Answer:
Multiply the width to the length
Step-by-step explanation:
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:
![nCk=\frac{n!}{k!(n-k)!}](https://tex.z-dn.net/?f=nCk%3D%5Cfrac%7Bn%21%7D%7Bk%21%28n-k%29%21%7D)
So, the number of ways to select exactly 3 aces is:
![4C3*48C1=\frac{4!}{3!(4-3)!}*\frac{48!}{1!(48-1)!}=192](https://tex.z-dn.net/?f=4C3%2A48C1%3D%5Cfrac%7B4%21%7D%7B3%21%284-3%29%21%7D%2A%5Cfrac%7B48%21%7D%7B1%21%2848-1%29%21%7D%3D192)
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:
![P(B)=\frac{1}{270,725} +\frac{192}{270,725} =\frac{193}{270,725}](https://tex.z-dn.net/?f=P%28B%29%3D%5Cfrac%7B1%7D%7B270%2C725%7D%20%2B%5Cfrac%7B192%7D%7B270%2C725%7D%20%3D%5Cfrac%7B193%7D%7B270%2C725%7D)
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:
![P=\frac{1/270,725}{193/270,725} =\frac{1}{193}=0.0052](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B1%2F270%2C725%7D%7B193%2F270%2C725%7D%20%3D%5Cfrac%7B1%7D%7B193%7D%3D0.0052)
Answer:
![x=2](https://tex.z-dn.net/?f=x%3D2)
Step-by-step explanation:
![9 - 10x = 2x + 1 - 8x](https://tex.z-dn.net/?f=9%20-%2010x%20%3D%202x%20%2B%201%20-%208x)
![9-10x=-6x+1](https://tex.z-dn.net/?f=9-10x%3D-6x%2B1)
Subtract 9 from both sides:
![9-10x-9=-6x+1-9](https://tex.z-dn.net/?f=9-10x-9%3D-6x%2B1-9)
![-10x=-6x-8](https://tex.z-dn.net/?f=-10x%3D-6x-8)
Add 6x to both sides:
![-10x+6x=-6x-8+6x](https://tex.z-dn.net/?f=-10x%2B6x%3D-6x-8%2B6x)
![-4x=-8](https://tex.z-dn.net/?f=-4x%3D-8)
Divide both sides by -4:
![\frac{-4x}{-4}=\frac{-8}{-4}](https://tex.z-dn.net/?f=%5Cfrac%7B-4x%7D%7B-4%7D%3D%5Cfrac%7B-8%7D%7B-4%7D)
![x=2](https://tex.z-dn.net/?f=x%3D2)
I honestly don't know because i'm only in sixth grade but I think that it might be 30*.
Answer: 67°
Step-by-step explanation:
Complementary angle refers to the angle that when added together will be equal to 90°.
Let the measurement of the angle's complement be x.
Therefore, the angles are x and 2x + 21. Since it's a complementary angle, therefore,
x + 2x + 21 = 90
3x + 21 = 90
3x = 90 - 21
3x = 69
x = 69°/3
x = 23°
Therefore, the angle will be:
= 2x + 21
= 2(23°) + 21°
= 46° + 21°
= 67°
The angle is 67°.