For each integer n, define fn: r-> r by fn(x)=x+n. a) prove that for each integer n, fn is a permutation of r, that is fnes( b)prove that fn•(• meaning composed)fm=fn+m and fn^-1=f-n c) let g={fn: nez}. prove that g is a subgroup of s(r). d) prove that g is cyclic (find a generator of g).

Pick the description of a geometric object that best matches the real world object box for a deck of card

Ialready asked this but i never got an answer. will give a high rating and perhaps brainliest. choose the linear inequality that describes the graph. the gray area represents the shaded region. y ≤ –4x – 2 y > –4x – 2 y ≥ –4x – 2 y < 4x – 2

Which scenarios are most effectively explored by conducting an experiment? there is more than one correct answer. select all that apply. researchers want to study the effectiveness of a particular drug for treating migraines. they want to know which dosage of the drug yields the best results with the least side effects. to ensure fair results, the researchers want to ensure that participants and dosage administrators do not know which dosage participants receive. a teacher wants to plan a class fieldtrip and quickly determine where students prefer to go for the class fieldtrip. a car mechanic wants to know which of two engine brands makes better-performing engines. he wants to test the engines in identical situations and rate their performance in a way that can be fairly measured. a chemist studies the properties of a metal compound. she wants to know how the sample size of the metal affects its ability to conduct electricity. she wants to conduct the research in a controlled environment to minimize bias. a realty company wants to know the average income of its clients. the company wants to gather data income from current clients.