From the set of 20 observations find the 50^th , 80^th and 90^th percentiles. 9,6,12,10,13,15,16,14,14,16,17,16,2 4,21,22,18,19,18,20,17 (6 marks).

first you list them in ascending order:-

6,9,10,12,13,14,14,15,16,16,16,17,17,18,18,19,20,21,22,24

The 50 th percentile = middle number = mean of 16 and 16

50th percentile = 16 Answer

80th percentile = 19 and 90th = 21

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation:

answer: domain and range mean all possible values of x and y that could be substituted to the inequality. a solution means all possible values that make the inequality statement true. so while the range is still all real numbers, the solution is the shaded area, for which y will always be greater than the line of the function.