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a group of children are asked whether they prefer vanilla or chocolate ice cream. the data are collected in the table.

∆abc is reflected across the x-axis and translated 2 units up to give the image ∆a'b'c' with coordinates a'(1, 1), b'(2, -1), c'(2, 1). what are the coordinates of the preimage ∆abc? a. a(-1, 1), b(-2, 3), c(-2, 1) b. a(1, 1), b(2, 3), c(2, 1) c. a(1, -3), b(2, -1), c(2, -3) d. a(1, -3), b(2, -5), c(2, -3)

What kinds of numbers make up the set of numbers called the real numbers? give examples when you explain a number type. there are a limited set of types of numbers, but an unlimited number of examples of these numbers.

The hawaiian alphabet has 12 letters. how many permutations are posible for each number of letters?