Answer:
2 units
Step-by-step explanation:
Given data
The points are (2, 3) and (2, 5)
x1= 2
y1= 3
x2= 2
y2= 5
substitute into the distance between two points formula
d=√((x_2-x_1)²+(y_2-y_1)²)
d=√((2-2)²+(5-3)²)
d=√(2)²)
d=√4
d= 2 units
Hence the length is 2 units
The coordinates of B and D are the location of the vertices B and D in the rectangle
The coordinates of B and D are (55, 30) and (55, 14)
<h3>How to determine the coordinates of B and D?</h3>
From the figure of the rectangle, we have:
A = (25,30)
C = (40, 22)
Point B has the same y-coordinate as point A
So, we have:
B = (x, 30)
The x-coordinate is then calculated as:
Bx = 2Cx - Ax
This gives
Bx = 2*40 - 25
Bx = 55
So, the coordinates of B are:
B = (55, 30)
Point D has the same x-coordinate as point B
So, we have:
D = (55, y)
The y-coordinate is then calculated as:
Dy = Cy - (By - Cy)
This gives
Dy = 22 - (30 - 22)
Dy = 14
So, the coordinates of B are:
D = (55, 14)
Hence, the coordinates of B and D are (55, 30) and (55, 14)
Read more about rectangles at:
brainly.com/question/10737082
FIRST PARTWe need to find sin α, cos α, and cos β, tan β
α and β is located on third quadrant, sin α, cos α, and sin β, cos β are negative
Determine ratio of ∠α
Use the help of right triangle figure to find the ratio
tan α = 5/12
side in front of the angle/ side adjacent to the angle = 5/12
Draw the figure, see image attached
Using pythagorean theorem, we find the length of the hypotenuse is 13
sin α = side in front of the angle / hypotenuse
sin α = -12/13
cos α = side adjacent to the angle / hypotenuse
cos α = -5/13
Determine ratio of ∠β
sin β = -1/2
sin β = sin 210° (third quadrant)
β = 210°

SECOND PARTSolve the questions
Find sin (α + β)
sin (α + β) = sin α cos β + cos α sin β



Find cos (α - β)
cos (α - β) = cos α cos β + sin α sin β



Find tan (α - β)


Simplify the denominator


Simplify the numerator


Simplify the fraction

Answer:
8
Step-by-step explanation:
send <em>the</em><em> </em><em>-</em><em>5</em><em> </em><em>to</em><em> </em><em>where</em><em> </em><em>the</em><em> </em><em>+</em><em>3</em><em> </em><em>is</em><em> </em><em>then</em><em> </em><em>you</em><em> </em><em>can</em><em> </em><em>now</em><em> </em><em>add</em><em> </em><em>the</em><em> </em><em>value</em><em> </em><em>together</em><em>.</em>
Solution: The sample mean of sample 1 is:

The sample mean of sample 2 is:

The sample mean of sample 3 is:

The sample mean of sample 4 is:

The minimum sample mean of the four sample means is 3.6 and maximum sample mean of the four sample means is 4.4.
Therefore, using his four samples, between 3.6 and 4.4 will Ardem's actual population mean lie.
Hence the option 3.6 and 4.4 is correct