students that like either dubstep or trance is 40%

Step-by-step explanation:

Students preferring dubstep : Set [DS]  = 30%

Students preferring trance music : Set  [TM] = 25%

Students preferring house music : Set [HM] = 20%

Students preferring both dubstep & trance  : Set [DS ⋂ TM] = 15%

Formula : (A U B) = (A) + (B) - (A  ⋂ B)

[ DS U TM ] =  [DS] + [TM] - [DS ⋂ TM]

= 30% + 25%  - 15% → = 40%

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

do have an equation or graph or

step-by-step explanation: