Which equation, please list the equation
Answer:
B. ![\overline A \overline C \cong \overline B \overline D](https://tex.z-dn.net/?f=%5Coverline%20A%20%5Coverline%20C%20%5Ccong%20%5Coverline%20B%20%5Coverline%20D)
Step-by-step explanation:
The hypotenuse leg theorem (HL) requires the proof that the hypotenuse and the corresponding leg of the triangles to be equal in length. From the diagram, it can be found that
is a common (shared) side of both triangles, so the additional fact needed is for the hypotenuses to be the same length.
∴
is the additional fact needed to prove ![\triangle ADC \cong \triangle BCD](https://tex.z-dn.net/?f=%5Ctriangle%20ADC%20%5Ccong%20%5Ctriangle%20BCD)
Hope this helps :)
Answer:
x = -11
Step-by-step explanation:
Considering tripled means multiplied by 3 because of tri, we know that we can use the equation 3x = -33.
To solve this we can divide both sides by 3:
3x = -33
x = -11
This gives our answer of -11.
Step 1. TUrn the second fraction upside down (it becomes a reciprocal)
5/2 becomes 2/5
Step 2. Multiply the first fraction by the reciprocal: (Multiply tops.)
2/5 1/4 = 1x6/ 2x1= 6/3 (multiply bottom)
Step 3. Simplify the fraction (if needed.)
6/3= 2
Example: dividing by 5/2 is the same as multiplying by 2/5 so instead of dividing by a fraction. It's easier to turn that fraction upside down, then multiply.
Answer:
Mixed probabilty
Step-by-step explanation:
What is the probability that the first and second ball chosen are both targets, that is, X1 = 1 X2 = 2?
For this we must study the simple probability of each, for example for the target in that event is 5/13. However for the second chosen but also white in the second event where there is already a total of 12 balls is 4/12.
Thus
![P (X1 = 1, X2 = 1) = \frac{5}{13} * \frac{4}{12} = \frac{5}{39}](https://tex.z-dn.net/?f=P%20%28X1%20%3D%201%2C%20X2%20%3D%201%29%20%3D%20%5Cfrac%7B5%7D%7B13%7D%20%2A%20%5Cfrac%7B4%7D%7B12%7D%20%3D%20%5Cfrac%7B5%7D%7B39%7D)
In this way is generated for all probabilities
![P (X1 = 1, X2 = 0) = \frac{5}{13} *\frac{8}{12} = \frac{10}{39}\\P (X1 = 0, X2 = 1) = \frac{8}{13} * \frac{5}{12} = \frac{10}{39}\\P (X1 = 0, X2 = 0) = \frac{8}{13} *\frac{7}{12} =\frac{4}{39}\\](https://tex.z-dn.net/?f=P%20%28X1%20%3D%201%2C%20X2%20%3D%200%29%20%3D%20%5Cfrac%7B5%7D%7B13%7D%20%2A%5Cfrac%7B8%7D%7B12%7D%20%3D%20%5Cfrac%7B10%7D%7B39%7D%5C%5CP%20%28X1%20%3D%200%2C%20X2%20%3D%201%29%20%3D%20%5Cfrac%7B8%7D%7B13%7D%20%2A%20%5Cfrac%7B5%7D%7B12%7D%20%3D%20%5Cfrac%7B10%7D%7B39%7D%5C%5CP%20%28X1%20%3D%200%2C%20X2%20%3D%200%29%20%3D%20%5Cfrac%7B8%7D%7B13%7D%20%2A%5Cfrac%7B7%7D%7B12%7D%20%3D%5Cfrac%7B4%7D%7B39%7D%5C%5C)
b) In the same way analogous to the past example we can perform all cases of combinations, therefore it would be so
![P (X1 = 1, X2 = 1) = \frac{5}{13}*\frac{4}{12}*\frac{3}{11}= \frac{5}{143}](https://tex.z-dn.net/?f=P%20%28X1%20%3D%201%2C%20X2%20%3D%201%29%20%3D%20%5Cfrac%7B5%7D%7B13%7D%2A%5Cfrac%7B4%7D%7B12%7D%2A%5Cfrac%7B3%7D%7B11%7D%3D%20%5Cfrac%7B5%7D%7B143%7D)
![P (X1 = 0, X2 = 1) = \frac{8}{13} *\frac{5}{12} * \frac{4}{11} = \frac{40}{429}](https://tex.z-dn.net/?f=P%20%28X1%20%3D%200%2C%20X2%20%3D%201%29%20%3D%20%5Cfrac%7B8%7D%7B13%7D%20%2A%5Cfrac%7B5%7D%7B12%7D%20%2A%20%5Cfrac%7B4%7D%7B11%7D%20%3D%20%5Cfrac%7B40%7D%7B429%7D)
![P (X1 = 1, X2 = 1) = \frac{5}{13}*\frac{8}{12}*\frac{4}{11} = \frac{40}{429}](https://tex.z-dn.net/?f=P%20%28X1%20%3D%201%2C%20X2%20%3D%201%29%20%3D%20%5Cfrac%7B5%7D%7B13%7D%2A%5Cfrac%7B8%7D%7B12%7D%2A%5Cfrac%7B4%7D%7B11%7D%20%3D%20%5Cfrac%7B40%7D%7B429%7D)
![P (X1 = 1, X2 = 0) =\frac{5}{13}*\frac{4}{12}*\frac{8}{11} = \frac{40}{429}](https://tex.z-dn.net/?f=P%20%28X1%20%3D%201%2C%20X2%20%3D%200%29%20%3D%5Cfrac%7B5%7D%7B13%7D%2A%5Cfrac%7B4%7D%7B12%7D%2A%5Cfrac%7B8%7D%7B11%7D%20%3D%20%5Cfrac%7B40%7D%7B429%7D)
![P(X1 = 0, X2 = 1) = \frac{8}{13}* \frac{7}{12}*\frac{5}{11}=\frac{70}{429}](https://tex.z-dn.net/?f=P%28X1%20%3D%200%2C%20X2%20%3D%201%29%20%3D%20%5Cfrac%7B8%7D%7B13%7D%2A%20%5Cfrac%7B7%7D%7B12%7D%2A%5Cfrac%7B5%7D%7B11%7D%3D%5Cfrac%7B70%7D%7B429%7D)
![P (X1 = 0, X2 = 0) = \frac{8}{13} * \frac{7}{12} * \frac{5}{11} = \frac{70}{429}](https://tex.z-dn.net/?f=P%20%28X1%20%3D%200%2C%20X2%20%3D%200%29%20%3D%20%5Cfrac%7B8%7D%7B13%7D%20%2A%20%5Cfrac%7B7%7D%7B12%7D%20%2A%20%5Cfrac%7B5%7D%7B11%7D%20%3D%20%5Cfrac%7B70%7D%7B429%7D)
![P (X1 = 1, X2 = 0) = \frac{8}{13} * \frac{7}{12} * \frac{5}{11} = \frac{70}{429}](https://tex.z-dn.net/?f=P%20%28X1%20%3D%201%2C%20X2%20%3D%200%29%20%3D%20%5Cfrac%7B8%7D%7B13%7D%20%2A%20%5Cfrac%7B7%7D%7B12%7D%20%2A%20%5Cfrac%7B5%7D%7B11%7D%20%3D%20%5Cfrac%7B70%7D%7B429%7D)
![P (X1 = 0, X2 = 0) = \frac{8}{13} *\frac{7}{12} * \frac{6}{11} = \frac{28}{143}](https://tex.z-dn.net/?f=P%20%28X1%20%3D%200%2C%20X2%20%3D%200%29%20%3D%20%5Cfrac%7B8%7D%7B13%7D%20%2A%5Cfrac%7B7%7D%7B12%7D%20%2A%20%5Cfrac%7B6%7D%7B11%7D%20%3D%20%5Cfrac%7B28%7D%7B143%7D)