There are 13 hearts in a standard deck of 52 cards. The probability of drawing a heart on a single draw is 13 out of 52, which simplifies to 1 out of 4. Since the draws are independent (due to replacement), the probability that all three cards are hearts is calculated by raising the single draw probability to the power of three. This results in (1/4) multiplied by (1/4) multiplied by (1/4), which equals 1 out of 64.

Thus, the probability that every card drawn will be a heart is 1 out of 64.

To find the common ratio, we can divide any term by the previous term. For example:
Common ratio = 100 / 1000 = 0.1
Common ratio = 10 / 100 = 0.1
Common ratio = 1 / 10 = 0.1
Therefore, the common ratio of the sequence is 0.1.
a_n = a_1 * r^(n-1)
Using this formula, we can find that:
a_1 = 1000
r = 0.1
Therefore:
a_2 = a_1 * r = 100
a_3 = a_2 * r = 10
a_4 = a_3 * r = 1
So, the explicit rule for this geometric sequence is:
a_n = 1000 * (0.1)^(n-1)
Therefore, option C (10 (1/1000) to the X power -1) is correct.

Impartial is: treating all people and groups equally: not partial or biased.