The formula we use for continuous compounding is
where P is the initial amount invested, r is the rate as a decimal, and t is time in years. Our P = 1300, our r = .042, and our t = 5.75 (9 months is 3/4 of a year, and 3/4 in a decimal is .75). Putting all that into our formula we have
. We have to multiply those 2 powers together and then raise euler's number to it, then multiply by 1300. Doing all of that, we get the amount at the end to be $1,655.10
First you subtract 15 from 26 and get 11.
Second you multiply 11 by 2 and get 22.
Therefore your answer is 22.
To get the probability that randomly selected airfare between Boston and San Francisco will be more than $450, we proceed as follows:
the z-score is given by:
z=(x-μ)/σ
thus the z-score for our information will be:
z=(450-387.20)/68.50
z=0.9168
hence our probability will be:
P(X>x)=1-P(z)
P(z)=0.8212
thus
P(X>x)=1-0.8212=0.1788~17.88%
Answer:
D
Step-by-step explanation:
We can use the fact that, for 
,
Notice that
![\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1{1-x}\right]=\dfrac1{(1-x)^2}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5B%5Cdfrac1%7B1-x%7D%5Cright%5D%3D%5Cdfrac1%7B%281-x%29%5E2%7D)
so that
![f(x)=\displaystyle\frac5{(1-x)^2}=5\frac{\mathrm d}{\mathrm dx}\left[\sum_{n=0}^\infty x^n\right]](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdisplaystyle%5Cfrac5%7B%281-x%29%5E2%7D%3D5%5Cfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5B%5Csum_%7Bn%3D0%7D%5E%5Cinfty%20x%5En%5Cright%5D)
By the ratio test, this series converges if
so the series has radius of convergence 
.
