Convert them to have the same denominator then subtract
Answer:
160pi
Step-by-step explanation:
the volume of a cylinder is found using the formula V=pi x r² x h. taking r=4 this means we have pi x 16 x10 =160pi
Answer: Both the mean and median decreased.
Step-by-step explanation:
The addition of the 500 lb baby elephant will have a huge impact on the mean, since you'll be finding the average (adding all numbers then dividing). So the only logical answer would be the chosen. The median will most likely either decrease or stay the same, but since staying the same isn't an option for the median, it's most likely going to be decrease.
[I do apologize in advance if it's wrong, and next time try submitting work on time :)) Hope I helped!]
Answer:
We want to find:
![\lim_{n \to \infty} \frac{\sqrt[n]{n!} }{n}](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B%5Csqrt%5Bn%5D%7Bn%21%7D%20%7D%7Bn%7D)
Here we can use Stirling's approximation, which says that for large values of n, we get:
Because here we are taking the limit when n tends to infinity, we can use this approximation.
Then we get.
![\lim_{n \to \infty} \frac{\sqrt[n]{n!} }{n} = \lim_{n \to \infty} \frac{\sqrt[n]{\sqrt{2*\pi*n} *(\frac{n}{e} )^n} }{n} = \lim_{n \to \infty} \frac{n}{e*n} *\sqrt[2*n]{2*\pi*n}](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B%5Csqrt%5Bn%5D%7Bn%21%7D%20%7D%7Bn%7D%20%3D%20%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B%5Csqrt%5Bn%5D%7B%5Csqrt%7B2%2A%5Cpi%2An%7D%20%2A%28%5Cfrac%7Bn%7D%7Be%7D%20%29%5En%7D%20%7D%7Bn%7D%20%3D%20%20%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7Bn%7D%7Be%2An%7D%20%2A%5Csqrt%5B2%2An%5D%7B2%2A%5Cpi%2An%7D)
Now we can just simplify this, so we get:
![\lim_{n \to \infty} \frac{1}{e} *\sqrt[2*n]{2*\pi*n} \\](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B1%7D%7Be%7D%20%2A%5Csqrt%5B2%2An%5D%7B2%2A%5Cpi%2An%7D%20%5C%5C)
And we can rewrite it as:
The important part here is the exponent, as n tends to infinite, the exponent tends to zero.
Thus:
Answer:
Soleil and Malvin would have $ 5,000 all together after 13 days.
Step-by-step explanation:
Since Soleil and Malvin each work a job, and Soleil starts with $ 700 and makes $ 100 per day while Malvin starts out with $ 200 and makes $ 120 per day, to determine after how many days will they have at least $ 5000 all together it must be done the following calculation:
5,000 - 700 - 200 = 4,100
200X + 120X = 4,100
320X = 4,100
X = 4,100 / 320
X = 12.8
So Soleil and Malvin would have $ 5,000 all together after 13 days.
