Answer:
x=-2/3
Step-by-step explanation:
Answer:
The mean is 39
The median is 42
Step-by-step explanation:
The median is the best measure of center for the above data because half of the values are less than the median and half of the values are more than the median. It's probably the best measure of center to use in a skewed distribution.
The measure of variability is the range because is the simplest measure of variability to calculate but can be misleading if the dataset contains extreme values.
The variability is 67.25
This is how I did it
Answer:
Determinant are special number that can only be defined for square matrices.
Step-by-step explanation:
Determinant are particularly important for analysis. The inverse of a matrix exist, if the determinant is not equal to zero.
How to find determinant
For a 2×2 matrix
![det ( \left[\begin{array}{cc}x&y\\a&z\end{array}\right] ) = xz-ay](https://tex.z-dn.net/?f=det%20%28%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dx%26y%5C%5Ca%26z%5Cend%7Barray%7D%5Cright%5D%20%29%20%3D%20xz-ay)
For a 3×3 matrix
we first decompose it to 2×2
![det (\left[\begin{array}{ccc}k&l&m\\o&p&q\\r&s&t\end{array}\right] )\\\\= k*det(\left[\begin{array}{cc}p&q\\s&t\end{array}\right] ) - l*det(\left[\begin{array}{cc}o&q\\r&t\end{array}\right] ) + m*det(\left[\begin{array}{cc}o&p\\r&s\end{array}\right] ) \\\\=k(pt-sq) - l(ot-rq) + m(os-rp)](https://tex.z-dn.net/?f=det%20%28%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dk%26l%26m%5C%5Co%26p%26q%5C%5Cr%26s%26t%5Cend%7Barray%7D%5Cright%5D%20%29%5C%5C%5C%5C%3D%20k%2Adet%28%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dp%26q%5C%5Cs%26t%5Cend%7Barray%7D%5Cright%5D%20%29%20-%20l%2Adet%28%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Do%26q%5C%5Cr%26t%5Cend%7Barray%7D%5Cright%5D%20%29%20%2B%20m%2Adet%28%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Do%26p%5C%5Cr%26s%5Cend%7Barray%7D%5Cright%5D%20%29%20%5C%5C%5C%5C%3Dk%28pt-sq%29%20-%20l%28ot-rq%29%20%2B%20m%28os-rp%29)
Example
Find the values of λ for which the determinant is zero
![\left[\begin{array}{ccc}s&-1&0\\-1&s&-1\\0&-1&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Ds%26-1%260%5C%5C-1%26s%26-1%5C%5C0%26-1%261%5Cend%7Barray%7D%5Cright%5D)
![det(\left[\begin{array}{ccc}s&-1&0\\-1&s&-1\\0&-1&1\end{array}\right])\\\\= s*det(\left[\begin{array}{cc}s&-1\\-1&1\end{array}\right] ) - (-1)*det(\left[\begin{array}{cc}-1&-1\\0&1\end{array}\right] ) + 0*det(\left[\begin{array}{cc}-1&s\\0&-1\end{array}\right] )\\\\= s(s(1)-(-1*-1)) - (-1)(-1*1 - (-1*0)) + 0\\= s(s - 1)) + 1(-1 + 0) \\=s^{2} -s-1](https://tex.z-dn.net/?f=det%28%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Ds%26-1%260%5C%5C-1%26s%26-1%5C%5C0%26-1%261%5Cend%7Barray%7D%5Cright%5D%29%5C%5C%5C%5C%3D%20s%2Adet%28%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Ds%26-1%5C%5C-1%261%5Cend%7Barray%7D%5Cright%5D%20%29%20-%20%28-1%29%2Adet%28%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%26-1%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D%20%29%20%2B%200%2Adet%28%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%26s%5C%5C0%26-1%5Cend%7Barray%7D%5Cright%5D%20%29%5C%5C%5C%5C%3D%20s%28s%281%29-%28-1%2A-1%29%29%20-%20%28-1%29%28-1%2A1%20-%20%28-1%2A0%29%29%20%2B%200%5C%5C%3D%20s%28s%20-%201%29%29%20%2B%201%28-1%20%2B%200%29%20%5C%5C%3Ds%5E%7B2%7D%20-s-1)
Equating the determinant to zero

s =
* (1 ±5 )
s = 1.61 or -0.61
Answer:
Step-by-step explanation:
10x + 14y = 18.....reduce by dividing everything by 2 and u end up with 5x + 7y = 9
notice how both equations are now the same....means same line.....this means ur solution is : INFINITE SOLUTIONS
9514 1404 393
Answer:
726 rpm
Step-by-step explanation:
The angular speed is not dependent upon the radius. The rotational speed is 726 rpm at any radius.