For this case we have that the main function is given by:
We apply the following transformation:
Vertical displacements:
Assume k> 0
To graph y = f (x) - k, move the graph k units down.
For k = 3 we have:
Answer:
when the function is changed to f (x) - 3 the change that will occur is:
Vertical displacement 3 units down.
Answer:
The value of the test statistic is 
Step-by-step explanation:
The null hypothesis is:
The alternate hypotesis is:
Our test statistic is:
In which X is the sample mean, 
is the value tested at the null hypothesis, 
is the standard deviation(square roof of the variance) and n is the size of the sample.
In this problem, we have that:
So
The value of the test statistic is
Answer:
composite numbers are numbers that can be divided by other numbers and itself.
Step-by-step explanation:
Answer:
Step-by-step explanation:
To find measures of angles m and n
The triangle to the left has three sides of equal length.
This means that it will also have three angles of equal measure.
The internal angles of a triangle sum to 180°
So the internal angles of the left triangle are 180/3 = 60°
The top right angle is made up of one of the 60° angles and angle n
60 + n = 90
n = 30°
Again the internal angles of a triangle sum to 180°, so the right triangle
m + n + 90 = 180
m = 180 - 90 - 30
m = 60°
or we could realize that the top and bottom horizontal lines are parallel because the vertical line on the right makes right angles to both of them.
Knowing that they are parallel, we also know that angle m and the top right 60° angle of the left triangle are opposite internal angles of a line intersecting parallel lines and must be identical angles, therefore
m = 60°
Answer:
Look below
Step-by-step explanation:
First you multiply the top and bottom
5/12 x 6/7
5x6 and 12x7
you get your new fraction of 30/84
then you simplify it by 6 to get 5/14
hope this helps
