Let q ≥ 2 be a given integer. a full q-ary tree is a rooted tree (t, r) such that every vertex has either 0 or q children. a. show that if (t, r) is a full q-ary tree with p parents, then there must be exactly (q − 1)p + 1 non-parents. b. if (t, r) is a full q-ary tree, let vk be the set of vertices of t that are at level k. use the fact (do not reprove ) that |v0 | = 1 and for any k ≥ 0, |vk+1 | ≤ q |vk |, to show that |vk | ≤ q k. c. find the minimum possible height of a full 5-ary tree with 109 total vertices.

Asequence {an} is defined recursively, with a1 = 1, a2 = 2 and, for n > 2, an = an-1 an-2 . find the term a241. a) 0 b) 1 c) 2 d) 1 2

It appears that people who are mildly obese are less active than leaner people. one study looked at the average number of minutes per day that people spend standing or walking. among mildly obese people, the mean number of minutes of daily activity (standing or walking) is approximately normally distributed with mean 376 minutes and standard deviation 64 minutes. the mean number of minutes of daily activity for lean people is approximately normally distributed with mean 528 minutes and standard deviation 107 minutes. a researcher records the minutes of activity for an srs of 7 mildly obese people and an srs of 7 lean people. use z-scores rounded to two decimal places to answer the following: what is the probability (image for it appears that people who are mildly obese are less active than leaner people. one study looked at the averag0.0001) that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes? what is the probability (image for it appears that people who are mildly obese are less active than leaner people. one study looked at the averag0.0001) that the mean number of minutes of daily activity of the 6 lean people exceeds 420 minutes?

In a 45-45-90 right triangle, what is the ratio of the length of one leg to the length of the other leg? а . 1: 2 в. 2: 1 с. 2: 1 d. 1: 1