There are 26 letters in the English alphabet and six of them are vowels: a, e,i, o,u, y. In how many ways can the 26 letters of the alphabet be arranged in a line so that there are never four or more consecutive consonants (i. e. non-vowels)?

3a + 5b - 7 = 0 a - 2b - 4 = 0 solve the system by the elimination method. check your work {(96/11, -5/11)} {(34/11, -5/11)} {(32/33, 5/11)}

Anull hypothesis states that the difference between 8 hours of sleep and 3 hours of sleep has no effect on the number of pictures a student will remember during a picture memory interface test (pmit). examining the mit database, an extremely small t-value of 0.1611 is found. this t-value is much smaller than the smallest t-value on the chart for p-value reference. from this information we can: select one: a. accept the null hypothesis because the p-value obtained shows that the difference between the two groups being tested is not statistically significant b. accept the null hypothesis because the p-value obtained was statistically significant c. reject the null hypothesis because of the p-value obtained d. reject the null hypothesis because the data obtained is statistically significant

Assume that females have pulse rates that are normally distributed with a mean of mu equals 72.0 beats per minute and a standard deviation of sigma equals 12.5 beats per minute. complete parts (a) through (c) below. a. if 1 adult female is randomly selected, find the probability that her pulse rate is between 65 beats per minute and 79 beats per minute. the probability is? b. if 16 adult females are randomly selected, find the probability that they have pulse rates with a mean between 65 beats per minute and 79 beats per minute. the probability is? c. why can the normal distribution be used in part (b), even though the sample size does not exceed 30?