Make up at least three of your own statements like those in exercise 1, and translate them into quantifier language. make sure that at least one of your statements, when translated, begins either "for each a there exists b such " or "there exists a such that for each "; that is, you should use nested quantifiers.

Part of the total score for each program is the sum of five program component scores. on the free program, the sum of these five program component scores is multiplied by a factor of 2.0. yuzuru hanyu, of japan, earned scores of 9.07, 8.96, 8.89, 9.21, and 9.36 for the program components portion of his free program. how many total points did he receive for this portion?

Simplify -4z+2y-y+-18z a.-22z+y b.-14z+2 c.3y+22z d.y +14z

In the diagram, ab is tangent to c, ab = 4 inches, and ad = 2 inches. find the radius of the circle.