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%29%5E%7Bkt%7D-1%20%7D%7B%20%5Cfrac%7Br%7D%7Bn%7D%20%7D%20%5D)
where

is the future value

is the periodic deposit

is the interest rate in decimal form

is the number of times the interest is compounded per year

is the number of deposits per year
We know for our problem that

and

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

. Since Ruben makes the deposits every 6 months,

. The interest is compounded semiannually, so 2 times per year; therefore,

.
Lets replace the 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%29%5E%7Bkt%7D-1%20%7D%7B%20%5Cfrac%7Br%7D%7Bn%7D%20%7D%20%5D)
![FV=(1+ \frac{0.1}{2} )*420[ \frac{(1+ \frac{0.1}{2})^{(2)(15)}-1 }{ \frac{01}{2} } ]](https://tex.z-dn.net/?f=FV%3D%281%2B%20%5Cfrac%7B0.1%7D%7B2%7D%20%29%2A420%5B%20%5Cfrac%7B%281%2B%20%5Cfrac%7B0.1%7D%7B2%7D%29%5E%7B%282%29%2815%29%7D-1%20%7D%7B%20%5Cfrac%7B01%7D%7B2%7D%20%7D%20%5D)
We can conclude that the correct answer is <span>
$29,299.53</span>
<u>Supplementary:</u> 1 and 2 & 3 and 4
Supplementary angles: A pair of angles whose sum is equal to 180°.
<u />
<u>Vertical:</u> 1 and 3 & 2 and 4
Vertical angles: A pair of opposite angles that are made by two intersecting lines.
<u>Complimentary:</u> None
Complimentary angles: A pair of angles whose sum is equal to 90°.
Hope this helps! :D
Irratonal numbers can't be written as a/b where a and b are integers and b≠0
so if it can be written in form a/b then it is not irrational

, it's rational
1/5 is rational

it's irrational because we can't simplify the square root further
6.3=6.3/1=63/100, rationanl
answer is

is irrational
Hey!
Let's walk through this together.
Possible Answers: {5, 7, 9, 11, 13}
Let's start with 5.
5-4<8
1<8
So, 5 is CORRECT.
Next, 7.
7-4<8
3<8
So, 7 is CORRECT.
Next, 9.
9-4<8
5<8
So, 9 is CORRECT.
Next, 11.
11-4<8
7<8
So, 11 is CORRECT.
Last, 13.
13-4<8
11<8
So, 13 is INCORRECT.
Your answers are: {5,7,9,11}
So D.
Hope this helps!
<h2><em>
~~~PicklePoppers~~~</em></h2>