Contestants A, B, C, and D are in a 10K race. How many different ways can a race with 4 runners be completed? (Assume there is no tie.) In how many ways can A finish first and C finish second? What is the probability that A finishes first and C finishes second? Enter a reduced fraction or decimal.

Which function is odd check all that apply a. y=sin x b. y=csc x c. y=cot x d. y=sec x

Atextile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. the company wishes to test the hypothesis upper h subscript 0 baseline colon mu equals 12 against upper h subscript 1 baseline colon mu less-than 12 using a random sample of n equals 4 specimens. calculate the p-value if the observed statistic is x overbar equals 11.8. round your final answer to five decimal places (e. g. 98.76543).

1. ∠1 is complementary to ∠2 and ∠3 is complementary to ∠2. subtraction property of equality 2. m∠1 + m∠2 = 90 and m∠3 + m∠2 = 90 substitution 3. m∠1 + m∠2 = m∠3 + m∠2 definition of complementary 4. m∠1 = m∠3 given