Let a be real symmetric and positive semidefinite. let α1 ≤ · · · ≤ αn be the eigenvalues of a. show that for any nonzero vector x ∈ rn, we have α1 ≤ ila xll / xll ≤ αn.

The weights of players in a basketball league are distributed normally. the distance (d) of each player's weight (w) from the mean of 86 kilograms was computed as follows: d = |w - 86| if d is greater than 7 for approximately 5% of the players, what is the approximate standard deviation of the players' weights? a. 1.75 kilograms b. 3.5 kilograms c. 4.3 kilograms d. 7 kilograms

Axel follows these steps to divide 40 by 9: start with 40. 1. divide by 9 and write down the remainder. 2. write a zero after the remainder. 3. repeat steps 1 and 2 until you have a remainder of zero. examine his work, and then complete the statements below.

Find the domain and range of the following function f(x) = 51x - 21+ 4