To be able to solve clearly this problem, the best thing
to do is to plot the graph (see attached pic). From the graph we can see that
the points form a trapezoid.
The base is formed by the segment connecting point A and
point B.
While the two heights: shorter one by the segment
connecting points A and D, and the longer one by the segment connecting points
B and C.
The formula for area of trapezoid is given as:
A = b (h1 + h2) / 2
Where,
<span>b = base of the trapezoid
= 3 – (-4) = 7</span>
h1 = shorter height = 2 – (-2) = 4
h2 = longer height = 2 – (-5) = 7
Therefore the area is:
A = 7 (4 + 7) / 2
A = 77 / 2
<span>A = 38.5 </span>
The probability that between 8.0 gallons and 9.0 gallons are pumped during a randomly selected minute is 0.3749 or 37.49%
The Mean of the uniform distribution for an interval from a to b is given by the formula :
μ = 
Here, the given interval is from 7.5 to 10.5 gallons per minute, that means a= 7.5 and b= 10.5
So, Mean(μ) = 
Now, the standard deviation of the uniform distribution is given by the formula:
σ = 
So, the standard deviation(σ) = 
As we need to find the probability that between 8.0 gallons and 9.0 gallons are pumped, so now we will find z-score for both 8.0 and 9.0
The formula for z-score: z = (X - μ)/σ
So, z(X= 8.0) = 
and z(X= 9.0) = 
Now according to the z-score table, P(z=-1.1547) = 0.1251 and P(z=0) = 0.5
So, P(8.0 < x < 9.0)
= P(-1.1547 < z <0)
= 0.5 - 0.1251
= 0.3749
= 37.49%
Thus, the probability that between 8.0 gallons and 9.0 gallons are pumped during a randomly selected minute is 0.3749 or 37.49%
Answer:
Step-by-step explanation:
Remark
The solution to this is to add the two vertically opposite arcs and take 1/2 of the result to get the intersecting angle of the chords.
Solution
<x = 1/2 (arc measure of 116 + 74)
<x = 1/2 (190)
<x = 95
Answer:
All that apply is 18 20 22 24
Step-by-step explanation:
Given:
Manuel has 18 yards of fabric to make table runners.
It takes 3/4 yard to make each runner.
The question is
How many yards runners can Manuel make i.e. 3/4 yard runner with 18 yards
To get all that apply, we will have to divided the yards of fabrics by yards used
= 18 ÷ ¾
= 18 X (4/3)
= 18 x 1.3333
= 23.9
≅ 24
