$5,000.00 invested for a period of 6 years doubles to $10,000.00.
What is the interest rate?
You will need to apply logarithms:
<span>log(1 + rate) = {log(total) - log(Principal)} ÷ Years
</span>log(1 + rate) = <span>{log(10,000) - log(5,000)} ÷ 6
</span>log(1 + rate) = (4 - 3.6989700043) / 6
log(1 + rate) =
<span>
<span>
<span>
0.301029957 / 6
</span></span></span>log(1 + rate) =
<span>
<span>
<span>
0.0501716595
</span>
</span>
</span>
Next, raise 10 to the power of
<span>
<span>
<span>
0.0501716595
</span>
</span>
</span>
which results in
<span>
<span>
<span>
1.1224620317
</span>
</span>
</span>
This value represents 1 plus the interest rate, so the interest rate is
0.1224620317 or 12.24620317 percent.
This concludes Part ONE.
Now, onto Part TWO.
How many years does it take for $300 to increase to $9,600 at an annual rate of <span>12.24620317%?
You will use the following formula:
</span>(More logarithms involved).
Years = {log(total) - log(Principal)} ÷ log(1 + rate)
Years = {log(9,600) - log(300)} / log(<span>1.1224620317)
</span>Years = (3.982271233 - 2.4771212547) / 0.050171659518
<span><span><span>Years = 1.5051499783 /
</span>
</span>
</span>.050171659518
Years = 30
Answer:
x = 25
Step-by-step explanation:
Given that ray AP divides angle CAT, it implies that
Also, 
This leads to, 
As stated,
Consequently,
Grouping similar terms together,
Thus, x is 25.
Option (C.) is the right choice!
It's about constructing the perpendicular bisector..!!!
Answer: OPTION B
Step-by-step explanation:
The red graph depicts the fundamental form of a quadratic function (the most basic version), with its vertex located at the origin.
The function g(x) results from moving the parent function 2 units to the right and 1 unit upwards.
As a consequence, considering this, the transformation takes the following structure:
The horizontal displacement is dictated by the value of h, while the vertical shift is determined by k.
<pThus, the resulting function is:
Response:
Thorough analysis:
I believe that option 4 is the right choice
