Answer:
The angle between the two vectors is 84.813°.
Step-by-step explanation:
Statement is incomplete. Complete form is presented below:
<em>Let be (6,-3, 1) and (8, 9, -11) vector with same origin. Find the angle between the two vectors. </em>
Let 
and 
, the angle between the two vectors is determined from definition of dot product:
(1)
Where:
, 
- Vectors.
, 
- Norms of each vector.
Note: The norm of a vector in rectangular form can be determined by either the Pythagorean Theorem or definition of Dot Product.
If we know that 
and 
, then the angle between the two vectors is:
![\theta = \cos^{-1}\left[\frac{(6)\cdot (8) + (-3)\cdot (9) + (1)\cdot (-11)}{\sqrt{6^{2}+(-3)^{2}+1^{2}}\cdot \sqrt{8^{2}+9^{2}+(-11)^{2}}} \right]](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20%5Ccos%5E%7B-1%7D%5Cleft%5B%5Cfrac%7B%286%29%5Ccdot%20%288%29%20%2B%20%28-3%29%5Ccdot%20%289%29%20%2B%20%281%29%5Ccdot%20%28-11%29%7D%7B%5Csqrt%7B6%5E%7B2%7D%2B%28-3%29%5E%7B2%7D%2B1%5E%7B2%7D%7D%5Ccdot%20%5Csqrt%7B8%5E%7B2%7D%2B9%5E%7B2%7D%2B%28-11%29%5E%7B2%7D%7D%7D%20%5Cright%5D)
The angle between the two vectors is 84.813°.
Answer:
x
3
Step-by-step explanation:
You add 5 to both sides. Then divide it by 4 to get your answer.
7+4-5+21-2+4=29 Then I used football knowledge to find that they started on the other teams 28 yard line :)
I'm assuming a 5-card hand being dealt from a standard 52-card deck, and that there are no wild cards.
A full house is made up of a 3-of-a-kind and a 2-pair, both of different values since a 5-of-a-kind is impossible without wild cards.
Suppose we fix both card values, say aces and 2s. We get a full house if we are dealt 2 aces and 3 2s, or 3 aces and 2 2s.
The number of ways of drawing 2 aces and 3 2s is
and the number of ways of drawing 3 aces and 2 2s is the same,
so that for any two card values involved, there are 2*24 = 48 ways of getting a full house.
Now, count how many ways there are of doing this for any two choices of card value. Of 13 possible values, we are picking 2, so the total number of ways of getting a full house for any 2 values is
The total number of hands that can be drawn is
Then the probability of getting a full house is
Step-by-step explanation:
If we use this formula then
X is 54 y is 45
54 + 45 = 11(54 + 45)
99 = 11(99)
99 = 1089
= 1089 - 99
= 990
