A survey was conducted of 450 high school students asking which class they prefer, math or
history and the data was broken down by grade level.
High School Students' Subject Preferences
Math
History
Total
Freshmen
115
Sophomore
120
Junior
110
Senior
105
Total
450
Part A: If 84 freshmen prefer math, 60 sophomores prefer math, 65 juniors prefer history and 45 seniors prefer history. how many students overall perfer math.
choices:249,144,201,110
part b: What is the marginal relative frequency of those who prefer math?
choices:0.244,0.32,0.447,0.553

A: 249

B: 0.553

Step-by-step explanation:

the balance is found at the link

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.