Radio stations in a certain country use a sequence of 5 or 6 letters as their station identification call letters. the first letter must be upper y comma upper n comma upper a comma upper q comma or upper r. assume there are no restrictions on the remaining letters, and repetition is allowed. a) how many 5-letter station identifications are possible? b) how many 6-letter station identifications are possible? c) how many total station identifications are possible? d) the identification for a randomly-chosen radio station is 5 letters in length. what is the probability that all five letters are different?

∠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.

a; x = 0.5

step-by-step explanation:

-10x = -5

x = 0.5

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