In a certain city, 30% of the families have a mastercard, 20% have an american express card, and 25% have a visa card. eight percent of the families have both a mastercard and an american express card. twelve percent have both a visa card and a mastercard. six percent have both an american express card and a visa card. is possession of a visa card independent of possession of a mastercard? why or why not? no, because p (m | v) ≠ p (v) no, because p (v | m) ≠ p (v) yes, because p (m) = p(v) yes, because p (v ∩ m) ≠ 0 no, because visa and mastercard are different things

answer: no

step-by-step explanation:

b. astronomers

∠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.