Sinα=h/w
w=h/sinα, we are told that h=15 ft and α=70° so
w=15/sin70° ft
w≈15.96 ft (to nearest hundredth of a foot)
The initial investment = $250
<span>annual simple interest rate of 3% = 0.03
</span>
Let the number of years = n
the annual increase = 0.03 * 250
At the beginning of year 1 ⇒ n = 1 ⇒⇒⇒ A(1) = 250 + 0 * 250 * 0.03 = 250
At the beginning of year 2 ⇒ n = 2 ⇒⇒⇒ A(2) = 250 + 1 * 250 * 0.03
At the beginning of year 3 ⇒ n = 3 ⇒⇒⇒ A(2) = 250 + 2 * 250 * 0.03
and so on .......
∴ <span>The formula that can be used to find the account’s balance at the beginning of year n is:
</span>
A(n) = 250 + (n-1)(0.03 • 250)
<span>At the beginning of year 14 ⇒ n = 14 ⇒ substitute with n at A(n)</span>
∴ A(14) = 250 + (14-1)(0.03*250) = 347.5
So, the correct option is <span>D.A(n) = 250 + (n – 1)(0.03 • 250); $347.50
</span>
Answer: 24
Step-by-step explanation:
From the question, we are informed that Micah is buying items for a party and that there are 6 cups in a package and 8 plates in a package.
We are further told that he wants to have the same amount of each item. The least number of packages of cups he needs to buy would be calculated by finding the least common multiple of 6 and 8.
Multiples of 6 = 6, 12 18, 24, 30
Multiples of 8 = 8, 16, 24, 32, 40
The answer is 24 cups
Let's think about the information in the problem. The problem tells us a few key points:
- The number of rabbits grows exponentially
- We start with 20 rabbits (
, 
) - After 6 months (
), we have 100 rabbits (
)
Since we know we are going to be working with an exponential model, we can start with a base exponential model:
is the principal, or starting amount
is the growth/decay rate (in this case, growth)
is the number of months
is the number of rabbits
Based on the information in the problem, we can create two equations:
The first equation tells us that 
, or that we start with 20 rabbits. Thus, we can change the second equation to:
Now, we don't know , but we want to, so let's solve for it.
![r = \sqrt[6]{5}](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%5B6%5D%7B5%7D)
Now, the problem is asking us how many rabbits we are going to have after one year (
), so let's find that:
![a = 20 \cdot (\sqrt[6]{5})^{12}](https://tex.z-dn.net/?f=a%20%3D%2020%20%5Ccdot%20%28%5Csqrt%5B6%5D%7B5%7D%29%5E%7B12%7D)
After one year, we will have 500 rabbits.
$44 is equal to the original price [P] take away 20% or 0.20 of the original price
44 = 0.80*P
In other words, 44 is 80percent of the original price P
P = 55
