Answer:
The correct option is C). (9,4)
The coordinates of a point N is (9,4)
Step-by-step explanation:
Theory: If point P(x,y) lies on line segment AB and AP: PB=m:n, then we say P divides line AB internally in ratio of m:n and Point is given by
P=
Given that point, M is lying somewhere between point L and point N.
The coordinates of a point L is (-6,14)
The coordinates of a point M is (-3,12)
Also, LM: MN = 1:4
We can write as,
Let,
Point L(-6,14)=(X1, Y1)
Point M(-3,12)=(x,y)
Point N is (X2, Y2)
m=1 and n=4
M(-3,12)=
M(-3,12)=
M(-3,12)=
(-15)=X2-24
X2=9
(60)=Y2+56
Y2=4
Thus,
The coordinates of a point N is (9,4)
Result: The correct option is C). (9,4)
If you add the standard deviation to the average, it is 14.84. Because Marcus's score was lower than that, he will not receive a certificate.
I think this should be right for the reason and the calculation.
Answer: 
Step-by-step explanation:
Since the center of dilation is not at the origin, we can use the following formula in order to find the coordinates of the vertices of the triangle D'E'F':
Where "O" is the center of dilation at (a,b) and "k" is the scale factor.
In this case you can identify that:
Therefore, susbtituting values into the formula shown above, you get that the coordinates ot the resulting triangle D'E'F, are the following:
Vertex D' → 
Vertex E' → 
Vertex F' → 
Here, as the sides are equal, middle line would be exact half then the longer (bottom) side of the triangle.
48 = 2(3x)
6x = 48
x = 48/6
x = 8
In short, Your Answer would be Option D
Hope this helps!
Answer:
'A' is true; theoretically, 50% of the data items reside between the first and third quartiles (40 and 67.5)
Step-by-step explanation:
Range is 84-28 which is 56
Median is 51
1.5 x Interquartile Range (IQR) = 1.5(67.5-40) which equals 41.25
Q1 is 40
Q1 - IQR = -1.25
Low outliers are below -1.25 - 41.25; there are not data items below -42
