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2 years ago

What is greater, 2/5, 3/10, 1/2, or 1/10?

Mathematics

2 answers:

Pani-rosa [81]2 years ago

7 0

2/5 = 40%
3/10= 30%
1/2= 50%
1/10= 10%

so it's 1/2

Otrada [13]2 years ago

6 0

1/2 is the greatest. 1/2 equals 50%. 1/10 equals 10%, 3/10 equals 30%, and 2/5 equals 40%.

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3 years ago

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2 years ago

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2 years ago

What is the inverse of the function f(x) = 2x + 1?

soldier1979 [14.2K]

Answer: The inverse of the linear function f(x)=2x+1 is f^(-1) (x) = (1/2)x-1/2

Solution

f(x)=2x+1

y=f(x)

y=2x+1

Isolating x: Subtracting 1 both sides of the equation:

y-1=2x+1-1

y-1=2x

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(1/2)(y-1)=(1/2)2x

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2 years ago

A source of information randomly generates symbols from a four letter alphabet {w, x, y, z }. The probability of each symbol is

koban [17]

The expected length of code for one encoded symbol is

$\displaystyle\sum_{\alpha\in\{w,x,y,z\}}p_\alpha\ell_\alpha$

where $p_\alpha$ is the probability of picking the letter $\alpha$ , and $\ell_\alpha$ is the length of code needed to encode $\alpha$ . $p_\alpha$ is given to us, and we have

$\begin{cases}\ell_w=1\\\ell_x=2\\\ell_y=\ell_z=3\end{cases}$

so that we expect a contribution of

$\dfrac12+\dfrac24+\dfrac{2\cdot3}8=\dfrac{11}8=1.375$

bits to the code per encoded letter. For a string of length $n$ , we would then expect $E[L]=1.375n$ .

By definition of variance, we have

$\mathrm{Var}[L]=E\left[(L-E[L])^2\right]=E[L^2]-E[L]^2$

For a string consisting of one letter, we have

$\displaystyle\sum_{\alpha\in\{w,x,y,z\}}p_\alpha{\ell_\alpha}^2=\dfrac12+\dfrac{2^2}4+\dfrac{2\cdot3^2}8=\dfrac{15}4$

so that the variance for the length such a string is

$\dfrac{15}4-\left(\dfrac{11}8\right)^2=\dfrac{119}{64}\approx1.859$

"squared" bits per encoded letter. For a string of length $n$ , we would get $\mathrm{Var}[L]=1.859n$ .

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2 years ago