Answer:
A
Step-by-step explanation:
When solving for x as an exponent, we need to use logarithms in order to undo the operation and rearrange the terms. We use log rules to bring down the exponent and solve. Logarithms are the inverse operations to exponents and vice versa. We have one special kind of logarithm called the natural logarithm whose base is e. We write it as ln. Since our base is e here, we will use the natural logarithm to rearrange and isolate x.
![e^{4x-1} =3](https://tex.z-dn.net/?f=e%5E%7B4x-1%7D%20%3D3)
We begin by applying the natural logarithm to each side.
![ln(e^{4x-1}) =ln(3)](https://tex.z-dn.net/?f=ln%28e%5E%7B4x-1%7D%29%20%3Dln%283%29)
Log rules allow use to rearrange the exponent as multiplication in front of the log.
![(4x-1)ln(e) =ln(3)](https://tex.z-dn.net/?f=%284x-1%29ln%28e%29%20%3Dln%283%29)
ln e as an inverse simplifies to 1.
![(4x-1)(1)=ln(3)](https://tex.z-dn.net/?f=%284x-1%29%281%29%3Dln%283%29)
We now apply the inverse operations for subtraction and multiplication.
![4x-1+1=1+ln(3)\\4x=1+ln(3)\\\frac{4x}{4} =\frac{1+ln3}{4} \\x =\frac{1+ln3}{4}](https://tex.z-dn.net/?f=4x-1%2B1%3D1%2Bln%283%29%5C%5C4x%3D1%2Bln%283%29%5C%5C%5Cfrac%7B4x%7D%7B4%7D%20%3D%5Cfrac%7B1%2Bln3%7D%7B4%7D%20%5C%5Cx%20%3D%5Cfrac%7B1%2Bln3%7D%7B4%7D)
Option A is correct.
I think it is the fourth one
Answer:
See there y-intersept and if slope is negative or positive to see if they intersect
Answer:
11/20
Step-by-step explanation:
At the beginning, the number of marbles in the box are:
10 green marbles
11 white marbles
The first marble chosen is green, and then it is not replaced in the box. Therefore, the number of green marbles left in the box is 9.
Therefore, the total number of marbles left in the box is:
![n=9+11=20](https://tex.z-dn.net/?f=n%3D9%2B11%3D20)
Now we want to find the probability to choose a white marble. The number of white marble is
![w=11](https://tex.z-dn.net/?f=w%3D11)
Therefore, the probability of choosing a white marble is:
![p(w)=\frac{w}{n}=\frac{11}{20}](https://tex.z-dn.net/?f=p%28w%29%3D%5Cfrac%7Bw%7D%7Bn%7D%3D%5Cfrac%7B11%7D%7B20%7D)