Chemistry class had two exams. on the first exam the mean score was 70 with a standard deviation of 10. on the second exam the mean score was 60 with a standard deviation of 15. the correlation coefficient between the scores of the two exams was r = 0.6. we run a regression analysis with the first exam score as the independent variable and the second exam score as the dependent variable. we use the result to estimate the score on the second exam for each student based on their score on the first exam. for at least 75% of the students in the class, the regression estimated score for the second exam will be correct to within how many points?

60% correction

Step-by-step explanation:

From the given data,

Let xb = 70 (first exam score mean)

yb = 60 (second exam score mean)

σx = 10 (standard deviation of first exam)

σy = 15 (standard deviation of second exam)

ε = 0.6

From regression equation y = βo + β1*x

and β1 = ε * σy/σx

= 0.6 * 15 / 10 = 0.9

Also, βo = yb - β1*xb

Substituting the values to the equation,

βo = -3

Hence y = -3 + 0.9x

For x = 75 (supposing a student gets 75 in first exam to calculate second exam score), we have y = 64.5

Hence, ε = 0.6 means we have about a 60% dependency between the exam scores, so 60% point's corrects the second exam scores

∠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:

descending order means to order the polynomials from the term with the largest exponent to the term with the smallest exponent.  

therefore, the correct answer is d.