<u>Answer</u>
3
<u>Explanation</u>
Y varies directly as x
Y ∝ x Inserting constant of variation, k,
Y = kx
k = Y/x
= 18/6
= 3
Answer:
1 inch
Step-by-step explanation:
The formula for the volume of a cylinder:
V = πr²h, where r=radius and h = height
Using 7.1 for 'V' and 1.5 for 'r' (1/2 of the diameter), we can fill in the values and solve for 'h':
7.1 = π(1.5)²h or 7.1 = 7.065h
h = 1 inch
First, Alvin gave Joyce and Sean 2/3 of the remainder, to solve first find the common denominator, which in this case is 24. Then, 1/3=?/24, 24/3=8 so it is 8/24 for the total given by Alvin. Joyce got 5/8, 5/8=?/24, 24/8=3,3 x 5=15, 15/24.
15/24 - 8/24= 7/24 is the answer
To solve this we are going to use formula for the future value of an ordinary annuity:
![FV=P[ \frac{(1+ \frac{r}{n} )^{nt} -1}{ \frac{r}{n} } ]](https://tex.z-dn.net/?f=FV%3DP%5B%20%5Cfrac%7B%281%2B%20%5Cfrac%7Br%7D%7Bn%7D%20%29%5E%7Bnt%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 years
We know from our problem that the periodic payment is $50 and the number of years is 3, so

and

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


Since the interest is compounded monthly, it is compounded 12 times per year; therefore,

.
Lets replace the values in our formula:
![FV=P[ \frac{(1+ \frac{r}{n} )^{nt} -1}{ \frac{r}{n} } ]](https://tex.z-dn.net/?f=FV%3DP%5B%20%5Cfrac%7B%281%2B%20%5Cfrac%7Br%7D%7Bn%7D%20%29%5E%7Bnt%7D%20-1%7D%7B%20%5Cfrac%7Br%7D%7Bn%7D%20%7D%20%5D)
![FV=50[ \frac{(1+ \frac{0.04}{12} )^{(12)(3)} -1}{ \frac{0.04}{12} } ]](https://tex.z-dn.net/?f=FV%3D50%5B%20%5Cfrac%7B%281%2B%20%5Cfrac%7B0.04%7D%7B12%7D%20%29%5E%7B%2812%29%283%29%7D%20-1%7D%7B%20%5Cfrac%7B0.04%7D%7B12%7D%20%7D%20%5D)

We can conclude that after 3 years you will have $1909.08 in your account.