Let (xn) be an irreducible ergodic markov chain on a finite state space. show that xn and xm become independent as n, m → o so that also n – m → o

Express the following as a function of a single angle. cos(60) cos(-20) - sin(60) sin(-20)

Consider the following geometry problems in 3-space enter t or f depending on whether the statement is true or false. (you must enter t or f -- true and false will not work.) f equation editorequation editor 1. a plane and a line either intersect or are parallel t equation editorequation editor 2. two planes parallel to a third plane are parallel f equation editorequation editor 3. two lines either intersect or are parallel f equation editorequation editor 4. two planes orthogonal to a third plane are parallel f equation editorequation editor 5. two planes orthogonal to a line are parallel f equation editorequation editor 6. two planes either intersect or are parallel f equation editorequation editor 7. two lines orthogonal to a third line are parallel t equation editorequation editor 8. two lines parallel to a third line are parallel t equation editorequation editor 9. two planes parallel to a line are parallel f equation editorequation editor 10. two lines parallel to a plane are parallel f equation editorequation editor 11. two lines orthogonal to a plane are parallel

The poll report includes a table titled, “americans using cash now versus five years ago, by age.” the age intervals are not equal. why do you think the gallup organization chose the age intervals of 23–34, 35–54, and 55+ to display these results?