A machine in a large factory is designed to mill a small lawnmower engine part out of a solid piece of aluminum. The distribution of times that it takes the machine to mill a part is approximately normally distributed with a mean of 39.2 seconds with a standard deviation of 14.2 seconds. Let X = the amount of time required to mill the engine part out of a randomly selected piece of aluminum. Using the 68-95-99.7 rule, calculate P(X > 10.8).

1

step-by-step explanation:

it's the only multiple of both and the least

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∠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.

the answers are in the images, i received 100% on this assignment. hope this !