Answer:
![\huge\boxed{(-5,\ -6)}](https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7B%28-5%2C%5C%20-6%29%7D)
Step-by-step explanation:
![\text{The standard form of an equation of a circle:}\\\\(x-h)^2+(y-k)^2=r^2\\\\(h,\ k)-\text{center}\\r-\text{radius}](https://tex.z-dn.net/?f=%5Ctext%7BThe%20standard%20form%20of%20an%20equation%20of%20a%20circle%3A%7D%5C%5C%5C%5C%28x-h%29%5E2%2B%28y-k%29%5E2%3Dr%5E2%5C%5C%5C%5C%28h%2C%5C%20k%29-%5Ctext%7Bcenter%7D%5C%5Cr-%5Ctext%7Bradius%7D)
![\text{We have}\\\\x^2+y^2+10x+12y+25=0\\\\\text{You can use}\\\\(x-h)^2+(y-k)^2=r^2\\x^2-2hx+h^2+y^2-2ky+k^2=r^2\qquad\text{subtract}\ r^2\ \text{from both sides}\\x^2-2hx+h^2+y^2-2ky+k^2-r^2=0\\x^2+y^2-2xh-2yk+h^2+k^2-r^2=0\\\\\text{Used}\ (a-b)^2=a^2-2ab+b^2](https://tex.z-dn.net/?f=%5Ctext%7BWe%20have%7D%5C%5C%5C%5Cx%5E2%2By%5E2%2B10x%2B12y%2B25%3D0%5C%5C%5C%5C%5Ctext%7BYou%20can%20use%7D%5C%5C%5C%5C%28x-h%29%5E2%2B%28y-k%29%5E2%3Dr%5E2%5C%5Cx%5E2-2hx%2Bh%5E2%2By%5E2-2ky%2Bk%5E2%3Dr%5E2%5Cqquad%5Ctext%7Bsubtract%7D%5C%20r%5E2%5C%20%5Ctext%7Bfrom%20both%20sides%7D%5C%5Cx%5E2-2hx%2Bh%5E2%2By%5E2-2ky%2Bk%5E2-r%5E2%3D0%5C%5Cx%5E2%2By%5E2-2xh-2yk%2Bh%5E2%2Bk%5E2-r%5E2%3D0%5C%5C%5C%5C%5Ctext%7BUsed%7D%5C%20%28a-b%29%5E2%3Da%5E2-2ab%2Bb%5E2)
![\begin{array}{cccccc}x^2&y^2&10x&12y&25\\\downarrow&\downarrow&\downarrow&\downarrow&\downarrow\\x^2&y^2&-2xh&-2yk&h^2+k^2-r^2\end{array}\\\\\text{Therefore}\\\\\begin{array}{ccc}-2xh=10x&-2yk=12y&h^2+k^2-r^2=25\\\boxed{h=-5}&\boxed{k=-6}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bcccccc%7Dx%5E2%26y%5E2%2610x%2612y%2625%5C%5C%5Cdownarrow%26%5Cdownarrow%26%5Cdownarrow%26%5Cdownarrow%26%5Cdownarrow%5C%5Cx%5E2%26y%5E2%26-2xh%26-2yk%26h%5E2%2Bk%5E2-r%5E2%5Cend%7Barray%7D%5C%5C%5C%5C%5Ctext%7BTherefore%7D%5C%5C%5C%5C%5Cbegin%7Barray%7D%7Bccc%7D-2xh%3D10x%26-2yk%3D12y%26h%5E2%2Bk%5E2-r%5E2%3D25%5C%5C%5Cboxed%7Bh%3D-5%7D%26%5Cboxed%7Bk%3D-6%7D%5Cend%7Barray%7D)
![\text{If you want calculate the radius:}\\\text{Substitute}\ h=-5,\ k=-6\ \text{to}\ h^2+k^2-r^2=25\\\\(-5)^2+(-6)^2-r^2=25\\25+36-r^2=25\\61-r^2=25\qquad\text{subtract 61 from both sides}\\-r^2=-36\qquad\text{change the signs}\\r^2=36\to r=\sqrt{36}\to \boxed{r=6}](https://tex.z-dn.net/?f=%5Ctext%7BIf%20you%20want%20calculate%20the%20radius%3A%7D%5C%5C%5Ctext%7BSubstitute%7D%5C%20h%3D-5%2C%5C%20k%3D-6%5C%20%5Ctext%7Bto%7D%5C%20h%5E2%2Bk%5E2-r%5E2%3D25%5C%5C%5C%5C%28-5%29%5E2%2B%28-6%29%5E2-r%5E2%3D25%5C%5C25%2B36-r%5E2%3D25%5C%5C61-r%5E2%3D25%5Cqquad%5Ctext%7Bsubtract%2061%20from%20both%20sides%7D%5C%5C-r%5E2%3D-36%5Cqquad%5Ctext%7Bchange%20the%20signs%7D%5C%5Cr%5E2%3D36%5Cto%20r%3D%5Csqrt%7B36%7D%5Cto%20%5Cboxed%7Br%3D6%7D)
14.54 tons of grapes are needed for 7850 bottles.
Step-by-step explanation:
Given,
4320 bottles of wine = 8 tons of grapes
1 bottle of wine = ![\frac{8}{4320}](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B4320%7D)
1 bottle of wine = ![\frac{1}{540}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B540%7D)
Expected demand = 7850 bottles
7850 bottles = x tons of grapes
![x= 7850*\frac{1}{540}\\x=\frac{7850}{540}\\x=14.54](https://tex.z-dn.net/?f=x%3D%207850%2A%5Cfrac%7B1%7D%7B540%7D%5C%5Cx%3D%5Cfrac%7B7850%7D%7B540%7D%5C%5Cx%3D14.54)
14.54 tons of grapes are needed for 7850 bottles.
Keywords: fractions, multiplication
Learn more about fractions at:
#LearnwithBrainly
X=10. so x-3 would be 7. e would equal 7. so 5x7=35
Answer:
see explaination
Step-by-step explanation:
Using the formulla that
sum of terms number of terms sample mean -
Gives the sample mean as \mu=17.954
Now varaince is given by
s^2=\frac{1}{50-1}\sum_{i=1}^{49}(x_i-19.954)^2=9.97
and the standard deviation is s=\sqrt{9.97}=3.16
b) The standard error is given by
\frac{s}{\sqrt{n-1}}=\frac{3.16}{\sqrt{49}}=0.45
c) For the given data we have the least number in the sample is 12.0 and the greatest number in the sample is 24.1
Q_1=15.83, \mathrm{Median}=17.55 and Q_3=19.88
d) Since the interquartile range is Q_3-Q_1=19.88-15.83=4.05
Now the outlier is a number which is greater than 19.88+1.5(4.05)=25.96
or a number which is less than 15.83-1.5(4.05)=9.76
As there is no such number so the given sample has no outliers
Answer:
9) 0.87 10) 1.24 11) 3.40