Answer:
Step-by-step explanation:
If 
, then 
and are alternate interior angles.
This means that line segment AC is a transversal.
This implies that line segment AD is parallel to line segment BC.
The second choice is the correct answer.
Answer:
triangles are equilateral, scalene, right, and isosceles
And an angle would be acute, obtuse , and right
Hope this helps
Answer:
![\left[\begin{array}{ccc}-25&\dfrac{75}{2}&-\dfrac{25}{2}\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-25%26%5Cdfrac%7B75%7D%7B2%7D%26-%5Cdfrac%7B25%7D%7B2%7D%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
In the first equality
![5\times \left[\begin{array}{cc}-1&2\\4&8\end{array}\right] =\dfrac{2}{5}m\times \left[\begin{array}{cc}-1&2\\4&8\end{array}\right],](https://tex.z-dn.net/?f=5%5Ctimes%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%262%5C%5C4%268%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cdfrac%7B2%7D%7B5%7Dm%5Ctimes%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%262%5C%5C4%268%5Cend%7Barray%7D%5Cright%5D%2C)
the matrices in both parts are the saem. The equality will be true if the same matrices are multiplied by the same numbers, so
For the second equality
![(H+[1\ 4\ -2])+[3\ 2\ -6]=[-2\ 3\ -1]+([1\ 4\ -2]+[3\ 2\ -6]),](https://tex.z-dn.net/?f=%28H%2B%5B1%5C%204%5C%20-2%5D%29%2B%5B3%5C%202%5C%20-6%5D%3D%5B-2%5C%203%5C%20-1%5D%2B%28%5B1%5C%204%5C%20-2%5D%2B%5B3%5C%202%5C%20-6%5D%29%2C)
if ![H=[-2\ 3\ -1]](https://tex.z-dn.net/?f=H%3D%5B-2%5C%203%5C%20-1%5D)
, then this equality represents the assotiative property of matrix addition.
Hence,
![m\times H=\dfrac{25}{2}\times [-2\ 3\ -1]=\left[\begin{array}{ccc}-25&\dfrac{75}{2}&-\dfrac{25}{2}\end{array}\right]](https://tex.z-dn.net/?f=m%5Ctimes%20H%3D%5Cdfrac%7B25%7D%7B2%7D%5Ctimes%20%5B-2%5C%203%5C%20-1%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-25%26%5Cdfrac%7B75%7D%7B2%7D%26-%5Cdfrac%7B25%7D%7B2%7D%5Cend%7Barray%7D%5Cright%5D)
The given data is
Scores: 90-99 80-89 70-79 60-69 50-59
Students: 3 7 12 4 4
Because we are to take the middle value for each group.
Therefore the total score is
Sx = 3*94.5 + 7*84.5 + 12*74.5 + 4*64.5 + 4*54.5 = 2245
The number of students is 3+7+12+4+4 = 30
The mean is
m =2245/30 = 74.833
Calculate (Sx - m)²
(Sx - m)² = 3*(94.5-74.833)² + 7*(84.5-74.833)² + 12*(64.5-74.833)²
+ 4*(64.5-74.833)² + 4*(54.5-74.833)² = 3896.7
Calculate the standard deviation
s = √(3896.7/29) = 11.592
Answer:
mean = 74.83
std. deviation = 11.59
10 is in 3, so that's 30. There's another 9.
30 + 9 = 39.
39 tenths.
