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Rufina [12.5K]
3 years ago
8

Toll booths on the New York State Thruway are often congested because of the large number of cars waiting to pay. A consultant w

orking for the state concluded that if service times are measured from the time a car stops in line until it leaves, service times are exponentially distributed with a mean of 2.7 minutes. What proportion of cars can get through the toll booth in less than 3 minutes?
Mathematics
1 answer:
HACTEHA [7]3 years ago
6 0

Answer:

The proportion of cars can get through the toll booth in less than 3 minutes is 67%.

Step-by-step explanation:

Let the random variable <em>X</em> be defined as the service times at a tool booth.

The random variable <em>X</em> follows an Exponential distribution with parameter <em>μ</em> = 2.7 minutes.

The probability density function of <em>X</em> is:

f_{X}(x)=\frac{1}{\mu}e^{-x/\mu };\ x\geq 0,\ \mu>0

Compute the probability that a car can get through the toll booth in less than 3 minutes as follows:

P(X

                =\frac{1}{2.7}\cdot \int\limits^{3}_{0} {e^{-x/2.7}} \, dx \\\\=\frac{1}{2.7}\cdot [-\frac{e^{-x/2.7}}{1/2.7}]^{3}_{0}\\\\=1-e^{-3/2.7}\\\\=0.6708

Thus, the proportion of cars can get through the toll booth in less than 3 minutes is 67%.

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What is the perimeter of the triangle? Round to the nearest tenth.
Cerrena [4.2K]

Answer: 19.8 Units

Step-by-step explanation:

The triangle is shown in the attached figure, and have three vertices: AB, AC and BC.

Each vertice represents a point in the cartesian plane and the length of each side of the triangle is the modulus of each vector.

In this sense, the modulus m is calculated as shown:

m=\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}}

Hence, for each vector:

AB=\sqrt{(-2-3)^{2} + (3-0)^{2}}=\sqrt{34}

AC=\sqrt{(-2-(4))^{2} + (3-(-3))^{2}}=\sqrt{40}

BC=\sqrt{(-4-3)^{2} + (-3-0)^{2}}=\sqrt{58}

Now, the perimeter of a triangle is the sum of its three sides:

AB+AC+BC=\sqrt{34} + \sqrt{40} + \sqrt{58}

Finally:

AB+AC+BC=19.77 \approx 19.8

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3 years ago
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2 years ago
Which is the better value? 12 bottles of juice for $15.00, or 18 bottles of juice for $23.04?
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Read 2 more answers
fire work a travels at the speed 300 ft/s firework b travels 240 ft/s. firework b is launched 0.25s before firework a. how many
storchak [24]

Answer:

Both fireworks  will explode after 1 seconds after firework b launches.

Step-by-step explanation:

Given:

Speed of fire work A= 300 ft/s

Speed of Firework B=240 ft/s

Time before which fire work b is launched =0.25s

To Find:

How many seconds after firework b launches will both fireworks explode=?

Solution:

Let t be the time(seconds) after which both the fireworks explode.

By the time the firework a has been launched, Firework B has been launch 0.25 s, So we can treat them as two separate equation

Firework A= 330(t)

Firework B=240(t)+240(0.25)

Since we need to know the same time after which they explode, we can equate both the equations

330(t) = 240(t)+240(0.25)

300(t)= 240(t)+60

300(t)-240(t)= 60

60(t)=60

t=\frac{60}{60}

t=1

7 0
3 years ago
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