At a large university it is known that 51% of the students live on campus. The director of student life is going to take a random sample of 100 students. What is the probability that more than half of the sampled students live on campus?

Since an approximate method hasn't been specified,  we can use binomial distribution with n = 100, p = 0.51, q = 1 - p = 0.49

more than half means ≥ 51

P[x ≥ 50] = sum C(100,x) * 0.4^x *0.6^(200-x) for x = 51 to 100 = 0.54006

Step-by-step explanation:

Further explanation can be seen from:

https://www.wolframalpha.com/input/?i=sum+C%28100%2Cx%29+*+0.51%5Ex+*0.49%5E%28100-x%29+for+x+%3D+51+to+100

idk man good luck man

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