Answer:
5
Step-by-step explanation:
yes i think because i think so
Answer:
20.4 years (nearest tenth)
Step-by-step explanation:
<u>Compound Interest Formula</u>
![\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}](https://tex.z-dn.net/?f=%5Clarge%20%5Ctext%7B%24%20%5Csf%20A%3DP%5Cleft%281%2B%5Cfrac%7Br%7D%7Bn%7D%5Cright%29%5E%7Bnt%7D%20%24%7D)
where:
- A = final amount
- P = principal amount
- r = interest rate (in decimal form)
- n = number of times interest applied per time period
- t = number of time periods elapsed
Given:
- A = $15,000
- P = $6,000
- r = 4.5% = 0.045
- n = 12 (monthly)
Substitute the given values into the formula and solve for t:
![\implies \sf 15000=6000\left(1+\frac{0.045}{12}\right)^{12t}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%2015000%3D6000%5Cleft%281%2B%5Cfrac%7B0.045%7D%7B12%7D%5Cright%29%5E%7B12t%7D)
![\implies \sf \dfrac{15000}{6000}=\left(1.00375\right)^{12t}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%20%5Cdfrac%7B15000%7D%7B6000%7D%3D%5Cleft%281.00375%5Cright%29%5E%7B12t%7D)
![\implies \sf 2.5=\left(1.00375\right)^{12t}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%202.5%3D%5Cleft%281.00375%5Cright%29%5E%7B12t%7D)
![\implies \sf \ln (2.5)=\ln \left(1.00375\right)^{12t}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%20%5Cln%20%282.5%29%3D%5Cln%20%5Cleft%281.00375%5Cright%29%5E%7B12t%7D)
![\implies \sf \ln (2.5)=12t \ln \left(1.00375\right)](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%20%5Cln%20%282.5%29%3D12t%20%5Cln%20%5Cleft%281.00375%5Cright%29)
![\implies \sf t=\dfrac{\ln (2.5)}{12 \ln (1.00375)}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%20t%3D%5Cdfrac%7B%5Cln%20%282.5%29%7D%7B12%20%5Cln%20%281.00375%29%7D)
![\implies \sf t=20.40017123](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%20t%3D20.40017123)
Therefore, it would take 20.4 years (nearest tenth) for the investment to reach $15,000.
Answer:
x = 32
Step-by-step explanation:
Add 7 to both sides
Simplify
-7 + 7 = 0 and 1 + 7 = 8 because of this now ![\sqrt{2x} =8](https://tex.z-dn.net/?f=%5Csqrt%7B2x%7D%20%3D8)
Square both sides
2x = 64
Slove 2x = 64
64 ÷ 2 = 32 = x
Answer: 1
Step-by-step explanation:
If f(x) is an odd function, this means that f(x)=-f(-x). So, if 6 points lie in Quadrant I, then this means that 6 points must lie in Quadrant III.
This leaves us with 2 points.
Similarly, we know that for every point in Quadrant II, there must be a corresponding point in Quadrant IV.
This gives us 2/2 = 1 point.