Prove or disprove each of the following statements. (a) there exists a prime number x such that x + 16 and x + 32 are also prime numbers. (b) va, b, c, m € z+, if a = b (mod m), then c = c (mod m). (c) for any positive odd integer n, 3]n or nº = 1 (mod 12). (d) there exist 100 consecutive composite integers.

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.

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step-by-step explanation:

6 equilateral triangles