Let r be a relation, x a set of attributes of r, and a an attribute of r. (also, denoted by x the result of adding a to x.) define the support of x, written #x, as the number of distinct tuples in r|x (r restricted to, or projected onto, the attributes of x). prove that if x-> a, then #x=#xa. (8 points)

The number of hours per week that the television is turned on is determined for each family in a sample. the mean of the data is 37 hours and the median is 33.2 hours. twenty-four of the families in the sample turned on the television for 22 hours or less for the week. the 13th percentile of the data is 22 hours. approximately how many families are in the sample? round your answer to the nearest integer.

Write the fraction or mixed number and the decimal shown by the model

Alana has 12.5 cups of flour with which she is baking four loaves of raisin bread and one large pretzel. the pretzel requires 2.5 cups of flour to make. how much flour is in each loaf of raisin bread? explain the steps to follow to get the answer.