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iris [78.8K]
3 years ago
14

(7 points) Cars arrive at a toll both according to a Poisson process with mean 80 cars per hour. If the attendant makes a two-mi

nute phone call, what is the probability that at least 1 car arrives during the call
Mathematics
1 answer:
saveliy_v [14]3 years ago
5 0

Answer:

The probability that at least 1 car arrives during the call is 0.9306

Step-by-step explanation:

Cars arriving according to Poisson process - 80 Cars per hour

If the attendant makes a 2 minute phone call, then effective λ = 80/60 * 2 = 2.66666667 = 2.67   X ≅ Poisson (λ = 2.67)

Now, we find the probability: P(X≥1)

P(X≥1) = 1 - p(x < 1)

P(X≥1) = 1 - p(x=0)

P(X≥1) = 1 - [ (e^-λ) * λ^0] / 0!

P(X≥1) = 1 - e^-2.67

P(X≥1) = 1 - 0.06945

P(X≥1) = 0.93055

P(X≥1) = 0.9306

Thus, the probability that at least 1 car arrives during the call is 0.9306.

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Makovka662 [10]

Answer:

240 m³

Explanation:

The volume of a pyramid is equal to:

V=\frac{1}{3}\times B\times H

Where B is the area of the base and H is the height of the pyramid.

Then, the base of the pyramid is a triangle, so the area of a triangle is equal to:

B=\frac{b\times h}{2}

Where b is the base of the triangle and h is the height of the triangle. So, replacing b by 16 m and h by 9 m, we get:

B=\frac{16\times9}{2}=\frac{144}{2}=72m^2

Finally, replacing B by 72 m² and H by 10 m, we get that the volume of the pyramid is equal to:

V=\frac{1}{3}\times72\times10=\frac{1}{3}\times720=240m^3

Therefore, the volume is 240 m³

4 0
1 year ago
two models are shown. Each model has been shaded grey to represent a fraction. wgucj statement is true about the fractions 3/4 a
jeka57 [31]

Answer:

The third, they are equivalent because the size of the shaded area is the same.

8 0
3 years ago
Two similar prisms have heights 4 cm and 10cm what is the ratio of their surface areas
Slav-nsk [51]
Let k be the scale factor relating two similar prisms P_{1} and P_{2}, such that for corresponding parts of prisms P_{1} and P_{2} (for heights, in particular) we have k= \frac{height\  of \ P_{1} }{height \ of\  P_{2} }. In our case k= \frac{4}{10} = \frac{2}{5}.
For surfaces area we have \frac{Surface \ area \ of \  P_{1} }{Surface \ area \ of \  P_{2}} = k^{2} =( \frac{2}{5} )^{2}= \frac{4}{25}.
So, the right answer is 4:25 (choice B)



4 0
3 years ago
Which number line represents the solution set for the inequality 3(8-4x)&lt;6(x-5)
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Step-by-step explanation:

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1/36

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1/4 ÷ 9

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