Answer:
17.5% per annum
Step-by-step explanation:
<u>Given:</u>
Money invested = $20,000 at the age of 20 years.
Money expected to be $500,000 at the age of 40.
Time = 40 - 20 = 20 years
<em>Interest is compounded annually.</em>
<u>To find:</u>
Rate of growth = ?
<u>Solution:</u>
First of all, let us have a look at the formula for compound interest.

Where A is the amount after T years compounding at a rate of R% per annum. P is the principal amount.
Here, We are given:
P = $20,000
A = $500,000
T = 20 years
R = ?
Putting all the values in the formula:
![500000 = 20000 \times (1+\frac{R}{100})^{20}\\\Rightarrow \dfrac{500000}{20000} =(1+\frac{R}{100})^{20}\\\Rightarrow 25 =(1+\frac{R}{100})^{20}\\\Rightarrow \sqrt[20]{25} =1+\frac{R}{100}\\\Rightarrow 1.175 = 1+0.01R\\\Rightarrow R \approx17.5\%](https://tex.z-dn.net/?f=500000%20%3D%2020000%20%5Ctimes%20%281%2B%5Cfrac%7BR%7D%7B100%7D%29%5E%7B20%7D%5C%5C%5CRightarrow%20%5Cdfrac%7B500000%7D%7B20000%7D%20%3D%281%2B%5Cfrac%7BR%7D%7B100%7D%29%5E%7B20%7D%5C%5C%5CRightarrow%2025%20%3D%281%2B%5Cfrac%7BR%7D%7B100%7D%29%5E%7B20%7D%5C%5C%5CRightarrow%20%5Csqrt%5B20%5D%7B25%7D%20%3D1%2B%5Cfrac%7BR%7D%7B100%7D%5C%5C%5CRightarrow%201.175%20%3D%201%2B0.01R%5C%5C%5CRightarrow%20R%20%5Capprox17.5%5C%25)
So, the correct answer is
<em>17.5% </em>per annum and compounding annually.
Answer:
(-3,-8)
Step-by-step explanation:
okay so what we can do here is elimination
we can do this first by multiplying the entire second equation by 2
so then it would become
2(5x-2y=1)
10x-4y=2
now we can add the two equations together which will eliminate y
so
-8x+4y=-8 plus
10x-4y=2 equals
2x=-6
we did that by combining like terms
next we can simplify that
x=-3
now we can plug that into the equation
-8(-3)+4y=-8
simplify
24+4y=-8
4y=-32
y=-8
our answer would be
(-3,-8)
Answer:


![Interval = [666.78, 781.62]](https://tex.z-dn.net/?f=Interval%20%3D%20%5B666.78%2C%20781.62%5D)
Step-by-step explanation:
Given
The data for 25 undergraduates
Solving (a): Range and Standard deviation
The range is:

From the dataset:


So:



The standard deviation is:

First, calculate the mean



So, the standard deviation is:




Solving (b): The interval of the 95% of the observation.
Using the emperical rule, we have:
![Interval = [\bar x - 2*\sigma, \bar x+ 2*\sigma]](https://tex.z-dn.net/?f=Interval%20%3D%20%5B%5Cbar%20x%20-%202%2A%5Csigma%2C%20%5Cbar%20x%2B%202%2A%5Csigma%5D)
![Interval = [724.2 - 2*28.71, 724.2 + 2*28.71]](https://tex.z-dn.net/?f=Interval%20%3D%20%5B724.2%20-%202%2A28.71%2C%20724.2%20%2B%202%2A28.71%5D)
![Interval = [666.78, 781.62]](https://tex.z-dn.net/?f=Interval%20%3D%20%5B666.78%2C%20781.62%5D)
Consider that long row as 1 big rectangle with base 6+11+6+11=34 and height of 8
area=34*8=272 ft^2
the 2 rectangles on side
the sbase is 11
the height is 6 since it has to match with the other 2 side things
2*6*11=132
add to find total
132+272=404 ft^2