A1 digit number and a 3 digit number have a sum of 205. the same two number have a difference of 195, a product of 1,000 and a quotient of 40. what are the two numbers

Non-euclidean geometry was discovered when, in seeking cleaner alternatives to the fifth postulate, it was found that the negation could also be true a. true b.false

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.

According to a study conducted in 2015, 18% of shoppers said that they prefer to buy generic instead of name-brand products. suppose that in a recent sample of 1500 shoppers, 315 stated that they prefer to buy generic instead of name-brand products. at a 5% significance level, can you conclude that the proportion of all shoppers who currently prefer to buy generic instead of name-brand products is higher than .18? use both the p-value and the critical-value approaches.