Answer: 30
Step-by-step explanation:
Let the principal be 'x' then the Amount will be 4x.
As the interest is compounded monthly:
Rate of interest = 10.1 % = 10.1/(100*12) = 0.101/12
Time = 12t
Amount = Principal[1 + Rate/100]
⇒ 4x = x[1 + 0.101/12]¹²t
⇒ 4x/x [1 + 0.008416667]¹²t
⇒ 4 = [1.008416667]¹²t
⇒ log(4) = log[1.008416667]¹²t
⇒ 0.602059991327 = [0.003640014891]¹²t
⇒ 12t = 0.602059991327/0.003640014891
⇒ 12t = 165.400419876
⇒ t = 165.400419876/12
t = 13.78 years or 13 years 9 months.
So, it is about 13 years 9 months she will have 4 times the amount of money.
Answer:
Step-by-step explanation:
I am assuming that by "interior" angle you do not mean the central angle.
This is a 10-sided polygon, a decagon. That means that there are 10 triangles that can extend from the center, with their sides being equal to the radii of the decagon. If we extract one of these triangles we can find what the interior angle is. The vertex angle measures 360/10 which is 36.
Split this triangle in half from the vertex to the base, creating a right triangle. The vertex angle is also split in half, making this angle (the vertex angle is the one at the top of the triangle) 18 degrees. We already know that one angle inside this right triangle is 90 (definition of a right triangle) and to find the other one, we apply the Triangle Angle-Sum Theorem:
180 - 18 - 90 = 72 degrees. That is the measure of the base angle that is NOT the right angle, obviously.
Step-by-step explanation:
756 = 2² * 3³ * 7.
For 756n to be a perfect cube, all of its prime factors must have a power that is a multiple of 3.
How to get from 2² to 2³: Multiply by 2.
3³ has already a power that is a multiple of 3.
How to get from 7 to 7³: Multiply by 7².
Hence n = 2 * 7² = 98.
The answer is the second image from left to right (B). Examples of direct and inverse variations are showed in the image below. :)
