Audrey graco plans to conduct book signings in several cities to promote her new novel. she wishes to visit knoxville, chattanooga, chapel hill, charlotte, raleigh, and richmond. how many different ways can she visit each of these cities and return to her starting point in wilmington? o a. 720 o b. 30 o c. 29 o d. 120 click to select vour answer

The correct answer is:

              Option: A

                 A.   720

It is given that:

 Audrey plans to conduct books singing in different cities.

She wishes to visit Knoxville, Chattanooga, Chapel Hill, Charlotte, Raleigh, and Richmond.

i.e. she has to visit 6 cities.

The total number of different ways she can visit each city and return to her starting point in Wilmington is:

    6×5×4×3×2×1

( Since from Wilmington she may chose to go to any of one city out of 6 cities.

and the  from there she may chose any one of the five cities remaining from the visit and then from there to any one of the four cities left and so on till she is left with the last place and then from that last city there is just one possibility i.e. returning t Wilmington )

Hence, the total number of ways are:  720

need points to ask question

step-by-step explanation:

∠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.