<u>ANSWER: </u>
In 9 years, amount becomes 64 times of itself.
<u>SOLUTION:
</u>
Given, a certain sum quadruples in 3 years at compound interest, interest being compounded annually.
We know that, When interest is compound annually:
Given that,
Principal = Rs.100%
Amount = Rs.400
Rate = r%
Time = 3 years
By substituting the values in above formula, we get,
![400=100 \times\left[1+\left(\frac{R}{100}\right)\right]^{3}](https://tex.z-dn.net/?f=400%3D100%20%5Ctimes%5Cleft%5B1%2B%5Cleft%28%5Cfrac%7BR%7D%7B100%7D%5Cright%29%5Cright%5D%5E%7B3%7D)
![4=1\left[1+\left(\frac{R}{100}\right)\right]}^{3}](https://tex.z-dn.net/?f=4%3D1%5Cleft%5B1%2B%5Cleft%28%5Cfrac%7BR%7D%7B100%7D%5Cright%29%5Cright%5D%7D%5E%7B3%7D)
--- eqn 1
If sum become 64 times in the time n years then,
--- eqn 2
Using equation (1) in (2), we get
![\begin{array}{c}{\left(\left[1+\left(\frac{R}{100}\right)\right]^{3}=\left(1+\left(\frac{R}{100}\right)\right)^{2}\right.} \\ {\left[1+\left(\frac{R}{100}\right)\right]^{9}=\left(1+\left(\frac{R}{100}\right)\right)^{n}}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bc%7D%7B%5Cleft%28%5Cleft%5B1%2B%5Cleft%28%5Cfrac%7BR%7D%7B100%7D%5Cright%29%5Cright%5D%5E%7B3%7D%3D%5Cleft%281%2B%5Cleft%28%5Cfrac%7BR%7D%7B100%7D%5Cright%29%5Cright%29%5E%7B2%7D%5Cright.%7D%20%5C%5C%20%7B%5Cleft%5B1%2B%5Cleft%28%5Cfrac%7BR%7D%7B100%7D%5Cright%29%5Cright%5D%5E%7B9%7D%3D%5Cleft%281%2B%5Cleft%28%5Cfrac%7BR%7D%7B100%7D%5Cright%29%5Cright%29%5E%7Bn%7D%7D%5Cend%7Barray%7D)
Thus, n = 9 years by comparing on both sides.
Hence, in 9 years, amount becomes 64 times of itself.
Answer:
The equation of the line is y=1x and I will show you a picture of a graph with your points and a line of that equation.
Step-by-step explanation:
So if 3/4 of the seats are filled, there are a few methods we can use.
The simplest method:
Just multiply 3/4 by 500, to get 1500/4, or 375.
So 375 seats are filled.
A method that can be used with harder problems and will be more efficient in those cases:
Using proportions.
You could say,
?/500 = 3/4
And then cross multiply,
500 * 3 = 4 * x (say the ? = x)
1500 = 4x
/4 /4
x = 375
So either way we get the answer, 375 seats were filled.
Answer:
see explanation
Step-by-step explanation:
73.
18 = 3x
(divide both sides by 3 )
6 = x ( multiply both sides by )
6 = 3x [ × = 3 ]
divide both sides by 3
x = 2
74.
24 = 2x
( divide both sides by 2 )
12 = x ( multiply both sides by )
12 = 2x ( divide both sides by 2 )
x = 6
75.
9 × x = 18 ( divide both sides by 9 )
x = 2
76.
2 = x × 
( multiply both sides by )
2 = 4x ( divide both sides by 4 )
x = 
