If a and b are integers, the least common multiple of a and b, written as [a, bJ, is defined as that positive integer d such that (a) a I d and b I d. (b) Whenever a I x and b I x then d I x. Prove that [a, bJ exists and that [a, bJ

These box plots show the number of electoral votes one by democratic and republican presidential candidates for the elections from 1984 through 2012. which statement best compares the spread of the data sets

The height of a birch tree, f(x), in inches, after x months is shown in the graph below. how much does the birch tree grow per month, and what will be the height of the birch tree after 10 months? a. the birch tree grows 1 inch per month. the height of the birch tree will be 16 inches after 10 months. b. the birch tree grows 2 inches per month. the height of the birch tree will be 26 inches after 10 months. c. the birch tree grows 3 inches per month. the height of the birch tree will be 36 inches after 10 months. d. the birch tree grows 2 inches per month. the height of the birch tree will be 24 inches after 10 months.

Frank is lending $1,000 to sarah for two years. frank and sarah agree that frank should earn a real return of 4 percent per year. instructions: a. the cpi (times 100) is 100 at the time that frank makes the loan. it is expected to be 113 in one year and 127.7 in two years. what nominal rate of interest should frank charge sarah?