You manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 28%. The T-bill rate is 8%. Your
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Hey there!
In order to solve this problem, we can use the Pythagorean Theorem, which is . Since the Pythagorean Theorem would find only half of the length of x, we'll need to double it in the end.
First, let's plug in what we know to the Pythagorean Theorem:
Next, we'll simplify to that is by itself:
Then, we'll find the square root of 2.45, multiply that by 2 and round to the nearest tenth:
Therefore, x = 3.1 ft.
How to round to the nearest tenth:
In a decimal, the tenth is the first number after the decimal point. To round to the tenth, if the number in the hundredth place is less than 5, you keep the number as it is, but if the number in the hundredth place is more than 5, you increase the number in the tenth place by 1.
Hope this helps!! :)
We have 3⁴ = 81, so we can factorize this as a difference of squares twice:
Depending on the precise definition of "completely" in this context, you can go a bit further and factorize as yet another difference of squares:
And if you're working over the field of complex numbers, you can go even further. For instance,
But I think you'd be fine stopping at the first result,