The bowling team at Lincoln High School must choose a president, vice president, and secretary. If the team has 19 members, how many ways could the officers be chosen?

Officers can be chosen in 5,814 different ways.

Step-by-step explanation:

Given that the bowling team at Lincoln High School must choose a president, vice president, and secretary, to determine, if the team has 19 members, in how many ways could the officers be chosen, the following calculation must be performed:

19 x 18 x 17 = X

342 x 17 = X

5.814 = X

Therefore, officers can be chosen in 5,814 different ways.

∠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.