Answer:
The P-value for this test is P=0.00006.
Step-by-step explanation:
We have a matched-pair test, with a test statistic t=-14.9.
The degrees of freedom in a sample of 5 students is:
For a t=-14.9 and 4 degrees of freedom, a left-tail test will have a P-value of:
The claim is that the new unit on taking square roots is helping students to learn. This test concludes that there is statistical evidence to support the claim that the new unit is helping students to learn.
Check the picture below.
make sure your calculator is in Degree mode.
Answer:
Please check the explanation.
Step-by-step explanation:
We also know that the slope-intercept form of the line equation is
where m is the slope and b is the y-intercept
Given the lines
1)
Comparing with y=mx+b, the slope of y = 6х - 3:
m₁=6
Comparing with y=mx+b, the slope of y = - 1/6x + 7:
m₂=-1/6
As
m₁ × m₂ = -1
6 × - 1/6 = -1
-1 = -1
Thus, the lines y = 6х - 3 and y = - 1/6x + 7 are perpendicular.
2)
Comparing with y=mx+b, the slope of y = 3x + 2:
m₁=3
simplifying to write in slope-intercept form
y=3x-3
Comparing with y=mx+b, the slope of y=3x-3:
m₂=3
As the slopes of y = 3x + 2 and 2y = 6x - 6 are equal.
i.e. m₁ = m₂ → 3 = 3
Thus, the lines y = 3x + 2 and 2y = 6x - 6 are paralle.
3)
simplifying to write in slope-intercept form
y = 4x - 3/2
Comparing with y=mx+b, the slope of y = 4x - 3/2:
m₁=4
simplifying to write in slope-intercept form
y=-1/4x-1/4
Comparing with y=mx+b, the slope of y=-1/4x-1/4:
m₂=-1/4
As
m₁ × m₂ = -1
4 × - 1/4 = -1
-1 = -1
Thus, the lines 8x - 2y = 3 and x + 4y = - 1 are perpendicular.
4)
simplifying to write in slope-intercept form
y = -3/2x + 5/2
Comparing with y=mx+b, the slope of y = -3/2x + 5/2:
m₁=-3/2
simplifying to write in slope-intercept form
y = -2/3x - 1
Comparing with y=mx+b, the slope of y = -2/3x - 1:
m₂=-2/3
As m₁ and m₂ are neither equal nor their product is -1, hence the lines neither perpendicular nor parallel.
5)
simplifying to write in slope-intercept form
y=6x+5
Comparing with y=mx+b, the slope of y=6x+5:
m₁=6
simplifying to write in slope-intercept form
y=6x-1
Comparing with y=mx+b, the slope of y=6x-1:
m₂=6
As the slopes of y - 5 = 6x and y - 6x = -1 are equal.
i.e. m₁ = m₂ → 6 = 6
Thus, the lines y - 5 = 6x and y - 6x = -1 are paralle.
6)
Comparing with y=mx+b, the slope of y = 3х + 9:
m₁=3
Comparing with y=mx+b, the slope of y = 1/3x - 4:
m₂=1/3
As m₁ and m₂ are neither equal nor their product is -1, hence the lines neither perpendicular nor parallel.