Answer:
C
Step-by-step explanation:
We can easily rule out B and D because they have dotted lines and both equations are greater than or equal to and less than or equal to.
The formulas for conditional probability are:
![P(A\cap B')=P(A)\cdot P(B'|A)](https://tex.z-dn.net/?f=P%28A%5Ccap%20B%27%29%3DP%28A%29%5Ccdot%20P%28B%27%7CA%29)
![P(A\cap B')=P(B')\cdot P(A|B')](https://tex.z-dn.net/?f=P%28A%5Ccap%20B%27%29%3DP%28B%27%29%5Ccdot%20P%28A%7CB%27%29)
.
Since
![P(A\cap B')= \frac{1}{6}](https://tex.z-dn.net/?f=P%28A%5Ccap%20B%27%29%3D%20%5Cfrac%7B1%7D%7B6%7D%20)
and
![p(B')= \frac{7}{18}](https://tex.z-dn.net/?f=p%28B%27%29%3D%20%5Cfrac%7B7%7D%7B18%7D%20)
, you have the equation
![\frac{1}{6} = \frac{7}{18} \cdot P(A|B')](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B6%7D%20%3D%20%5Cfrac%7B7%7D%7B18%7D%20%5Ccdot%20P%28A%7CB%27%29)
.
Therefore,
![P(A|B')= \frac{1}{6} : \frac{7}{18} =\frac{1}{6} \cdot \frac{18}{7} = \frac{3}{7}](https://tex.z-dn.net/?f=P%28A%7CB%27%29%3D%20%5Cfrac%7B1%7D%7B6%7D%20%3A%20%5Cfrac%7B7%7D%7B18%7D%20%3D%5Cfrac%7B1%7D%7B6%7D%20%5Ccdot%20%5Cfrac%7B18%7D%7B7%7D%20%3D%20%5Cfrac%7B3%7D%7B7%7D%20)
.
Answer: The correct choice is D.
Answer:
Step-by-step explanation:
Figure (1)
x° = 107° [Vertically opposite angles]
Since, vertical angles are equal in measure.
Figure (2)
x + 71° = 90° [Given, complementary angles]
x = 90° - 71°
x = 19°
Figure (3)
x + 21° = 180° [Given as supplementary angles]
x = 180° - 21°
x = 159°
Figure (4)
x = 129° [Vertical angles]
Figure (5)
x° = 90° [Given]
z° + 34° = 90°
z° = 90° - 34°
z° = 56°
Since, x° + y° + z° = 180° [Linear angles]
90° + y° + 56° = 180°
y° + 146° = 180°
y° = 180° - 146°
y° = 34°
Answer: x^2 = 2
Step-by-step explanation: 3x^2 + 4x=12
6x^2=12
x^2= 12/6
x^2= 2
The value of the logarithmic expression
is 24.
Given the following logarithmic expressions
, we are to find the value of ![\log _a (\frac{x^3y}{z^4} )](https://tex.z-dn.net/?f=%5Clog%20_a%20%28%5Cfrac%7Bx%5E3y%7D%7Bz%5E4%7D%20%29)
from the above ![\log _ax = 3, x = a^3](https://tex.z-dn.net/?f=%5Clog%20_ax%20%3D%203%2C%20x%20%3D%20a%5E3)
![\log _ay = 7, y = a^7](https://tex.z-dn.net/?f=%5Clog%20_ay%20%3D%207%2C%20y%20%3D%20a%5E7)
Substituting x =
, y =
and z =
into the log function
we will have;
![\log _a (\frac{x^3y}{z^4} )\\=\log _a (\frac{(a^3)^3 \times a^7}{(a^{-2})^4} )\\= \log _a (\frac{a^9 \times a^7}{a^-^8} )\\= \log _a (\frac{a^1^6}{a^-^8} )\\= \log _a (\frac{x^3y}{z^4} )\\= \log _a a^2^4\\= 24 \log _a a\\= 24 \times 1\\= 24](https://tex.z-dn.net/?f=%5Clog%20_a%20%28%5Cfrac%7Bx%5E3y%7D%7Bz%5E4%7D%20%29%5C%5C%3D%5Clog%20_a%20%28%5Cfrac%7B%28a%5E3%29%5E3%20%5Ctimes%20a%5E7%7D%7B%28a%5E%7B-2%7D%29%5E4%7D%20%29%5C%5C%3D%20%5Clog%20_a%20%28%5Cfrac%7Ba%5E9%20%5Ctimes%20a%5E7%7D%7Ba%5E-%5E8%7D%20%29%5C%5C%3D%20%5Clog%20_a%20%28%5Cfrac%7Ba%5E1%5E6%7D%7Ba%5E-%5E8%7D%20%29%5C%5C%3D%20%5Clog%20_a%20%28%5Cfrac%7Bx%5E3y%7D%7Bz%5E4%7D%20%29%5C%5C%3D%20%5Clog%20_a%20a%5E2%5E4%5C%5C%3D%2024%20%5Clog%20_a%20a%5C%5C%3D%2024%20%5Ctimes%201%5C%5C%3D%2024)
Hence, the value of the logarithmic expression is 24
<h3>
What is logarithmic expression?</h3>
- In an exponential equation, the variable is expressed as an exponent. An equation using the logarithm of an expression containing a variable is referred to as a logarithmic equation.
- Check to determine if you can write both sides of the equation as powers of the same number before you attempt to solve an exponential equation.
To learn more about logarithmic expression with the given link
brainly.com/question/24211708
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