Athief steals an atm card and must randomly guess the correct three digit pin code from a 9 key keypad repetition of digits is allowed. that is the probability of a correct guess in the first try?

1/729

Step-by-step explanation:

Assuming that the probabilities of each digit in the pin is independent from the other digits, the answer to this question can be calculated. There are total of 9 digits, out of which 1 digit is correct. This is true for all the three digits. So the probability of choosing the correct digit in the first place in the first try will be 1/9. Since this is true for the rest of the digits as well and they are independent, we can safely multiply the probabilities. So P(Correct Guess in the first try) = 1/9 (first place) * 1/9 (second place) * 1/9 (third place) = = 1/729. So the correct answer is 1/729!!!

Polygon Q's area is 1/4 of Polygon P's area

Explanation:

Imagine we had a square with side length 8. The area of this square is 8*8 = 64.

Now let's reduce each side of the square by the scale factor 1/2. So each new side is 8*(1/2) = 4. The area of this smaller square is 4*4 = 16.

Comparing the new area (16) to the old one (64), we see that the new area is 16/64 = 1/4 of the old area.

In other words,

new smaller area = (1/4)*(old larger area)

So this is one example to see why (1/2)*(1/2) = 1/4 is the area scale factor based on the linear scale factor of 1/2. In short, (1/2)^2 = 1/4. Whatever the original scale factor is, square it and you'll get the area scale factor.