Prove that if m, d, and k are integers and d > 0, then (m + dk) mod d = m mod d.

1 answer:

6 0

From the rules of modular arithmetic, (A+B)mod C= (A)modC +(B)modC

So, (m + dk) mod d = (m) mod d+<span> (dk) mod d

clearly </span>(dk) mod d = 0, as one of the things (dk) mod d represents, is the remainder of dk, when divided by d, which is clearly 0.

Thus

(m + dk) mod d = (m) mod d+ (dk) mod d= (m) mod d+ 0=(m) mod d

(m + dk) mod d =(m) mod d

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FrozenT [24]

Answer:

mode = the most

mean =average of the numbers: a calculated "central" value of a set of numbers. ... add up all the numbers, • then divide by how many numbers there are.

median=The middle number; found by ordering all data points and picking out the one in the middle (or if there are two middle numbers, taking the mean of those two numbers).

Now we arrange all Mark's test scores first (arrange in a sequence), so it will become :

71, 74, 76, 82, 83, 94, 94

mode = 94

mean = (71 +74+76+82+83+94+94) over 7

= 574 over 7

= 82

median = 82

<h3>Irina</h3>

Now we arrange all Irina's test scores first (arrange in a sequence too) , so it will become :

79, 79, 82, 83, 89, 95, 95

mode (there are 2 modes in Irina test) which is 79 and 95 because both of them appears twice.

mean = (79+79+82+83+89+95+95) over 7