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)
The answer for this problem is D
The equivalent value of the expression is -7
<h3>Modulus of a function</h3>
The modulus of an expression of value is equal to the positive of such function or value.
Given the expression
2(2.5 - |-6|)
Since the value of -6 is a modulus, the expression will become;
2(2.5 - |-6|) = 2(2.5) - 2(6)
2(2.5 - |-6|) = 5 - 12
2(2.5 - |-6|) = -7
Hence the equivalent value of the expression is -7
Learn more on equation here: brainly.com/question/2972832
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Your answer would be the last option, D.
This is because spinning the spinner does not affect which marble you pick, as these are mutually exclusive events. This means that if the spinner lands on red, you could choose a black or white marble, and if the spinner lands on green you could also choose a black or white marble.
The only sample space that represents this is D because it's the only one that includes both black and white options after spinning red and green.
I hope this helps!
The answer is 7 1/3 hope it helps!
