This is the concept of probability, we are required to calculate for the probability of rolling a 4 with a single die four times in a row;
To solve this we proceed as follows;
The probability space of a die is x={1,2,3,4,5,6}
The probability of a die falling on any of this number is:
P(x)=1/6
Thus the probability of rolling a 4 with a single die four times which makes up mutually exclusive events will be:
1/6*1/6*1/6*1/6
=(1/6)^4
=1/1296
The answer is B] 1/1296
Answer:
Step-by-step explanation:
the given function is ![$\lim_{x\to\infty} (1 - \frac{1}{3x})^{x^2}](https://tex.z-dn.net/?f=%24%5Clim_%7Bx%5Cto%5Cinfty%7D%20%281%20-%20%5Cfrac%7B1%7D%7B3x%7D%29%5E%7Bx%5E2%7D)
The answer is ![$\lim_{x\to\infty} (1 - \frac{1}{3x})^{x^2} = 0](https://tex.z-dn.net/?f=%24%5Clim_%7Bx%5Cto%5Cinfty%7D%20%281%20-%20%5Cfrac%7B1%7D%7B3x%7D%29%5E%7Bx%5E2%7D%20%3D%200)
![\hspace{0.1cm}$\lim_{x\to\infty} e^{\ln( (1 - \frac{1}{3x})^{x^2})$\hspace{0.1cm} = \hspace{0.1cm} $\lim_{x\to\infty} e^{x^{2} \ln( (1 - \frac{1}{3x}))$](https://tex.z-dn.net/?f=%5Chspace%7B0.1cm%7D%24%5Clim_%7Bx%5Cto%5Cinfty%7D%20e%5E%7B%5Cln%28%20%281%20-%20%5Cfrac%7B1%7D%7B3x%7D%29%5E%7Bx%5E2%7D%29%24%5Chspace%7B0.1cm%7D%20%3D%20%5Chspace%7B0.1cm%7D%20%24%5Clim_%7Bx%5Cto%5Cinfty%7D%20e%5E%7Bx%5E%7B2%7D%20%5Cln%28%20%281%20-%20%5Cfrac%7B1%7D%7B3x%7D%29%29%24)
![= \hspace{0.1cm} $\lim_{x\to\infty} e^{x^{2} \ln( (1 - \frac{1}{3x}))$ = \hspace{0.1cm} $e^{\lim_{x\to\infty} x^{2} \ln( (1 - \frac{1}{3x}))$](https://tex.z-dn.net/?f=%3D%20%5Chspace%7B0.1cm%7D%20%24%5Clim_%7Bx%5Cto%5Cinfty%7D%20e%5E%7Bx%5E%7B2%7D%20%5Cln%28%20%281%20-%20%5Cfrac%7B1%7D%7B3x%7D%29%29%24%20%3D%20%20%5Chspace%7B0.1cm%7D%20%24e%5E%7B%5Clim_%7Bx%5Cto%5Cinfty%7D%20x%5E%7B2%7D%20%5Cln%28%20%281%20-%20%5Cfrac%7B1%7D%7B3x%7D%29%29%24)
![= \hspace{0.1cm} $e^{\lim_{x\to\infty}\frac{1}{\frac{d}{dx}(\frac{1}{ x^{2}} )} \frac{d}{dx} \ln( (1 - \frac{1}{3x}))$](https://tex.z-dn.net/?f=%3D%20%20%5Chspace%7B0.1cm%7D%20%24e%5E%7B%5Clim_%7Bx%5Cto%5Cinfty%7D%5Cfrac%7B1%7D%7B%5Cfrac%7Bd%7D%7Bdx%7D%28%5Cfrac%7B1%7D%7B%20x%5E%7B2%7D%7D%20%29%7D%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cln%28%20%281%20-%20%5Cfrac%7B1%7D%7B3x%7D%29%29%24)
= ![e^{\frac{1}{2} (\frac{-\infty}{3})} = e^{-\infty} = 0](https://tex.z-dn.net/?f=e%5E%7B%5Cfrac%7B1%7D%7B2%7D%20%28%5Cfrac%7B-%5Cinfty%7D%7B3%7D%29%7D%20%3D%20e%5E%7B-%5Cinfty%7D%20%3D%200)
Answer:
8x - 4
Step-by-step explanation:
Perimeter is the sun of all side lengths. We know the perimeter and two side lengths, so on order to find the third, we need to subtract the first two lengths from the sum. After subtraction, we get 8x - 4.
Ok so divide 39 by 4 which is 9.75 then mulitiply that by 3 to get your answer of $29.25
Answer:
x=19.36111..
Step-by-step explanation:
to get this you would cross multiply
the equation: 36/17=41/x
which you do 36 * x = 17 * 41
divide each side by 36 to cancel it out and leave you with x
giving you (17*41)/36
do this in a calculator...
you get x=19.3611