Which of the problems below is not a permutation? the number of ways 20 people can finish in the first three places in a race. how many different kinds of pizzas can be made with 12 optional toppings. how many ways 15 people can arrange themselves in a straight line. how many ways the top 20 hit songs can be arranged from a selection of 500 current singles.

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).

How do the number line graphs of the solutions sets of -23 > x and x-23 differ?

Given: circle o, cd is diameter, chord ab || cd. arc ab = 74°, find arc ca.