You can see this as.... you go to the bank, deposit your salary and they give you annually 3% in interest
how much will it be in 16 years?
![\bf \qquad \qquad \textit{Future Value of an ordinary annuity} \\\\ A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right] \\\\](https://tex.z-dn.net/?f=%5Cbf%20%5Cqquad%20%5Cqquad%20%5Ctextit%7BFuture%20Value%20of%20an%20ordinary%20annuity%7D%0A%5C%5C%5C%5C%0AA%3Dpymnt%5Cleft%5B%20%5Ccfrac%7B%5Cleft%28%201%2B%5Cfrac%7Br%7D%7Bn%7D%20%5Cright%29%5E%7Bnt%7D-1%7D%7B%5Cfrac%7Br%7D%7Bn%7D%7D%20%5Cright%5D%0A%5C%5C%5C%5C)
![\bf \begin{cases} A= \begin{array}{llll} \textit{original amount}\\ \textit{already compounded} \end{array} \begin{array}{llll} \end{array}\\ pymnt=\textit{periodic payments}\to &40,000\\ r=rate\to 3\%\to \frac{3}{100}\to &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\to &1\\ t=years\to &16 \end{cases} \\\\\\ A=40000\left[ \cfrac{\left( 1+\frac{0.03}{1} \right)^{1\cdot 16}-1}{\frac{0.03}{1}} \right]](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%0AA%3D%0A%5Cbegin%7Barray%7D%7Bllll%7D%0A%5Ctextit%7Boriginal%20amount%7D%5C%5C%0A%5Ctextit%7Balready%20compounded%7D%0A%5Cend%7Barray%7D%0A%5Cbegin%7Barray%7D%7Bllll%7D%0A%0A%5Cend%7Barray%7D%5C%5C%0Apymnt%3D%5Ctextit%7Bperiodic%20payments%7D%5Cto%20%2640%2C000%5C%5C%0Ar%3Drate%5Cto%203%5C%25%5Cto%20%5Cfrac%7B3%7D%7B100%7D%5Cto%20%260.03%5C%5C%0An%3D%0A%5Cbegin%7Barray%7D%7Bllll%7D%0A%5Ctextit%7Btimes%20it%20compounds%20per%20year%7D%5C%5C%0A%5Ctextit%7Bannually%2C%20thus%20once%7D%0A%5Cend%7Barray%7D%5Cto%20%261%5C%5C%0A%0At%3Dyears%5Cto%20%2616%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0AA%3D40000%5Cleft%5B%20%5Ccfrac%7B%5Cleft%28%201%2B%5Cfrac%7B0.03%7D%7B1%7D%20%5Cright%29%5E%7B1%5Ccdot%20%2016%7D-1%7D%7B%5Cfrac%7B0.03%7D%7B1%7D%7D%20%5Cright%5D)
The standard deviation is 6.09
The variance is 37.04.
<h3>What is the standard deviation and variance?</h3>
Standard deviation is used to determine how the values in a group differs from the mean of the values in the group. It is a measure of variation.
In order to determine the standard deviation, take the following steps:
- Determine the mean of the observation: (162 + 166 + 179 + 170 + 175) / 5 = 170.40
- Determine the difference between each value and the mean and then square the result:
(162 - 170.40)² + (166- 170.40)² + (179 - 170.40)² + (170 - 170.40)² + (175 - 170.40)²
70.56 + 19.36 + 73.96 + 0.16 + 21.16 = 185.20
- Determine the mean of the sum of the squared differences and then find the square root of the mean:
√185.20 / 5 = 6.09
Variance measures the rate of dispersion of a data point around the dataset. It can be calculated by finding the square of the standard deviation of a dataset.
6.09² = 37.04
To learn more about standard deviation, please check: brainly.com/question/26201837
#SPJ1
Switch y=2x+7 to 2x-y=-7 then multiply that equation by 2 to cancel out the y's. that ends up as 4x-2y=-14 which then you get x=-24. then you substitute x into one of the original equations y= 2(-24)+7 which equals y=-41
Answer:
4) k(7k+9)
5) (x+5)(x-5)
Step-by-step explanation:
4) k(7k+9)
5) (x+5)(x-5)
the answer is the second choice
