1- 2
2- 5
3- 4.37 or just put 4.3
The distance between 2 points

and

on the coordinate plane is

So the distance between the given points is

As every unit is 1 mile, so the distance should be 10.8*1=10.8miles.
Hope this helps.
Answer:
x= 55 degrees
w = 5
Step-by-step explanation:
Triangle PQR contains two triangles, QPS and PSR.
Looking at triangle QPS, it is an isosceles triangle. This is shown by the two short lines that cuts line QP and line QS.
In an isosceles triangle, two sides and two angles are equal. The two equal angles are the base angles.
Therefore,
angle P and angle S are equal. Also
Line QP and line PS are equal. This means
6w - 10 = w
6w-w = 10
5w = 10
w = 10/2 = 5
Angle Q + 100 degrees = 180 ( sum of angles on a straight line)
Angle Q = 180 - 100 = 80 degrees
Angle Q = Angle S(base angles of an isosceles triangle)
Angle PSR = 180 - 80 = 100 degrees( sum of angles on a straight line is 180)
Angle PSR + x + 25 = 180
x = 180 - 25 - 100 = 55 degrees
Answer:
<em>The test statistic Z = 1.844 < 1.96 at 0.05 level of significance</em>
<em>Null hypothesis is accepted </em>
<em>Yes he is right</em>
<em>The manager claims that at least 95 % probability that the plant is operating properly</em>
Step-by-step explanation:
<u>Explanation</u>:-
Given data Population mean
μ = 885 tons /day
Given random sample size
n = 60
mean of the sample
x⁻ = 875 tons/day
The standard deviation of the Population
σ = 42 tons/day
<em><u>Null hypothesis</u></em><em>:- H₀: </em>The manager claims that at least 95 % probability that the plant is operating properly
<u><em>Alternative Hypothesis :H₁</em></u>: The manager do not claims that at least 95 % probability that the plant is operating properly
<em>Level of significance</em> = 0.05
The test statistic



|Z| = |-1.844| = 1.844
<em>The tabulated value</em>
<em> </em>
<em></em>
<em>The calculated value Z = 1.844 < 1.96 at 0.05 level of significance</em>
<em>Null hypothesis is accepted </em>
<u><em>Conclusion</em></u><em>:-</em>
<em>The manager claims that at least 95 % probability that the plant is operating properly</em>
<em></em>
<em></em>