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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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Y = – 3
KonstantinChe [14]

The  best approximation for the solution to this system of equations is (-2.2,-3)

Option C is correct.

Step-by-step explanation:

Solving the system of equations to get the exact value of x:

y = -3\\y = x-0.8

Let

y = -3\,\,eq(1)\\y = x-0.8\,\,eq(2)

Putting value of y from eq(1) into eq(2)

-3=x-0.8

x=-3+0.8

x=-2.2

So, Value of x is -2.2

The  best approximation for the solution to this system of equations is:

x=-2.2 and y = -3

(-2.2,-3)

Option C is correct.

Keywords: System of equations

Learn more about system of equations at:

  • brainly.com/question/9045597
  • brainly.com/question/3739260
  • brainly.com/question/13168205

#learnwithBrainly

6 0
3 years ago
Read 2 more answers
Rksheet
VLD [36.1K]

See below for the terms, coefficients, and constants in the variable expressions

<h3>How to determine the terms, coefficients, and constants in the variable expressions?</h3>

To determine the terms, coefficients, and constants, we use the following instance:

ax + by + c

Where the variables are x and y

  • Then the terms are ax, by and c
  • The coefficients are a and b
  • The constant is c

Using the above as guide, we have:

A) 2b + 2ac+5

  • Terms: 2b, 2ac, 5
  • Coefficient: 2, 2 and 5
  • Constant 5

B) 34abx + 16y +1

  • Terms: 34abx, 16y, 1
  • Coefficient: 34ab, 16
  • Constant: 1

C) st +4u + v

  • Terms: st, 4u, v
  • Coefficient: 4

D) 14xy + 6

  • Terms: 14xy, 6
  • Coefficient: 14, 6
  • Constant 6

E) 14x + 12y

  • Terms: 14x, 12y
  • Coefficient: 14, 12

F) 3+ 6-7+a

  • Terms: 3, 6, -7, a
  • Coefficient: 1
  • Constant: 3, 6, -7

Read more about terms, coefficients, and constants at:

brainly.com/question/14625487

#SPJ1

5 0
1 year ago
Consider this expression.
schepotkina [342]

Answer:

9m^2 + 17m- 9

Step-by-step explanation:

Given

7m^2 + (2m - 1)(m + 9)

Required:

Simplify

We start by opening the bracket

7m^2 + (2m(m + 9) - 1(m + 9))

7m^2 + 2m^2 + 18m - m - 9

Collect Like Terms

9m^2 + 17m- 9

Hence, the equivalent expression is 9m^2 + 17m- 9

5 0
2 years ago
Find the missing value for the exponential function represented by the table below.
Virty [35]
The common ratio of sequential values is 
   18.2/26 = 0.7

The missing value is
   12.74*0.7 = 8.918

The appropriate choice is ...
   d.  8.918
3 0
3 years ago
Write the expression as an inequality.
g100num [7]

For the park's ride sign, there are two pieces we need to look at.

1) "At least 44"

2) "No more than 74"

The first piece tells us anyone more than 44 inches can ride. 45 inches is okay, since 45 is more than 44 (45 > 44 is true). 44 works too since 44 ≥ 44 is true. So you can say a person's height - h that is more than 44 makes it true, h ≥ 44. We reverse its orientation and say that 44 ≤ h.

The second piece says if you are under 74 inches you can ride. "No more than" means we don't include 74 inches but 73 inches would be fine. With symbols, 74 < 74 would be false, and 73 < 74 would be true. Using anyone's height - h - that means h < 74 is true.

Put the pieces together, and we have 44 ≤ h < 74 (choice B).

6 0
3 years ago
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