Prove that the set of all the quaternions, with the matrix addition and multiplication explained on pages 7 and 8, is a ring with unity. this ring is denoted by the symbol . find an example to show that is not commutative. (you may assume matrix addition and multiplication are associative and obey the distributive law.)

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

Is appreciated! graph the functions and approximate an x-value in which the exponential function surpasses the polynomial function. f(x) = 4^xg(x) = 4x^2options: x = -1x = 0x = 1x = 2

Which number line represents the solution set for the inequality - x 24?