Answer:
x = -10
Step-by-step explanation:
4 x 7 is 28, and 8 x 7 is 56. You can use 4 x 7 to find 8 x 7 by multiplying that first and doubling that quotient.
Half of 56 is 28, therefore doubling that allows us to find the quotient of 8 x 7.
Answer:
(3 * 100,000) + (0 * 10,000) + (4 * 1000) + (0 * 100) + (5 * 10) + (6 * 1)
Step-by-step explanation:
We want to represent the value of this number using expanded notation
Mathematically, that will be;
(3 * 100,000) + (0 * 10,000) + (4 * 1000) + (0 * 100) + (5 * 10) + (6 * 1)
= 300,000 + 0 + 4000 + 0 + 50 + 6
= 304,057
Answer:
The formula to calculate standard deviation from probability is \sqrt(n*p*(1-p)). n is the sample size, and 200 in this case (number of putts for practice). p is 80% or 0.8, the probability that he can make it. So the standard deviation is \sqrt(200*0.8*(1-0.8)=\sqrt(200*0.8*0.2)=\sqrt(16)=4.
In a hand of 5 cards, you want 4 of them to be of the same rank, and the fifth can be any of the remaining 48 cards. So if the rank of the 4-of-a-kind is fixed, there are
possible hands. To account for any choice of rank, we choose 1 of the 13 possible ranks and multiply this count by
. So there are 624 possible hands containing a 4-of-a-kind. Hence A occurs with probability

There are 4 aces in the deck. If exactly 1 occurs in the hand, the remaining 4 cards can be any of the remaining 48 non-ace cards, contributing
possible hands. Exactly 2 aces are drawn in
hands. And so on. This gives a total of

possible hands containing at least 1 ace, and hence B occurs with probability

The product of these probability is approximately 0.000082.
A and B are independent if the probability of both events occurring simultaneously is the same as the above probability, i.e.
. This happens if
- the hand has 4 aces and 1 non-ace, or
- the hand has a non-ace 4-of-a-kind and 1 ace
The above "sub-events" are mutually exclusive and share no overlap. There are 48 possible non-aces to choose from, so the first sub-event consists of 48 possible hands. There are 12 non-ace 4-of-a-kinds and 4 choices of ace for the fifth card, so the second sub-event has a total of 12*4 = 48 possible hands. So
consists of 96 possible hands, which occurs with probability

and so the events A and B are NOT independent.