Find the 12th term of the arithmetic sequence given a3=116 and a7=180

Step-by-step explanation:

nth term = a +(n-1)d

a3 = 116 ;   a + 2d = 116 (i)

a7 = 180;   a + 6d = 180 (ii)

multiply (ii) by -1. so a will be eliminated

           a + 2d = 116 (i)

(ii)*-1    -a - 6d = -180 (ii)   { Now add the two equations}

              - 4d = -64

                   d = -64/-4

                  d = 16

Plug in the value of d in equation (i),

a + 2*16 = 116

a + 32 = 116

        a = 116 - 32

        a = 84

12th term = 84 + 11* 16 = 84 + 176 = 260

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.

b). 4320 have a nice day