Mary wants to get her boyfriend a nice birthday present. she has to decide on a choice of one of five books that he would like, one of four ties or one of four x-box games. what is the total number of different outcomes available to her?

13 outcomes

Step-by-step explanation:

Given:

She wants to get a gift from the following choices;

- one of five books

- one of four ties

- one of four X-box

Since, the three groups of choices are joined with "OR" but not "AND" that means she is getting just one gift from any of the 3 groups.

Total number of gift she needed = 1

Total number of choices = 3 groups with total of 13 options

N = 13P1 = 13!/(13-1)! = 13!/12! =13

N = 13 outcomes.

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc