Answer:
1 : 7
Step-by-step explanation:
minutes : eaten pies
2 minutes : 14 eaten pies
2 : 14
2 ÷ 2 : 14 ÷ 2
1 : 7
------------------------------------------------------------------------
Find the value of y
------------------------------------------------------------------------
y - 18 = 14
+ 18 + 18
y = 32
------------------------------------------------------------------------
substitute y = 32 into 2 (y + 9)
------------------------------------------------------------------------
2( y + 9 ) = 2 ( 32 + 9 )
2 (y + 9 ) = 2 (41)
2 ( y + 9 ) = 82
------------------------------------
Answer: 82
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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
Answer:

Step-by-step explanation:
<em>The given options are not in anyway related to the question. So, I will do away with them.</em>
Given


Required
Determine the linear relationship
Let
y represents the total cost
x represents the number of shirts
The relationship between x and y is:

This gives:

