What makes a number rational and what makes a number irrational (simple explanation).

Researchers were interested in whether relaxation training decreases the number of headaches a person experiences. they randomly assigned 20 participants to a control group or a relaxation training group and noted the change in number of headaches each group reported from the week before training to the week after training. which statistical analysis should be performed to answer the researchers' question?

Acontainer full of water weighs 15.5 lbs. when ¼ of the water is poured out, the container now weighs 12 ½ lbs. how much does the container weigh when empty?

Walgreens sells both kleenex and nyquil. in a random sample of 5000 purchases, it was found that 1200 contained kleenex and 540 contained nyquil. these are not independent because sick people are more likely to buy both and healthy people more likely to buy neither. in looking into that, it was found that 360 purchases contained both. a. make a two-way table to display this information. fill in the table with the missing entries, and be sure your table has row and column totals. b. if we randomly select a purchase that contained kleenex, what is the probability it also contained nyquil? c. what percent of all purchases didn’t contain either product?