Answer: 7.58 years
Step-by-step explanation:
When it comes to finding out how long it will take for an investment to double, one can use the Rule of 72.
The Rule of 72 estimates the amount of time it will take to double an investment when you divide 72 by the interest rate:
= 72 / r
= 72 / 9.5
= 7.58 years
Answer:
The number of trees at the begging of the 4-year period was 2560.
Step-by-step explanation:
Let’s say that x is number of trees at the begging of the first year, we know that for four years the number of trees were incised by 1/4 of the number of trees of the preceding year, so at the end of the first year the number of trees was
, and for the next three years we have that
Start End
Second year
-------------- ![\frac{5}{4}x+\frac{1}{4}(\frac{5}{4}x) =\frac{5}{4}x+ \frac{5}{16}x=\frac{25}{16}x=(\frac{5}{4} )^{2}x](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B4%7Dx%2B%5Cfrac%7B1%7D%7B4%7D%28%5Cfrac%7B5%7D%7B4%7Dx%29%20%3D%5Cfrac%7B5%7D%7B4%7Dx%2B%20%5Cfrac%7B5%7D%7B16%7Dx%3D%5Cfrac%7B25%7D%7B16%7Dx%3D%28%5Cfrac%7B5%7D%7B4%7D%20%29%5E%7B2%7Dx)
Third year
-------------![(\frac{5}{4})^{2}x+\frac{1}{4}((\frac{5}{4})^{2}x) =(\frac{5}{4})^{2}x+\frac{5^{2} }{4^{3} } x=(\frac{5}{4})^{3}x](https://tex.z-dn.net/?f=%28%5Cfrac%7B5%7D%7B4%7D%29%5E%7B2%7Dx%2B%5Cfrac%7B1%7D%7B4%7D%28%28%5Cfrac%7B5%7D%7B4%7D%29%5E%7B2%7Dx%29%20%3D%28%5Cfrac%7B5%7D%7B4%7D%29%5E%7B2%7Dx%2B%5Cfrac%7B5%5E%7B2%7D%20%7D%7B4%5E%7B3%7D%20%7D%20x%3D%28%5Cfrac%7B5%7D%7B4%7D%29%5E%7B3%7Dx)
Fourth year
--------------![(\frac{5}{4})^{3}x+\frac{1}{4}((\frac{5}{4})^{3}x) =(\frac{5}{4})^{3}x+\frac{5^{3} }{4^{4} } x=(\frac{5}{4})^{4}x.](https://tex.z-dn.net/?f=%28%5Cfrac%7B5%7D%7B4%7D%29%5E%7B3%7Dx%2B%5Cfrac%7B1%7D%7B4%7D%28%28%5Cfrac%7B5%7D%7B4%7D%29%5E%7B3%7Dx%29%20%3D%28%5Cfrac%7B5%7D%7B4%7D%29%5E%7B3%7Dx%2B%5Cfrac%7B5%5E%7B3%7D%20%7D%7B4%5E%7B4%7D%20%7D%20x%3D%28%5Cfrac%7B5%7D%7B4%7D%29%5E%7B4%7Dx.)
So the formula to calculate the number of trees in the fourth year is
we know that all of the trees thrived and there were 6250 at the end of 4 year period, then
⇒![x=\frac{6250*4^{4} }{5^{4} }= \frac{10*5^{4}*4^{4} }{5^{4} }=2560.](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B6250%2A4%5E%7B4%7D%20%7D%7B5%5E%7B4%7D%20%7D%3D%20%5Cfrac%7B10%2A5%5E%7B4%7D%2A4%5E%7B4%7D%20%7D%7B5%5E%7B4%7D%20%7D%3D2560.)
Therefore the number of trees at the begging of the 4-year period was 2560.
Answer: The numbers are 14, 16 and 18.
Step-by-step explanation: First thing to note is that consecutive even numbers have a difference of 2 units between every two terms. That is, if the first number is a, the next would be a + 2, and the next would be a + 4, and so on.
Therefore the three consecutive even numbers shall be a, a + 2, and a + 4.
Our equation now becomes;
a + a + 2 + a + 4 = 48
3a + 6 = 48
Subtract 6 from both sides of the equation
3a = 42
Divide both sides of the equation by 3
a = 14
Therefore, the numbers are 14, 16 and 18.
The group of tiles represent answer A. There are 6 x² tiles, 3 x tiles, and 1 tile.
Answer:
Step-by-step explanation:
You already highlighted the term coordinate ratio in purple.