Below is the five Number summary for a 136 hikers who recently completed the John muir trail JMT the variable is the amount of time to complete the 212 mile Hike from Yosemite Valley across the high sierras To the top of Mount Whitney

5 number summary
Minimum 9 days
Q118 days
Median 21 days
Q328 days
Maximum 56 days

If we use the 1.5 IQR rule to determine whether there are any outliers what is the left a boundary

a. 56
b. 3
c. 43
d. 9

Now we can find the limits in order to determine outliers like this:

So for this case the left boundary would be 3, if a value is lower than 3 we consider this observation as an outlier

b. 3

Step-by-step explanation:

For this case we have the following summary:

represent the minimum value

represent the first quartile

represent the median

represent the third quartil

represent the maximum

If we use the 1.5 IQR we need to find first the interquartile range defined as:

Now we can find the limits in order to determine outliers like this:

So for this case the left boundary would be 3, if a value is lower than 3 we consider this observation as an outlier

b. 3

answer: d. $20

step-by-step explanation:

just took the test

∠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.