9514 1404 393
Answer:
0.06164
Step-by-step explanation:
The effective annual rate obtained by compounding nominal annual rate r monthly is ...
eff rate = (1 +r/12)^12 -1
Then the value of r is ...
r = 12×((eff rate) +1)^(1/12) -1)
For the given effective rate, that is ...
r = 12×(1.06341^(1/12) -1) ≈ 0.06164 . . . . nominal annual interest rate
Answer:
The sum of all positive integers less than 100, which are not divisible by 3 is 3267.
Step-by-step explanation:
The all positive integers less than 100 has sum, given by
S₁ = 1 + 2 + 3 + 4 + ......... + 99
⇒ S₁ = 
Now, the sum of all positive integers less than 100 which are divisible by 3 is
S₂ = 3 + 6 + 9 + 12 + 15 + ........ + 99
⇒ S₂ = 3(1 + 2 + 3 + ........ + 33)
⇒ S₂ = 
Therefore, the sum of all positive integers less than 100, which are not divisible by 3 is = S₁ - S₂ = 4950 - 1683 = 3267. (Answer)
Note : The sum of n natural numbers S is given by
S = 1 + 2 + 3 + 4 + ....... + n =
.
3x + 22 is the equation that represents the perimeter of the triangle. 4x + 10 is the perimeter of the rectangle. Setting the two equal:

and collecting like terms:

We find that the perimeter of both shapes is equal to 11 units.