Answer:
facts
Step-by-step explanation:
-2(-x + 3y) - 3(x - 5y)
-2(-x) - 2(3y) - 3(x) + 3(5y)
2x - 6y - 3x + 15y
2x - 3x - 6y + 15y
-x + 9y
Solution :
![$ P(A \cap B) = P(\text{coin}\ C_1 \text{ chosen and 4 heads in 10 trails})$](https://tex.z-dn.net/?f=%24%20P%28A%20%5Ccap%20B%29%20%3D%20P%28%5Ctext%7Bcoin%7D%5C%20C_1%20%5Ctext%7B%20chosen%20and%204%20heads%20in%2010%20trails%7D%29%24)
![$= \frac{1}{3} \times ^{10}C_4 \times 0.4^4 \times 0.6^6$](https://tex.z-dn.net/?f=%24%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Ctimes%20%5E%7B10%7DC_4%20%5Ctimes%200.4%5E4%20%5Ctimes%200.6%5E6%24)
= 0.0836
P(B)= P(coin
chosen and 4 heads in 10 trails) + P(coin
chosen and 4 heads in 10 trail) + P(coin
chosen and 4 heads in 10 trail)
![$=\frac{1}{3}\times ^{10}C_4 \times 0.4^4 \times 0.6^6 + \frac{1}{3}\times ^{10}C_4 \times 0.5^4 \times 0.5^6 + \frac{1}{3}\times ^{10}C_4 \times 0.2^4 \times 0.8^6$](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B1%7D%7B3%7D%5Ctimes%20%5E%7B10%7DC_4%20%5Ctimes%200.4%5E4%20%5Ctimes%200.6%5E6%20%2B%20%5Cfrac%7B1%7D%7B3%7D%5Ctimes%20%5E%7B10%7DC_4%20%5Ctimes%200.5%5E4%20%5Ctimes%200.5%5E6%20%2B%20%5Cfrac%7B1%7D%7B3%7D%5Ctimes%20%5E%7B10%7DC_4%20%5Ctimes%200.2%5E4%20%5Ctimes%200.8%5E6%24)
![$=0.0836+0.0684+0.0294$](https://tex.z-dn.net/?f=%24%3D0.0836%2B0.0684%2B0.0294%24)
![$=0.1813$](https://tex.z-dn.net/?f=%24%3D0.1813%24)
P(A|B) = ![$\frac{P(A \cap B)}{P(B)}$](https://tex.z-dn.net/?f=%24%5Cfrac%7BP%28A%20%5Ccap%20B%29%7D%7BP%28B%29%7D%24)
![$=\frac{0.0836}{0.1813}$](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B0.0836%7D%7B0.1813%7D%24)
![$=0.4611$](https://tex.z-dn.net/?f=%24%3D0.4611%24)
<span>|3x| = 12 actually represents two equations: 3x = 12 and -3x = 12.
Thus, the solutions are {-4, 4).</span>
6 | 1 1 -40 -4
. | 6 42 12
- - - - - - - - - - - - - -
. | 1 7 2 8
![\dfrac{x^3+x^2-40x-4}{x-6}=x^2+7x+2\text{ R }8](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%5E3%2Bx%5E2-40x-4%7D%7Bx-6%7D%3Dx%5E2%2B7x%2B2%5Ctext%7B%20R%20%7D8)
6 | 3 -9 -56 8
. | 18 54 -12
- - - - - - - - - - - - - - -
. | 3 9 -2 -4