<h3>
Answer: TV = 10</h3>
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Explanation
Let x be some positive real number such that
leading to the ratio
ST:TU:UV = 6x:2x:3x = 6:2:3
Note how I effectively started with 6:2:3 and multiplied all parts of the ratio by x to get 6x:2x:3x
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The parts of the ratio add up to the longest segment SV
ST+TU+UV = SV
6x+2x+3x = 22
11x = 22
x = 22/11
x = 2
Therefore,
- ST = 6x = 6*2 = 12
- TU = 2x = 2*2 = 4
- UV = 3x = 3*2 = 6
Note how ST+TU+UV = 12+4+6 = 22, which is the length of SV. This helps confirm we have the correct x value.
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The last step is to find the length of TV
TV = TU+UV
TV = 4+6
TV = 10
Or you could do
ST + TV = SV
12+TV = 22
TV = 22-12
TV = 10
First term = (2)5^(-2*1) =2/25
2nd term = (2)5^(-2*2) = 2/ 625
3rd term = 2(5)^(-2*3) = 2/ 15625
If we divide the 3rd term by the 2nd term or the 2nd term by the first we get the common ratio
Common ratio = 1/25 or 0.04 as a decimal fraction.
Answer:
21.01 cubic metres
Step-by-step explanation:
We have to find the value of 1 cubic foot and then convert to cubic metre.
1 foot = 0.3048 m
1 cubic foot = 
= 0.02832 cubic metre
A volume of 742 cubic foot will therefore be:
742 * 0.02832 = 21.01 cubic metres
The volume in cubic metres is 21.01 cubic metres
Answer:
The balance is $5989.5
Step-by-step explanation:
The savings plan balance is given by the following formula:
![A = P*\left[\frac{(1 + \frac{APR}{n})^{n*Y} - 1}{\frac{APR}{n}}\right]](https://tex.z-dn.net/?f=A%20%3D%20P%2A%5Cleft%5B%5Cfrac%7B%281%20%2B%20%5Cfrac%7BAPR%7D%7Bn%7D%29%5E%7Bn%2AY%7D%20-%201%7D%7B%5Cfrac%7BAPR%7D%7Bn%7D%7D%5Cright%5D)
In which A is the savings plan balance, P is the monthly payment, APR is the annual percentage rate(decimal), n is the number of payments per year and Y is the number of years.
In this problem, we have that
Find the savings plan balance after 3 years with an APR of 7% and monthly payments of $150.
So we have to find A when 
.
So
![A = 150*\left[\frac{(1 + \frac{0.07}{12})^{12*3} - 1}{\frac{0.07}{12}}\right]](https://tex.z-dn.net/?f=A%20%3D%20150%2A%5Cleft%5B%5Cfrac%7B%281%20%2B%20%5Cfrac%7B0.07%7D%7B12%7D%29%5E%7B12%2A3%7D%20-%201%7D%7B%5Cfrac%7B0.07%7D%7B12%7D%7D%5Cright%5D)
The balance is $5989.5
