Are the ratios 4:18 and 2:9 equivalent? yes no
2 answers:
Step-by-step explanation:
Two ratios are given to us and we need to tell whether they are equivalent or not . Firstly let us say we have two ratios q:p and r:s . Here p & q are co-primes and r & s are also co-primes. Then the two ratios will be equal if and only if
- q = r
- p = s .
Theefore , the Ratios are ,
Here we see that the ratio 2:9 is in simplest form that is HCF of 2 & 9 is 1 . But here 4:18 is not in simplest form . HCF of 4 & 18 is not 1 it's 2 .On dividing numerator and denominator by 2 , we have ,
Therefore since the Ratios are equal in the simplest form . Therefore the Ratios are equal.
You might be interested in
The formula of the present value of annuity due:
![PV=C*[\frac{1-(1+i)^{-n}}{i}]*(1+i)](https://tex.z-dn.net/?f=PV%3DC%2A%5B%5Cfrac%7B1-%281%2Bi%29%5E%7B-n%7D%7D%7Bi%7D%5D%2A%281%2Bi%29)
For your case:
C = $3000
i = 12% / 100 = 0.12
n = 3 * 2 = 6 (semiannually for 3 years means 6 payments)
So, the solution is:
![PV=3000*[\frac{1-(1+0.12)^{-6}}{0.12}]*(1+0.12)=3000*[\frac{1-0.5066}{0.12}]*1.12=](https://tex.z-dn.net/?f=PV%3D3000%2A%5B%5Cfrac%7B1-%281%2B0.12%29%5E%7B-6%7D%7D%7B0.12%7D%5D%2A%281%2B0.12%29%3D3000%2A%5B%5Cfrac%7B1-0.5066%7D%7B0.12%7D%5D%2A1.12%3D)
![=3000*[\frac{1-0.5066}{0.12}]*1.12=3000*4.1114*1.12=13814.32](https://tex.z-dn.net/?f=%3D3000%2A%5B%5Cfrac%7B1-0.5066%7D%7B0.12%7D%5D%2A1.12%3D3000%2A4.1114%2A1.12%3D13814.32)
For your case:
C = $3000
i = 12% / 100 = 0.12
n = 3 * 2 = 6 (semiannually for 3 years means 6 payments)
So, the solution is:
If something isn't clear or you're still confused about, let me know in the comments.
Step-by-step explanation:
Okay, here's my best try.
Suppose you have a bill for $8.45
If you are asked to add, say, 8% tax, you must calculate 8 percent of 8.45 and then add it to 8.45.
Begin by converting 8% to decimals by dividing by 100.
8% is 0.08 in decimal form.
To calculate a percentage of a number, you multiply the decimal percent by the number; example:
8.45 is being multiplied by 0.08. The result is: 0.676. (this is the tax; however you have to round up to two decimal places: $0.68)
After finding the tax amount, if you are asked to add it to the bill, you have to add it to the original bill; in this case, $8.45
This would be: 0.68+8.45=9.13.
Therefore, the total bill after tax is for $9.13
----------------------------------------------------------------------------------------------------
With tips is the same thing, however, you can have 2 situations.
Situation 1: You are asked to calculate 15% tip of total bill.
In this situation, you can do the same we do to calculate tax.
Convert the percentage to decimal by dividing by 100.
and multiply it by the original bill.
. Rounding up, this would be $1.27 for tip.
If you were to add it to the original bill, simply sum.
The total bill after tips is for $9.72
Situation 2: You are asked to calculate 15% tip of the total bill with a tax of 8% included.
In this situation, you must first calculate the total bill with the tax added, like we did above; we got a bill for $9.13 (Tax included)
Then you can calculate 15% tip of this new bill that has tax included.
Convert
Multiply by the new bill (because this is the one that includes tax)
Round up.... $1.37 for tips.
If you are asked to give a total amount of money including tax and tips, add this to the bill.
9.13+1.37=10.50
This bill would be for $10.50