Company is developing a new high-performance wax for cross country ski racing. In order to justify the price marketing wants, the wax needs to be very fast. Specifically, the mean time to finish their standard test course should be less than 55 seconds for a former Olympic champion. To test it, the champion will ski the course 8 times. The champion's times are 59.5, 64.7, 46.6, 54.8, 47.1, 46.1, 52.2, and 41.6 seconds to complete the test course. Complete parts a and b below. a) Should they market the wax? Assume the assumptions and conditions for appropriate hypothesis testing are met for the sample. Assume alphaequals0.05. What are the null and alternative hypotheses? Choose the correct answer below. A. H0: muless than55 vs. HA: muequals55 B. H0: muequals55 vs. HA: mugreater than55 C. H0: mugreater than55 vs. HA: muequals55 D. H0: muequals55 vs. HA: muless than55'

Correct option: (D) H₀: μ =  55 vs. Hₐ: μ < 55.

Step-by-step explanation:

In this case we need to test whether the new high-performance wax price is justifiable or not.

It is provided that the wax needs to be very fast specifically the mean time to finish their standard test course should be less than 55 seconds for a former Olympic champion, for the price to justifiable.

So, to test this a sample of n = 8 champion's times are recorded.

A one-sample t-test will be used to perform the test.

The hypothesis to test this is defined as follows:

H₀: The mean time to finish their standard test course is 55 seconds, i.e. μ =  55.

Hₐ: The mean time to finish their standard test course is less than 55 seconds, i.e. μ < 55.

Thus, the correct option is (D).

∠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.

square root of 36/6 = 2.449489743

square root of 16/6 = 1.632993162

square root of 6 = 2.449489743

the answer is square root of 16/6 because the square root of 36/6 is the same answer as square root of 6 = 2.449489743