Answer:
$13,054.13
Step-by-step explanation:
You are going to want to use the continuous compound interest formula, which is shown below.
![A = Pe^{rt}](https://tex.z-dn.net/?f=A%20%3D%20Pe%5E%7Brt%7D)
<em>A = total</em>
<em>P = principal amount</em>
<em>r = interest rate (decimal)</em>
<em>t = time (years)</em>
<em />
First, lets change 7.25% into a decimal:
7.25% ->
-> 0.0725
Now, plug the values into the equation:
![A=4,400e^{0.0725(15)}](https://tex.z-dn.net/?f=A%3D4%2C400e%5E%7B0.0725%2815%29%7D)
![A=13,054.13](https://tex.z-dn.net/?f=A%3D13%2C054.13)
Your balance will be $13,054.13
Answer:
Proved
Step-by-step explanation:
Solving (a):
Let the numbers be: ![x, x + 1, x + 2.](https://tex.z-dn.net/?f=x%2C%20x%20%2B%201%2C%20x%20%2B%202.)
Their sum is:
![Sum = x + x + 1 + x + 2](https://tex.z-dn.net/?f=Sum%20%3D%20x%20%2B%20x%20%2B%201%20%2B%20x%20%2B%202)
Collect Like Terms
![Sum = x + x + x + 1 + 2](https://tex.z-dn.net/?f=Sum%20%3D%20x%20%2B%20x%20%2B%20x%20%2B%201%20%2B%202)
![Sum = 3x + 3](https://tex.z-dn.net/?f=Sum%20%3D%203x%20%2B%203)
Divide sum by 3.
![Result = \frac{Sum}{3}](https://tex.z-dn.net/?f=Result%20%3D%20%5Cfrac%7BSum%7D%7B3%7D)
![Result = \frac{3x+3}{3}](https://tex.z-dn.net/?f=Result%20%3D%20%5Cfrac%7B3x%2B3%7D%7B3%7D)
![Result = \frac{3(x+1)}{3}](https://tex.z-dn.net/?f=Result%20%3D%20%5Cfrac%7B3%28x%2B1%29%7D%7B3%7D)
![Result = x + 1](https://tex.z-dn.net/?f=Result%20%3D%20x%20%2B%201)
<em>Hence, this is true because there is no fractional part after the division</em>
<em></em>
Solving (b):
Let the numbers be: ![x, x + 1, x + 2,x+3,x+4](https://tex.z-dn.net/?f=x%2C%20x%20%2B%201%2C%20x%20%2B%202%2Cx%2B3%2Cx%2B4)
Their sum is:
![Sum = x + x + 1 + x + 2+x + 3 + x + 4](https://tex.z-dn.net/?f=Sum%20%3D%20x%20%2B%20x%20%2B%201%20%2B%20x%20%2B%202%2Bx%20%2B%203%20%2B%20x%20%2B%204)
Collect Like Terms
![Sum = x + x + x + x + x+1 + 2 + 3 + 4](https://tex.z-dn.net/?f=Sum%20%3D%20x%20%2B%20x%20%2B%20x%20%2B%20x%20%2B%20x%2B1%20%20%2B%202%20%2B%203%20%2B%204)
![Sum = 5x+10](https://tex.z-dn.net/?f=Sum%20%3D%205x%2B10)
Divide sum by 5.
![Result = \frac{5x + 10}{5}](https://tex.z-dn.net/?f=Result%20%3D%20%5Cfrac%7B5x%20%2B%2010%7D%7B5%7D)
![Result = \frac{5(x + 2)}{5}](https://tex.z-dn.net/?f=Result%20%3D%20%5Cfrac%7B5%28x%20%2B%202%29%7D%7B5%7D)
![Result = x + 2](https://tex.z-dn.net/?f=Result%20%3D%20x%20%2B%202)
<em>Hence, this is true because there is no fractional part after the division</em>
<em></em>
Solving (c):
Let the numbers be: ![x, x + 1, x + 2,x+3](https://tex.z-dn.net/?f=x%2C%20x%20%2B%201%2C%20x%20%2B%202%2Cx%2B3)
Their sum is:
![Sum = x + x + 1 + x + 2+x + 3](https://tex.z-dn.net/?f=Sum%20%3D%20x%20%2B%20x%20%2B%201%20%2B%20x%20%2B%202%2Bx%20%2B%203)
Collect Like Terms
![Sum = x + x + x + x + 1 + 2 + 3](https://tex.z-dn.net/?f=Sum%20%3D%20x%20%2B%20x%20%2B%20x%20%2B%20x%20%2B%201%20%20%2B%202%20%2B%203)
![Sum = 4x+6](https://tex.z-dn.net/?f=Sum%20%3D%204x%2B6)
Divide sum by 4.
![Result = \frac{4x + 6}{4}](https://tex.z-dn.net/?f=Result%20%3D%20%5Cfrac%7B4x%20%2B%206%7D%7B4%7D)
Split
![Result = \frac{4x}{4} + \frac{6}{4}](https://tex.z-dn.net/?f=Result%20%3D%20%5Cfrac%7B4x%7D%7B4%7D%20%2B%20%5Cfrac%7B6%7D%7B4%7D)
![Result = x + 1.5](https://tex.z-dn.net/?f=Result%20%3D%20x%20%2B%201.5)
<em>The 1.5 means that the sum can not be divisible by 4</em>
I think its 140140 divided by 66 ....i think so
It is A, the Child is equally likely to choose a Red or a stripped ball.
So first let's find ∠BCE: (Assume that the line ABCD is a straight line)
The angle on a line is 180°.
So ∠BCE = 180° - 64° - 90° = 26°
Now, let's find ∠EBC:
∠EBC = 180° - 3x.
The sum of the angles in a triangle is also 180°. So if you add up the angles in the triangle, you should get 180°.
∠BCE + ∠EBC + ∠BEC = 180°
26° + (180° - 3x) + x = 180°
Now, combine like terms:
206° - 2x = 180°
Subtract both sides by 206°.
-2x = -26
Divide both sides by -2 and you'll get:
x = 13°.