Using distributive property, find the product of (x+3)(x^2-2x+4)
2 answers:
We multiply each monomial of the first parenthesis by each monomial of the second parenthesis:
Use
combine like terms
The distributive property says that the following is true:
In our problem, we will consider the term outside (or in the first equation) to be
and we will consider the expression inside the parentheses to be
. To use the distributive property, we are going to apply the outside term to all terms within the second expression. This is represented as:
We can now use the distributive property again to simplify the new expression:
The answer is x³ + x² - 2x + 12.
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Answer:
The probability is 0.0052
Step-by-step explanation:
Let's call A the event that the four cards are aces, B the event that at least three are aces. So, the probability P(A/B) that all four are aces given that at least three are aces is calculated as:
P(A/B) = P(A∩B)/P(B)
The probability P(B) that at least three are aces is the sum of the following probabilities:
- The four card are aces: This is one hand from the 270,725 differents sets of four cards, so the probability is 1/270,725
- There are exactly 3 aces: we need to calculated how many hands have exactly 3 aces, so we are going to calculate de number of combinations or ways in which we can select k elements from a group of n elements. This can be calculated as:
So, the number of ways to select exactly 3 aces is:
Because we are going to select 3 aces from the 4 in the poker deck and we are going to select 1 card from the 48 that aren't aces. So the probability in this case is 192/270,725
Then, the probability P(B) that at least three are aces is:
On the other hand the probability P(A∩B) that the four cards are aces and at least three are aces is equal to the probability that the four card are aces, so:
P(A∩B) = 1/270,725
Finally, the probability P(A/B) that all four are aces given that at least three are aces is: