There are four 7's in a standard card. Chance of getting a 7 first is 4/52 = 1/13
There are four queens in a standard card. Chance of getting a queen in the second drawing is 4/51 and chance of getting a queen in the third drawing is 3/50.
Therefore, chance of drawing a seven and two queens is 1/13 x 4/51 x 3/50 = 2/5525
Answer:
20.16 meters
82.77º
Step-by-step explanation:
We have that the ramp would have the shape of a rectangular triangle, where the height and width would be the legs and the slope the hypotenuse.
We can solve it by means of the Pythagorean theorem that tells us:
c ^ 2 = a ^ 2 + b ^ 2
a = 2.5 and b = 20, replacing:
c ^ 2 = 2.5 ^ 2 + 20 ^ 2
c ^ 2 = 406.25
c = 20.16
Therefore the slope would be 20.16 meters.
The angle, we will do it using the function: Sin A ° = opposite / hypotenuse
where the opposite is the height, that is to say 20 and the hypotenuse that is the slope is equal to 20.16, replacing:
Without Aº = 20 / 20.16
Without Aº = 0.992
Aº = arc sin (0.992)
Aº = 82.77
Which means that the angle is of the slope with the horizontal is 82.77º
![(a + b)^2 = a^2 + 2ab + b^2](https://tex.z-dn.net/?f=%20%28a%20%2B%20b%29%5E2%20%3D%20a%5E2%20%2B%202ab%20%2B%20b%5E2%20)
![(\dfrac{1}{4}A + \dfrac{1}{4}B)^2 =](https://tex.z-dn.net/?f=%20%28%5Cdfrac%7B1%7D%7B4%7DA%20%2B%20%5Cdfrac%7B1%7D%7B4%7DB%29%5E2%20%3D%20)
![= \dfrac{1}{16}A^2 + \dfrac{1}{8}AB + \dfrac{1}{16}B^2](https://tex.z-dn.net/?f=%20%3D%20%5Cdfrac%7B1%7D%7B16%7DA%5E2%20%2B%20%5Cdfrac%7B1%7D%7B8%7DAB%20%2B%20%5Cdfrac%7B1%7D%7B16%7DB%5E2%20)
Answer: A.
Another way to solve by factoring 1/4.
![(\dfrac{1}{4}A + \dfrac{1}{4}B)^2 =](https://tex.z-dn.net/?f=%20%28%5Cdfrac%7B1%7D%7B4%7DA%20%2B%20%5Cdfrac%7B1%7D%7B4%7DB%29%5E2%20%3D%20)
![= [\dfrac{1}{4}(A + B)]^2](https://tex.z-dn.net/?f=%20%3D%20%5B%5Cdfrac%7B1%7D%7B4%7D%28A%20%2B%20B%29%5D%5E2%20)
![= (\dfrac{1}{4})^2(A + B)^2](https://tex.z-dn.net/?f=%20%3D%20%28%5Cdfrac%7B1%7D%7B4%7D%29%5E2%28A%20%2B%20B%29%5E2%20)
![= \dfrac{1}{16}(A^2 + 2AB + B^2)](https://tex.z-dn.net/?f=%20%3D%20%5Cdfrac%7B1%7D%7B16%7D%28A%5E2%20%2B%202AB%20%2B%20B%5E2%29%20)
![= \dfrac{1}{16}A^2 + \dfrac{1}{16}2AB + \dfrac{1}{16}B)^2](https://tex.z-dn.net/?f=%20%3D%20%5Cdfrac%7B1%7D%7B16%7DA%5E2%20%2B%20%5Cdfrac%7B1%7D%7B16%7D2AB%20%2B%20%5Cdfrac%7B1%7D%7B16%7DB%29%5E2%20)
![= \dfrac{1}{16}A^2 + \dfrac{1}{8}AB + \dfrac{1}{16}B)^2](https://tex.z-dn.net/?f=%20%3D%20%5Cdfrac%7B1%7D%7B16%7DA%5E2%20%2B%20%5Cdfrac%7B1%7D%7B8%7DAB%20%2B%20%5Cdfrac%7B1%7D%7B16%7DB%29%5E2%20)
Answer:
A line is an undefined term because it describes something that does not have width or depth. However, lines can extend its length in both side infinitely. It contains arrowheads indicating it can extend.
Step-by-step explanation:
I hope it will help you
Answer:
5. (8,33) (-1, -21) (5, 15)
6. (-5, 29) (2, 1) (4, -7)
7. (-4, -9) (0, -1) (7, 13)
8. (-9, 0) (1, 8) (5, 4)
Step-by-step explanation:
Since X is given, you plug it into the equations.
Then put the answers into the Y. hope it helps!!