Prove that the relation~defined in lemma 10.2 is an equivalence relation on that is, for edges e, f, h e e(g), verify that (i) e~e (reflexive; (ii) if e~f, then f (iii) if e~f andf symmetric); h, then e~ h [transitive] n e

A3x4x5 rectangular cuboid (e.g. a brick) is painted blue and cut into 1x1 cubes. what is the expected value for the painted sides of a randomly selected cube?

For what values of the variable x is the expression square root of 7x+14+ square root of 7-x a real number?

Last month, a 770 g box of cereal was sold at a grocery store for $3.10. however, this month, the cereal manufacturer launched the same cereal in a 640 g box, which is being sold at $2.50. what is the percent change in the unit price?