Amovie theater conducted a survey to see what customers preferred at the concession stand. the theater asked every fifth person who entered the movie theater every friday for a month what his or her favorite movie snack was. were the results of the survey valid? yes, because the theater surveyed a random sample. yes, because the theater only surveyed children. no, because the theater did not survey everyone in the theater. no, because the theater did not use a random sample.

Yes, because the theater surveyed a random sample.  Please give me hearts and stars.

Step-by-step explanation:

Results of a survey are valid if the sample space is representative of the population. The movie theater surveyed every fifth person which means all age groups and genders were represented, and the people were selected randomly.  Therefore, the results of the survey were valid because the theater surveyed a random sample.

∠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.