Find the domain and range !!! 10 points math 3
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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.
we know the blue and white paints are on a 1.5 : 5 ratio, thus, if we have a total of 16.25 gallons of paint to be split along that ratio, we can simply divide 16.25 by (1.5+5) and distribute accordingly.
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Answer:
---- Starting with: ----
x² - 10x + 24
Since we have a leading coefficient of 1, simply find two numbers that sum up to -10 and multiply into 24.
By guessing and checking, we get the numbers -6 and -4. Put these into factors:
(x - 6)(x - 4)
Therefore, a binomial present in factored form is D. x - 4