Consider the variation of the game called Nim. The game begins with n ≥ 1 matches. Two players take turns removing matches, either one, two, three, or four at a time. The player removing the last match loses. If the game begins with 76 matches, then the player who moves first can ensure a victory by removing matches.

Can you simplify 4/7? 24 points will be awarded!

Juliana says that she can use the patterns of equivalent ratios in the multiplication table below to write an infinite number of ratios that are equivalent to 6: 10. which statement explains whether juliana is correct? she is correct because she can multiply 6 and 10 by any number to form an equivalent ratio. she is correct because 6: 10 can be written as 1: 2 and there are an infinite number of ratios for 1: 2. she is not correct because the multiplication table does not include multiples of 10. she is not correct because 6: 10 is equivalent to 3: 5 and there are only 9 ratios in the multiplication table that are equivalent to 3: 5.

The angles in a triangle are represented by 5x, 8x, and 2x+9. what is the value of ? a.10.8 b.11.4 c.9.7 d.7.2