Answer:
The mean is also increased by the constant k.
Step-by-step explanation:
Suppose that we have the set of N elements
{x₁, x₂, x₃, ..., xₙ}
The mean of this set is:
M = (x₁ + x₂ + x₃ + ... + xₙ)/N
Now if we increase each element of our set by a constant K, then our new set is:
{ (x₁ + k), (x₂ + k), ..., (xₙ + k)}
The mean of this set is:
M' = ( (x₁ + k) + (x₂ + k) + ... + (xₙ + k))/N
M' = (x₁ + x₂ + ... + xₙ + N*k)/N
We can rewrite this as:
M' = (x₁ + x₂ + ... + xₙ)/N + (k*N)/N
and (x₁ + x₂ + ... + xₙ)/N was the original mean, then:
M' = M + (k*N)/N
M' = M + k
Then if we increase all the elements by a constant k, the mean is also increased by the same constant k.
X = cos(pi/6) = √3/2
y = sin(pi/6) = 1/2
So at point (√3/2, 1/2)
Answer:
The graph in the attached figure
Step-by-step explanation:
we know that
The equation of a vertical parabola in vertex form is equal to
where
a is a coefficient
(h,k) is the vertex
In this problem we have
(h,k)=(1,-4)
substitute
we have
An x-intercept of (-1,0)
substitute and solve for a
The equation is
<u><em>Verify the y-intercept</em></u>
For x=0
The y-intercept is the point (0,-3) -----> is correct
using a graphing tool
see the attached figure
