Pasty makes lemonade every morning. She uses 2 1/4 cup of sugar and 4 3/5 cups of lemon juice. How may cups of sugar and lemon juice does she use altogether?

Jeffery conducted a survey in his school and found that 30 of the 50 eighth grade students' favorite subject is mathematics. based on the results, jeffery concluded that out of the 200 students in his school, 120 students' favorite subject is mathematics. select the statement that is true about jeffery's conclusion. a. jeffery's conclusion is not valid because the sample was biased since only 200 students were surveyed. b. jeffery's conclusion is valid because the sample was random since all of the students were eighth grade students. c. jeffery's conclusion is valid because the sample was random. d. jeffery's conclusion is not valid because the sample was biased since all of the students were eighth grade students.

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 triangles are similar. what is the value of x? show your work.