<span>(12xy)^2
Expand:
12^2*x^2*y^2
= 144x^2*y^2</span>
Answer:
![Mean = 100](https://tex.z-dn.net/?f=Mean%20%3D%20100)
![Median = 96](https://tex.z-dn.net/?f=Median%20%3D%2096)
Step-by-step explanation:
Given
--- coefficient of variation
![mode = 88](https://tex.z-dn.net/?f=mode%20%3D%2088)
![Skp = 0.4](https://tex.z-dn.net/?f=Skp%20%3D%200.4)
Required
The mean and the median
The coefficient of variation is calculated using:
![C_v = \frac{\sigma}{\mu}](https://tex.z-dn.net/?f=C_v%20%3D%20%5Cfrac%7B%5Csigma%7D%7B%5Cmu%7D)
Where:
mean
So:
![30\% = \frac{\sigma}{\mu}](https://tex.z-dn.net/?f=30%5C%25%20%3D%20%5Cfrac%7B%5Csigma%7D%7B%5Cmu%7D)
Express percentage as decimal
![0.30 = \frac{\sigma}{\mu}](https://tex.z-dn.net/?f=0.30%20%3D%20%5Cfrac%7B%5Csigma%7D%7B%5Cmu%7D)
Make
the subject
![\sigma = 0.30\mu](https://tex.z-dn.net/?f=%5Csigma%20%3D%200.30%5Cmu)
The coefficient of skewness is calculated using:
![Skp = \frac{\mu - Mode}{\sigma}](https://tex.z-dn.net/?f=Skp%20%3D%20%5Cfrac%7B%5Cmu%20-%20Mode%7D%7B%5Csigma%7D)
This gives:
![0.4 = \frac{\mu - 88}{\sigma}](https://tex.z-dn.net/?f=0.4%20%3D%20%5Cfrac%7B%5Cmu%20-%2088%7D%7B%5Csigma%7D)
Make
the subject
![\sigma = \frac{\mu - 88}{0.4 }](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Cfrac%7B%5Cmu%20-%2088%7D%7B0.4%20%7D)
Equate both expressions for
![0.30\mu = \frac{\mu - 88}{0.4 }](https://tex.z-dn.net/?f=0.30%5Cmu%20%3D%20%5Cfrac%7B%5Cmu%20-%2088%7D%7B0.4%20%7D)
Cross multiply
![0.4*0.30\mu = \mu - 88](https://tex.z-dn.net/?f=0.4%2A0.30%5Cmu%20%3D%20%5Cmu%20-%2088)
![0.12\mu = \mu - 88](https://tex.z-dn.net/?f=0.12%5Cmu%20%3D%20%5Cmu%20-%2088)
Collect like terms
![0.12\mu - \mu = - 88](https://tex.z-dn.net/?f=0.12%5Cmu%20-%20%5Cmu%20%3D%20%20-%2088)
![-0.88\mu = - 88](https://tex.z-dn.net/?f=-0.88%5Cmu%20%3D%20%20-%2088)
Divide both sides by -0.88
![\mu = 100](https://tex.z-dn.net/?f=%5Cmu%20%3D%20%20100)
Hence:
![Mean = 100](https://tex.z-dn.net/?f=Mean%20%3D%20100)
Calculate
![\sigma = 0.30\mu](https://tex.z-dn.net/?f=%5Csigma%20%3D%200.30%5Cmu)
![\sigma = 0.30 * 100](https://tex.z-dn.net/?f=%5Csigma%20%3D%200.30%20%2A%20100)
![\sigma = 30](https://tex.z-dn.net/?f=%5Csigma%20%3D%2030)
So:
Also, the coefficient of skewness is calculated using:
![Skp = \frac{3 * (Mean - Median)}{\sigma}](https://tex.z-dn.net/?f=Skp%20%3D%20%5Cfrac%7B3%20%2A%20%28Mean%20-%20Median%29%7D%7B%5Csigma%7D)
![0.4= \frac{3 * (100 - Median)}{30}](https://tex.z-dn.net/?f=0.4%3D%20%5Cfrac%7B3%20%2A%20%28100%20-%20Median%29%7D%7B30%7D)
Multiply both sides by 30
![0.4*30= 3 * (100 - Median)](https://tex.z-dn.net/?f=0.4%2A30%3D%203%20%2A%20%28100%20-%20Median%29)
Divide both sides by 3
![0.4*10= 100 - Median](https://tex.z-dn.net/?f=0.4%2A10%3D%20100%20-%20Median)
![4= 100 - Median](https://tex.z-dn.net/?f=4%3D%20100%20-%20Median)
Collect like terms
![Median = 100 - 4](https://tex.z-dn.net/?f=Median%20%3D%20100%20-%204)
![Median = 96](https://tex.z-dn.net/?f=Median%20%3D%2096)
Answer:
Center:(-6,-4)
Circumference:45.31
Area:163.4
Step-by-step explanation:
The given circle has diameter with endpoints P(-12,-8) and Q(0,0).
The center is the midpoint of P(-12,-8) and Q(0,0).
We use the midpoint rule to find the center.
![( \frac{x_2+x_1}{2}, \frac{y_2+y_1}{2} )](https://tex.z-dn.net/?f=%28%20%5Cfrac%7Bx_2%2Bx_1%7D%7B2%7D%2C%20%5Cfrac%7By_2%2By_1%7D%7B2%7D%20%29)
![( \frac{ - 12 + 0}{2} , \frac{ - 8 + 0}{2} ) = ( - 6, - 4)](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B%20-%2012%20%2B%200%7D%7B2%7D%20%2C%20%5Cfrac%7B%20-%208%20%2B%200%7D%7B2%7D%20%29%20%3D%20%28%20-%206%2C%20-%204%29)
Use the distance formula to find radius using the center (-6,-4) and the point on the circle (0,0) or (-12,-8).
![d = \sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}](https://tex.z-dn.net/?f=d%20%3D%20%20%5Csqrt%7B%28x_2-x_1%29%5E2%20%2B%28y_2-y_1%29%5E2%7D%20)
![r = \sqrt{( { - 6 - 0)}^{2} + ( { - 4 - 0)}^{2} }](https://tex.z-dn.net/?f=r%20%3D%20%20%5Csqrt%7B%28%20%7B%20-%206%20-%200%29%7D%5E%7B2%7D%20%20%2B%20%28%20%7B%20-%204%20-%200%29%7D%5E%7B2%7D%20%7D%20)
![r = \sqrt{36 + 16} = \sqrt{52}](https://tex.z-dn.net/?f=r%20%3D%20%20%5Csqrt%7B36%20%2B%2016%7D%20%20%3D%20%20%5Csqrt%7B52%7D%20)
The circumference is
![C=2\pi \: r](https://tex.z-dn.net/?f=C%3D2%5Cpi%20%5C%3A%20r)
![C=2 \: \pi \: \times \sqrt{52}](https://tex.z-dn.net/?f=C%3D2%20%5C%3A%20%5Cpi%20%5C%3A%20%20%20%5Ctimes%20%5Csqrt%7B52%7D%20)
![C=45.31 \: units](https://tex.z-dn.net/?f=C%3D45.31%20%5C%3A%20units)
The area is given by:
![A=\pi {r}^{2}](https://tex.z-dn.net/?f=A%3D%5Cpi%20%7Br%7D%5E%7B2%7D%20)
![A=\pi \times {( \sqrt{52} )}^{2}](https://tex.z-dn.net/?f=A%3D%5Cpi%20%5Ctimes%20%20%7B%28%20%5Csqrt%7B52%7D%20%29%7D%5E%7B2%7D%20)
![A=163.4 \: \: {units}^{2}](https://tex.z-dn.net/?f=A%3D163.4%20%5C%3A%20%20%5C%3A%20%20%7Bunits%7D%5E%7B2%7D%20)
<span><span>"y=f(x)</span><span>y=f(x)</span></span>
<span><span>y=2f(x)</span><span>y=2f(x)
</span></span>
vertical stretch;
<span>yy</span>-values are doubled;
points get farther away
<span>from </span><span>xx</span><span>-axis"
</span>
Answer:
0.00305 (rounded)
Step-by-step explanation:
this is a geometric sequence so the formula is
an=a×r×n-1