Hello!
![\large\boxed{x = 21}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7Bx%20%3D%2021%7D)
![\frac{-x}{3} + 2 = -5](https://tex.z-dn.net/?f=%5Cfrac%7B-x%7D%7B3%7D%20%2B%202%20%3D%20-5)
Begin isolating for x by subtracting 2 from both sides:
![\frac{-x}{3} + 2 - 2 = -5 - 2\\\\\frac{-x}{3} = -7](https://tex.z-dn.net/?f=%5Cfrac%7B-x%7D%7B3%7D%20%2B%202%20-%202%20%3D%20-5%20-%202%5C%5C%5C%5C%5Cfrac%7B-x%7D%7B3%7D%20%3D%20-7)
Further simplify by multiplying both sides by 3:
![\frac{-x}{3} * 3= -7 * 3\\\\-x= -21](https://tex.z-dn.net/?f=%5Cfrac%7B-x%7D%7B3%7D%20%2A%203%3D%20-7%20%2A%203%5C%5C%5C%5C-x%3D%20-21)
Multiply both sides by -1 to cancel out the -x:
![-x(-1) = -21(-1)\\\\x = 21](https://tex.z-dn.net/?f=-x%28-1%29%20%3D%20-21%28-1%29%5C%5C%5C%5Cx%20%3D%2021)
Answer:
![a.\frac{1}{13}\\b.\frac{1}{2}\\c.\frac{1}{13}\\d.\frac{1}{13}](https://tex.z-dn.net/?f=a.%5Cfrac%7B1%7D%7B13%7D%5C%5Cb.%5Cfrac%7B1%7D%7B2%7D%5C%5Cc.%5Cfrac%7B1%7D%7B13%7D%5C%5Cd.%5Cfrac%7B1%7D%7B13%7D)
Step-by-step explanation:
P(A|B) = P(A and B) / P(B)
Total number of cards = 52
a)
Let A denotes the event that the card is a diamond and B denotes the card is red.
![P\left ( A|B \right )=\frac{P\left ( A\cap B \right )}{P(B)}\\=\frac{\frac{2}{52}}{\frac{26}{52}}\\=\frac{1}{13}](https://tex.z-dn.net/?f=P%5Cleft%20%28%20A%7CB%20%5Cright%20%29%3D%5Cfrac%7BP%5Cleft%20%28%20A%5Ccap%20B%20%5Cright%20%29%7D%7BP%28B%29%7D%5C%5C%3D%5Cfrac%7B%5Cfrac%7B2%7D%7B52%7D%7D%7B%5Cfrac%7B26%7D%7B52%7D%7D%5C%5C%3D%5Cfrac%7B1%7D%7B13%7D)
b)
Let A denotes the event that the card is red and B denotes the card is diamond.
![P\left ( A|B \right )=\frac{P\left ( A\cap B \right )}{P(B)}=\frac{\frac{2}{52}}{\frac{4}{52}}\\=\frac{1}{2}](https://tex.z-dn.net/?f=P%5Cleft%20%28%20A%7CB%20%5Cright%20%29%3D%5Cfrac%7BP%5Cleft%20%28%20A%5Ccap%20B%20%5Cright%20%29%7D%7BP%28B%29%7D%3D%5Cfrac%7B%5Cfrac%7B2%7D%7B52%7D%7D%7B%5Cfrac%7B4%7D%7B52%7D%7D%5C%5C%3D%5Cfrac%7B1%7D%7B2%7D)
c)
Let A denotes the event that the card is nine and B denotes the card is red.
![P\left ( A|B \right )=\frac{P\left ( A\cap B \right )}{P(B)}=\frac{\frac{2}{52}}{\frac{26}{52}}\\=\frac{1}{13}](https://tex.z-dn.net/?f=P%5Cleft%20%28%20A%7CB%20%5Cright%20%29%3D%5Cfrac%7BP%5Cleft%20%28%20A%5Ccap%20B%20%5Cright%20%29%7D%7BP%28B%29%7D%3D%5Cfrac%7B%5Cfrac%7B2%7D%7B52%7D%7D%7B%5Cfrac%7B26%7D%7B52%7D%7D%5C%5C%3D%5Cfrac%7B1%7D%7B13%7D)
d)
Let A denotes the event that the card is a king and B denotes the card is a face card.
![P\left ( A|B \right )=\frac{P\left ( A\cap B \right )}{P(B)}=\frac{\frac{4}{52}}{\frac{12}{52}}\\=\frac{1}{13}](https://tex.z-dn.net/?f=P%5Cleft%20%28%20A%7CB%20%5Cright%20%29%3D%5Cfrac%7BP%5Cleft%20%28%20A%5Ccap%20B%20%5Cright%20%29%7D%7BP%28B%29%7D%3D%5Cfrac%7B%5Cfrac%7B4%7D%7B52%7D%7D%7B%5Cfrac%7B12%7D%7B52%7D%7D%5C%5C%3D%5Cfrac%7B1%7D%7B13%7D)
This will be a maximum point as the coefficient of x^2 is negative.
y' = -2x + 3 = 0
x = 1.5
y = 5 + 3(1.5) - 1.5^2 = 7.25
required point is (1.5,7.25)
Answer:
[ 0 ]
Step-by-step explanation:
The order of the matrix [ 3 1 1 ] is 1 by 3 and the order of the other matrix is 3 by 1 so this means that the order of the answer matrix is 1 by 1. So we multiply matrices row by columns.
[ 3 1 1 ] × | 2|
| -6|
| 0|
[ 3 × 2 + 1 × -6 + 1 × 0 ]
[ 6 - 6 + 0 ]
[ 0 ]
Answer:
104 but not sure
Step-by-step explanation: