Let g be a group of order 9, and let x be a set of cardinality 8. suppose g admits a left group action on x. prove that this group must have a fixed point; that is, prove that there exists x ∈ x such that for all g ∈ g, we have g · x = x. equivalently, prove that there exists x ∈ x such that ox = {x}.

What is the length of the segment joining the points at (4,5) and (6,-2) round to the nearest tenth if necessary

Which number completes the inequality? 2/3 < _ < 7/9

At the "no mutants allowed" country farm, every sheep has 4 legs, every chicken has two legs, and all animals have only 1 head. asked to count how many sheep and chicken are in the fields, a farm boy reports back that there are 140 feet and 50 heads. how many sheep and chicken are there? there are sheep and chicken at the farm.