Wilson made punch from a recipe that called for 1 1/2 cups of orange juice and 3/4 cup lemonade. Wilson used 1 1/8 cups of orange juice and cups of lemonade. How many batches of punch did he make

Prove that the value of the expression 7^8–7^7+7^6 is divisible by 43.

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.

Which of the following is an example of a rational number? a. π b. √ 9 c. √ 8 d. 3.8362319