1 DOC
2 BOC
3 EOC
4 AOD
5 AOC
Answer:
Maureen earned $123.19 doing odd jobs
Step-by-step explanation:
The compound interest formula is given by:
![A(t) = P(1 + \frac{r}{n})^{nt}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20P%281%20%2B%20%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.
In this question:
Compounded quarterly means that ![n = 4](https://tex.z-dn.net/?f=n%20%3D%204)
10 years, so ![t = 10](https://tex.z-dn.net/?f=t%20%3D%2010)
9% interest, so ![r = 0.09](https://tex.z-dn.net/?f=r%20%3D%200.09)
There is $300.00 in the account, which means that ![A = 300](https://tex.z-dn.net/?f=A%20%3D%20300)
How much did Maureen earn doing odd jobs?
This is P.
![A(t) = P(1 + \frac{r}{n})^{nt}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20P%281%20%2B%20%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
![300 = P(1 + \frac{0.09}{4})^{4*10}](https://tex.z-dn.net/?f=300%20%3D%20P%281%20%2B%20%5Cfrac%7B0.09%7D%7B4%7D%29%5E%7B4%2A10%7D)
![(1.0225)^{40}P = 300](https://tex.z-dn.net/?f=%281.0225%29%5E%7B40%7DP%20%3D%20300)
![P = \frac{300}{(1.0225)^{40}}](https://tex.z-dn.net/?f=P%20%3D%20%5Cfrac%7B300%7D%7B%281.0225%29%5E%7B40%7D%7D)
![P = 123.19](https://tex.z-dn.net/?f=P%20%3D%20123.19)
Maureen earned $123.19 doing odd jobs
The radius of the donut is 3.14
Answer: x = 10
Step-by-step explanation:
The sum of all interior angles in a polygon add up to 360°
Meaning to find X we grab those numbers/variables and make them equal to 360°. This will give us an equation.
106 + 94 + 135 + x + ( x + 5 ) = 360
335 + x + x + 5 = 360
340 + 2x = 360
subtract 340 from both sides
2x = 20
Divide by 2
x = 10
Now solve the angle equations to find their angle.
( 10 + 5 ) = 15
x = 10
Now to check if it's right add them together
106 + 94 + 15 + 10 + 135 = 360 ( ITS CORRECT )
Step-by-step explanation:
cos θ - sin θ = √2 sin θ
cos θ + sin θ = √2 sin θ + 2sin θ
cos θ + sin θ = √2(sin θ + √2sin θ)
cos θ + sin θ = √2 cos θ. (Proven)