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2 years ago

Step on how to calculate variance

Mathematics

1 answer:

suter [353]2 years ago

4 0

Answer:

Step-by-step explanation:

calculate the mean of your data set(x bar)
Subtract each data value from the mean and calculate the square
add all of these squares
divide by n-1 (For a sample) to get the variance

If you’re calculating the variance of a population(not sample) divide by N.

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Solve the system of equations:<br> y = 3x<br> y=x2-4

Lubov Fominskaja [6]

Answer:

x = -4

y = -12

Step-by-step explanation:

Since y is 3x,

3x = 2x - 4

On solving we get x as -4

Substitute x and we get y as -12

3 0

2 years ago

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If kevin makes c toys in m minutes, how many toys can he make per hour

mina [271]

Answer:

$\frac{60c}{m}$

Step-by-step explanation:

We can use the unity rule to solve this problem.

Number of toys made in m minutes = c

Number of toys made in 1 minute = $\frac{c}{m}$

Number of toys made in 60 minutes = $\frac{c}{m} \times 60 = \frac{60c}{m}$

Since 60 minutes = 1 hours, we can write:

Number of toys made in 1 hour = $\frac{60c}{m}$

Therefore, we can say that Kevin makes $\frac{60c}{m}$ toys per an hour.

7 0

2 years ago

URGENT!!!!!!!!

LuckyWell [14K]

Answer:

x+y=24 so we can say

x=24-y making 3x+5y=100 become

3(24-y)+5y=100

72-3y+5y=100

72+2y=100

2y=28

y=14, since x=24-y

x=10

So there are 10 3-point questions and 14 5-point questions.

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2 years ago

A model airplane is built at a scale of 1 inch to 6 feet. If the model plane is 8 inches long, how many feet long is the actual

noname [10]

The airplane is 48 feet long in real dimensions.

To find out how long the airplane actually is, we can use the scale and input our amount of inches that it is measured by.

So, 1 inch equals to 6 feet.

Our model plane is 8 inches.

Now, we plug it in.

8 inches = 6(8)

8 inches = 48 feet

Therefore, the length of the real airplane is 48 feet.

48 feet

5 0

2 years ago

Read 2 more answers

Find a particular solution to <img src="https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20%20%5Cfrac%7B%20d%5E%7B2%7Dy%20%7D%7Bd%20x%5E%7

Digiron [165]

$y=x^r$
$\implies r(r-1)x^r+6rx^r+4x^r=0$
$\implies r^2+5r+4=(r+1)(r+4)=0$
$\implies r=-1,r=-4$

so the characteristic solution is

$y_c=\dfrac{C_1}x+\dfrac{C_2}{x^4}$

As a guess for the particular solution, let's back up a bit. The reason the choice of $y=x^r$ works for the characteristic solution is that, in the background, we're employing the substitution $t=\ln x$ , so that $y(x)$ is getting replaced with a new function $z(t)$ . Differentiating yields

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac1x\dfrac{\mathrm dz}{\mathrm dt}$
$\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac1{x^2}\left(\dfrac{\mathrm d^2z}{\mathrm dt^2}-\dfrac{\mathrm dz}{\mathrm dt}\right)$

Now the ODE in terms of $t$ is linear with constant coefficients, since the coefficients $x^2$ and $x$ will cancel, resulting in the ODE

$\dfrac{\mathrm d^2z}{\mathrm dt^2}+5\dfrac{\mathrm dz}{\mathrm dt}+4z=e^{2t}\sin e^t$

Of coursesin, the characteristic equation will be $r^2+6r+4=0$ , which leads to solutions $C_1e^{-t}+C_2e^{-4t}=C_1x^{-1}+C_2x^{-4}$ , as before.

Now that we have two linearly independent solutions, we can easily find more via variation of parameters. If $z_1,z_2$ are the solutions to the characteristic equation of the ODE in terms of $z$ , then we can find another of the form $z_p=u_1z_1+u_2z_2$ where

$u_1=-\displaystyle\int\frac{z_2e^{2t}\sin e^t}{W(z_1,z_2)}\,\mathrm dt$
$u_2=\displaystyle\int\frac{z_1e^{2t}\sin e^t}{W(z_1,z_2)}\,\mathrm dt$

where $W(z_1,z_2)$ is the Wronskian of the two characteristic solutions. We have

$u_1=-\displaystyle\int\frac{e^{-2t}\sin e^t}{-3e^{-5t}}\,\mathrm dt$
$u_1=\dfrac23(1-2e^{2t})\cos e^t+\dfrac23e^t\sin e^t$

$u_2=\displaystyle\int\frac{e^t\sin e^t}{-3e^{-5t}}\,\mathrm dt$
$u_2=\dfrac13(120-20e^{2t}+e^{4t})e^t\cos e^t-\dfrac13(120-60e^{2t}+5e^{4t})\sin e^t$

$\implies z_p=u_1z_1+u_2z_2$
$\implies z_p=(40e^{-4t}-6)e^{-t}\cos e^t-(1-20e^{-2t}+40e^{-4t})\sin e^t$

and recalling that $t=\ln x\iff e^t=x$ , we have

$\implies y_p=\left(\dfrac{40}{x^3}-\dfrac6x\right)\cos x-\left(1-\dfrac{20}{x^2}+\dfrac{40}{x^4}\right)\sin x$

4 0

2 years ago

Step on how to calculate variance ​

Step on how to calculate variance