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Evgesh-ka [11]
2 years ago
14

A village wishes to measure the quantity of water that is piped to a factory during a typical morning. A gauge on the water line

gives the flow rate (in cubic meters per hour) at any instant. The flow rate is about 120 m3/hr at 6 am and increases steadily to about 280 m3/hr at 9 am. Using only this information, give your best estimate of the total volume of water used by the factory between am and am. Best estimate ____________ m3
Mathematics
1 answer:
nignag [31]2 years ago
4 0
122 is the
answer. i think this help
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The article "Expectation Analysis of the Probability of Failure for Water Supply Pipes"† proposed using the Poisson distribution
oksian1 [2.3K]

Answer:

a. P(X ≤ 5) = 0.999

b. P(X > λ+λ) = P(X > 2) = 0.080

Step-by-step explanation:

We model this randome variable with a Poisson distribution, with parameter λ=1.

We have to calculate, using this distribution, P(X ≤ 5).

The probability of k pipeline failures can be calculated with the following equation:

P(k)=\lambda^{k} \cdot e^{-\lambda}/k!=1^{k} \cdot e^{-1}/k!=e^{-1}/k!

Then, we can calculate P(X ≤ 5) as:

P(X\leq5)=P(0)+P(1)+P(2)+P(4)+P(5)\\\\\\P(0)=1^{0} \cdot e^{-1}/0!=1*0.3679/1=0.368\\\\P(1)=1^{1} \cdot e^{-1}/1!=1*0.3679/1=0.368\\\\P(2)=1^{2} \cdot e^{-1}/2!=1*0.3679/2=0.184\\\\P(3)=1^{3} \cdot e^{-1}/3!=1*0.3679/6=0.061\\\\P(4)=1^{4} \cdot e^{-1}/4!=1*0.3679/24=0.015\\\\P(5)=1^{5} \cdot e^{-1}/5!=1*0.3679/120=0.003\\\\\\P(X\leq5)=0.368+0.368+0.184+0.061+0.015+0.003=0.999

The standard deviation of the Poisson deistribution is equal to its parameter λ=1, so the probability that X exceeds its mean value by more than one standard deviation (X>1+1=2) can be calculated as:

P(X>2)=1-(P(0)+P(1)+P(2))\\\\\\P(0)=1^{0} \cdot e^{-1}/0!=1*0.3679/1=0.368\\\\P(1)=1^{1} \cdot e^{-1}/1!=1*0.3679/1=0.368\\\\P(2)=1^{2} \cdot e^{-1}/2!=1*0.3679/2=0.184\\\\\\P(X>2)=1-(0.368+0.368+0.184)=1-0.920=0.080

4 0
1 year ago
Mr.Anderson is building a triangular- shaped roof for his shed. The triangle must be isosceles with its base (noncongruent) side
goldfiish [28.3K]
The side of the congruent side of the triangle should be greater than 7 feet.
4 0
2 years ago
1. & 2. In the diagram below, points A, B, and C are collinear. Answer each of the following questions. The figure shown bel
KiRa [710]

Answer:

a). AB = 8 in

b). AB = 9.75 in

c). AC = 6.5 in

d). BC = 1.5 in

Step-by-step explanation:

a). Since, AB = AC + CB

   Length of AC = 5 in. and CB = 3 in.

   Therefore, AB = 5 + 3 = 8 in.

b). Given : AC = 6.25 in and CB = 3.5 in

   Therefore, AB = AC + CB = 6.25 + 3.5

   AB = 9.75 in.

c). Given: AB = 10.2 in. and BC = 3.7 in.

    AB = AC + BC

    AC = AB - BC

    AC = 10.2 - 3.7

    AC = 6.5 in

d). Given: AB = 4.75 in and AC = 3.25 in.

   BC = AB - AC

   BC = 4.75 - 3.25 = 1.5 in.

4 0
1 year ago
Jordan solved the equation −7x + 25 = 48; his work is shown below. Identify the error and where it was made. −7x + 25 = 48 Step
almond37 [142]

Answer:

Step 4 : he should have divided both sides by negative seven

Step-by-step explanation:

6 0
1 year ago
The sides of a square are five to the power of two fifths inches long. What is the area of the square?
Feliz [49]
I believe the correct answer from the choices listed above is the first option. If the  sides of a square are five to the power of two fifths inches long, then the are of the square would be <span>five to the power of four fifths square inches. Hope this answers the question.</span>
3 0
1 year ago
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