A singer's newly announced concert on social media received 600 mentions after the first week of its announcement. The total number of mentions increases by half every week. Based on this information, after how many weeks since the concert was announced will the total number of mentions increase to about 4,556?

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.