Calories consumed by members of a track team the day before a race are normally distributed, with a mean of 1,800 calories and a standard deviation of 100 calories. if a normal curve is sketched using these data, what is the range for 3 standard deviations to the right and to the left of the mean?
0–3,600
1,700–1,900
1,600–2,000
1,500–2,100

1500 - 2100

Step-by-step explanation:

Three standard deviations below the mean:

1800 − 3(100) = 1500

Three standard deviations above the mean:

1800 + 3(100) = 2100

∠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.