Answer:
The amount of money that should be invested at the rate of 5.25% is $12,000 and the amount money that should be invested at the rate of 4% is $13,000
Step-by-step explanation:
we know that
The simple interest formula is equal to
where
I is the Final Interest Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
Let
x ------> the amount of money that should be invested at the rate of 5.25%
25,000-x -----> the amount money that should be invested at the rate of 4%
in this problem we have
substitute in the formula above
Solve for x
therefore
The amount of money that should be invested at the rate of 5.25% is $12,000 and the amount money that should be invested at the rate of 4% is $13,000
<span>PQR is a triangle
QR = x </span>⇒ x>0
If x>0 then:
QR is the smallest side
PQ is the largest side
<span>In the triangle, the largest angle lies opposite the largest side.
</span>The angles of Δ<span>PQR in order from largest to smallest:
</span>∠R is largest [opposite to PQ]
∠Q is middle [opposite to RP]
∠P is smallest [opposite to QR]
Surface Area of Cylinder = 2πrh.
Radius, r = 7 cm, height = 12 cm.
Surface Area = 2*π*7* 12 = 168π cm²
π ≈ 3.14159
168π = 168*3.14159
Surface Area ≈ 527.79 cm²
Answer:
0.57 yr
Step-by-step explanation:
To find the doubling time with continuous compounding, we should look at the formula:
FV = future value, and
PV = present value
If FV is twice the PV, we can calculate the doubling time, t
1. David's doubling time
2. Violet's doubling time
The formula for interest compounded periodically is
where
n = the number of payments per year
3. David's doubling time vs Violet's
11.317 - 10.750 = 0.57 yr
It would take 0.57 yr longer for David's money to double than Violet's.
Answer:
Option A.
Step-by-step explanation:
The given expression is
![\dfrac{\sqrt[7]{x^2}}{\sqrt[5]{y^3}}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%5B7%5D%7Bx%5E2%7D%7D%7B%5Csqrt%5B5%5D%7By%5E3%7D%7D)
where, 
.
We need to find the expression which is equivalent to the given expression.
The given expression can be rewritten as
![[\because \sqrt[n]{x}=x^{\frac{1}{n}}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Csqrt%5Bn%5D%7Bx%7D%3Dx%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D%5D)
![[\because (a^m)^n=a^{mn}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%28a%5Em%29%5En%3Da%5E%7Bmn%7D%5D)
![[\because a^{-n}=\dfrac{1}{a^n}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20a%5E%7B-n%7D%3D%5Cdfrac%7B1%7D%7Ba%5En%7D%5D)
Therefore, the correct option is A.
