The frequency of vibration of a piano string varies directly as the square root of the tension on the string and inversely as the length of the string. the middle a string has a frequency of 440 vibrations per second. find the frequency of a string that has 1.25 times as much tesnsion and is 1.2 times as long.

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.