To solve this we are going to use the future value of annuity due formula:
![FV=(1+ \frac{r}{n} )*P[ \frac{(1+ \frac{r}{n} )^{kt} -1}{ \frac{r}{n} } ]](https://tex.z-dn.net/?f=FV%3D%281%2B%20%5Cfrac%7Br%7D%7Bn%7D%20%29%2AP%5B%20%5Cfrac%7B%281%2B%20%5Cfrac%7Br%7D%7Bn%7D%20%29%5E%7Bkt%7D%20-1%7D%7B%20%5Cfrac%7Br%7D%7Bn%7D%20%7D%20%5D)
where

is the future value

is the periodic payment

is the interest rate in decimal form

is the number of times the interest is compounded per year

is the number of payments per year

is the number of years
We know for our problem that

and

. To convert the interest rate to decimal for, we are going to divide the rate by 100%:


Since the payment is made quarterly, it is made 4 times per year; therefore,

.
Since the type of the annuity is due, payments are made at the beginning of each period, and we know that we have 4 periods, so

.
Lets replace those values in our formula:
![FV=(1+ \frac{r}{n} )*P[ \frac{(1+ \frac{r}{n} )^{kt} -1}{ \frac{r}{n} } ]](https://tex.z-dn.net/?f=FV%3D%281%2B%20%5Cfrac%7Br%7D%7Bn%7D%20%29%2AP%5B%20%5Cfrac%7B%281%2B%20%5Cfrac%7Br%7D%7Bn%7D%20%29%5E%7Bkt%7D%20-1%7D%7B%20%5Cfrac%7Br%7D%7Bn%7D%20%7D%20%5D)
![FV=(1+ \frac{0.1}{4} )*295[ \frac{(1+ \frac{0.1}{4} )^{(4)(6)} -1}{ \frac{0.1}{4} } ]](https://tex.z-dn.net/?f=FV%3D%281%2B%20%5Cfrac%7B0.1%7D%7B4%7D%20%29%2A295%5B%20%5Cfrac%7B%281%2B%20%5Cfrac%7B0.1%7D%7B4%7D%20%29%5E%7B%284%29%286%29%7D%20-1%7D%7B%20%5Cfrac%7B0.1%7D%7B4%7D%20%7D%20%20%5D%20)
We can conclude that the amount of the annuity after 10 years is $9,781.54
1 2/3 divided by 3/16
5/3 / 3/16
KCF (Keep, Change, Flip)
5/3 * 16/3
5 * 16 = 80
3 * 3 = 9
5/3 * 16/3 = 80/9
8 8/9
Hope this helps!
300 divided by 55 = 5.45
It’s 5 since it’s the whole number
Answer:
B. A dilation with a scale factor of 0.5
Step-by-step explanation:
A. is wrong because it is congruent transformation because reflections keep the angles and side lengths of the figure the same.
B. is right because it is NOT congruent because a dilation of any scale factor other than 1 results in a similar figure, because the side lengths are proprtional but not equivalent
C. is wrong because translations keep the angles and side lengths of the figure the same.
D. is wrong because a scale factor of 1 changes nothing about the figure.