2. what is the value of x? show all of your work.

Use the Pythagorean theorem:

x^2 + 6^2 = √117 ^2

x^2 + 36 = √117 ^2

Simplify"

x^2 + 36 = 117

Subtract 36 from both sides:

x^2 = 81

Square both sides:

X = 9

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.