Determine whether the samples are independent or dependent. upper a data set includes the weight of 140 students before and after their first year of college. choose the correct answer below. a. the samples are independent because there is a natural pairing between the two samples. b. the samples are dependent because there is not a natural pairing between the two samples. c. the samples are dependent because there is a natural pairing between the two samples. d. the samples are independent because there is not a natural pairing between the two samples

Option C)

Step-by-step explanation:

The samples are dependant.  There should be a relation between the weights of the students, even though there could be changes, as any value can go up or down. A student with a weight around of 30 has a higher chance of getting a weight around of 35 after the firts year than a student with weight around of 55. This means that the probability a student has for getting certain amount of weight after the first year may change depending on the weight the student had at the start of the year. You can therefore naturally relate the weight a student had before the first year with the weight the student had after the first year.

So, the samples are dependant because there is a natural pairing between the to samples, as option C says.

∠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.

step-by-step explanation:

milk=16 large

soda=280 kids

juice box=82 regular

63 soda +63 regular

124 large total