Suppose you are hired by the STAR Lab to analyze vehicle arrivals at the right lane of the Evergreen Point Bridge on Westbound SR-520 for the period from 12:00am to 4:00am in a weekday. It is known that vehicle arrivals follow a Poisson process at this location and time period. There is a single-loop detector embedded on this lane at the east end of the bridge. Since you do not want to go to the bridge to count vehicles at this time period, you decided to use the loop detector data for the analysis. Of the 720 20-second intervals (the loop detection system stores data every 20 seconds), 508 intervals were identified to have at least one vehicle detected. Assume the loop detector is free of error. Please estimate the vehicle arrival rate (vehicles per second) for this lane. With the estimated arrival rate, please calculate the probability of having three or more vehicles detected in a 20-second interval and the probability of having a headway shorter than 10 seconds. [15 points]

Answers

Answer 1

Answer:

0.126

Step-by-step explanation:

Given :

Total time interval = 720

Number of interval in which one vehicle is detected =508

Proportion of atleast one detected vehicle :

508 / 720 = 0.7056

The mean arrival rate per second :

P(x ≥ 3) = 1 - P(x ≤ 3)

P(x ≥ 3) =1 - [p(x =0) + p(x = 1) + p(x =2) + p(x = 3)]

P(x ≥ 3) = 1 - 0.8745

P(x ≥ 3) = 0.1255

P(x ≥ 3) = 0.126


Related Questions

A pet store has 40 freshwater fish. Of all the fish in the store, 80% are freshwater fish. How many fish does the store have in all?

Answers

Answer:

50 fish

Step-by-step explanation:

80% 40 fish :8

10% 5 fish x10

100% 50 fish

Which statement about the reflection below is true?

Answers

Answer:

A

Step-by-step explanation:

took le test review and got that question right

Answer:

A

Step-by-step explanation:

got it right edge2021


Is the equation y=5x+90 proportional?

Answers

Answer:

yes, x does have an exact proportion of y

Step-by-step explanation:

Please help me with this. I give brainliest and give ratings. Don't answer just to take my points or you're getting reported

Answers

Answer:

3/4

Step-by-step explanation:

You have to Subtract 6 ¼ by 5 ½

Jay's allowance is reduced $1.25 every time he forgets to clean his room. If he forgets to clean his room 7 times this month, how much is Jay's allowance reduced?

Answers

Answer:

$8.75

Step-by-step explanation:

1.25 times 7 equals 8.75 so it is reduced by 8.75

NEED HELP ASAP PLEASE HELP

Answers

Answer:

the second one or b. :)

Step-by-step explanation:

B. What is the largest whole number to the left of 3.52?​

Answers

Answer:

3

Step-by-step explanation:

<---------1-----------2---------3----3.52----4----->

Computer keyboard failures can be attributed to electrical defects or mechanical defects. A repair facility currently has 25 failed keyboards, 12 of which have electrical defects and 13 of which have mechanical defects. (a) How many ways are there to randomly select 6 of these keyboards for a thorough inspection (without regard to order)

Answers

Answer:

There are 177,100 ways.

Step-by-step explanation:

Since there is no regard to order, we use the combinations formula to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

6 keyboards from a set of 25. So

[tex]C_{25,6} = \frac{25!}{6!(25-6)!} = 177100[/tex]

There are 177,100 ways.

in which equation is y a nonlinear function of x ? will Mark brainiest is for the correct answer please help me​

Answers

9514 1404 393

Answer:

  (B)

Step-by-step explanation:

The power of x is 1 everywhere except equation (B), where it is 1/2.

Equation B is a nonlinear function of x.

Answer:

Step-by-step explanation: D

From $5 to $8 in percent

Answers

Answer:

Step-by-step explanation:

That would be 8/5 = 1.3 = 130/100 = 130%

66666666666666666666

Find the slope and y-intercept of the graph of the equation y=1/2x+7

Answers

slope: 1/2
y int: 7

nsnfjwjfjsj

Simplify
6sqrt20 + 8sqrt5 – 5sqrt45

Answers

Answer:

5√5

Step-by-step explanation:

Simplify

6√20 + 8√5 - 5√45 = 6√4(5) + 8√5 - 5√9(5) =6(2)√5 + 8√5 - 5(3)√5 = (12 + 8 - 15)√5 =5√5

PLEASE HELP ME!!!!!!!!

Answers

Answer:

x = 50

Step-by-step explanation:

x = 180 - 130 = 50

Answer:

x=50

Step-by-step explanation:

What is the value of
2021

2223
+
2425
2021

2223
+
2425
?

Answers

Answer:

the answer is 2223 please mark as brainliest

Answer:

2223

Step-by-step explanation:

its a simple math issue

You purchase a new mountain bike for $1,575. You put a 10% down payment and $65.56 per month on a 24 month purchase plan. Determine the total finance charge.

Answers

Answer:

c believe me

Step-by-step explanation:

The prom committee has no more than $600 to spend on centerpieces for the prom. If each centerpiece costs $25, what is the maximum number of centerpieces the committee can buy?

Answers

Answer:

600/25 = 24

Brainiest plz :)

Answer:

600/25 = 24

Have a good day I hope this helps.

The University of South Texas is interested in determining if there is a difference in the average weight gain between male students (group 2) and female students (group 1) during their freshman year. They take a random sample of 10 male students and 10 female students. Find the confidence interval with 95% confidence. The 95% confidence interval is (2.4, 20.4). A. We are 95% confident that the population mean weight gain for male University of South Texas students is 2.4 more to 20,4 more than female University of South Texas students. B. We are 95% confident that the population mean weight gain for female University of South Texas students is 2.4 more to 20.4 more than male University of South Texas students. C. We are 95% confident that the sample mean weight gain for female University of South Texas students is 2.4 more to 20.4 more than male University of South Texas students. D. We are 95% confident that the sample mean weight gain for male University of South Texas students is 2.4 less to 20.4 more than female University of South Texas students.

Answers

Answer: A. We are 95% confident that the population mean weight gain for male University of South Texas students is 2.4 more to 20,4 more than female University of South Texas students.

Step-by-step explanation:

Given a 95% confidence interval of : (2.4, 20.4)

The lower boundary of the interval = 2.4

The upper boundary of the interval = 20.4

Male = group 2, Female = group 1

P2 - P1 is between lower boundary more and upper boundary more ;

Hence

Population mean weight for male is 2.4 more to 20.4 more than female

POINTS PLZ HELP
A baker determined the annual profit in dollars from selling pies using p n( ) = 52n − 0.05n2 , where n is the number of pies sold. What is the annual profit if the baker sells 400 pies?
F $20,780
G $12,800
H $28,800
J $20,760

Answers

Answer:

G

Step-by-step explanation:

Answer:$12,800

Step-by-step explanation:

Add 400 to every n in the equation, I’ll be using y for the “p(n)” part cus it always confuses me like that.

Y=52(400)-0.05 x 400^2

=20,800 - 0.05 x 160,000

=20,800 - 8,000

=12,800

63 over 22 as a decimal

Answers

Answer:

Step-by-step explanation:

63/22 = 2.86363 = 2.86

2.86 you’d want to divide 63 by 22 and round it to the nearest hundredth

What is the average rate of change between:
x= 1 and x = 2?
x = 2 and x = 3?
x= 3 and x = 4?

Answers

Answer:

The average rate of change between x = 1 to x = 2 is 2, from x = 2 to x = 3 is 4 and from x = 3 to x = 4 is 8.

Step-by-step explanation:

43 POINTS IF U DO THIS! + ILL MARK BRAINLIEST!

Answers

Answer:

The second one

210 lbs

Step-by-step explanation:

The difference between 7 and 4 is 3

90/3 = 30

30 times 7 = 210

Answer:

Second Diagram

Step-by-step explanation:

Consider a square-based straight pyramid. Suppose that the base is a square with sides 10 km long, and all other edges are 17 km long. Find an approximate value of the angle formed between the base and a triangular face. Present your answer in degrees, accurate up to four or more decimal places.

Answers

Answer:

72.06

Step-by-step explanation:

Given that :

Side Lenght, a = 10

Edge length, b = 17

Using Pythagoras :

h = height of pyramid

h = sqrt (b² - 1/2a²)

h = sqrt(17^2 - 10^2/2)

h = sqrt(289 - 50)

h = 15.46

Slant height :

L = sqrt(h² + a²/4)

L = sqrt(15.46² + 25)

L = sqrt(239 + 25)

L = sqrt(264)

L = 16.25

Sinα = h/L

α = sin^-1 (15.46/16.25)

α = 72.060933

= 72.06

The approximate value of the angle formed between the base and a triangular face is 72.0775°.

Let [tex]h[/tex] be the distance between the center of the square base and the midpoint of the side of the square and let [tex]H[/tex] the height of the triangular face of the pyramid. By properties of the square and the Pythagorean theorem we derive expressions for [tex]h[/tex] and [tex]H[/tex], respectively:

Square base

[tex]h = 0.5\cdot L[/tex] (1)

Triangular face

[tex]H = \sqrt{l^{2}-0.25\cdot L^{2}}[/tex] (2)

Where:

[tex]L[/tex] - Side length of the square base, in kilometers.[tex]l[/tex] - Remaining side length of the triangular face, in kilometers.

Finally, by trigonometry we can derive an expression for the angle between the base and a triangular face ([tex]\theta[/tex]), in sexagesimal degrees:

[tex]\theta = \cos^{-1} \frac{h}{H}[/tex] (3)

If we know that [tex]L = 10\,km[/tex] and [tex]l = 17\,km[/tex], then the angle between the base and a triangular face is:

[tex]h = 5\,km[/tex]

[tex]H = \sqrt{17^{2}-5^{2}}[/tex]

[tex]H \approx 16.248\,km[/tex]

[tex]\theta = \cos^{-1} \frac{5\,km}{16.248\,km}[/tex]

[tex]\theta \approx 72.0775^{\circ}[/tex]

The approximate value of the angle formed between the base and a triangular face is 72.0775°.

We kindly invite to check this question on pyramids: https://brainly.com/question/16303112

All the teachers at a school are either left footed or right footed.
At the school
the number of left footed teachers:the number of right footed teachers = 3:13
At the school, there are 18 left footed teachers.
How many right footed teachers are there?

Answers

Answer:

78

Step-by-step explanation:

Ratio of left-footed teachers to right-footed teachers = 3:13

18 left-footed teachers; 3x6 = 18 (3:13 is a simplified ratio and to get 18, you have to multiply 3 by 6)

13x6 = 78 (whatever you do to one side, you have to do the other)

78 right-footed teachers

The are 78 teachers are right footed.

What is Algebra?

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

The ratio of the number of left footed teachers: the number of right footed teachers = 3:13

Total left footed teachers = 18

let the Common ratio be x.

Then , number of left footed teachers= 3x

and, number of right footed teachers= 13x

So, 3x= 18

x= 6

Hence, there are 78 teachers are right footed.

Learn mor about algebra here:

https://brainly.com/question/24875240

#SPJ2

5. Five-eighth of a number is 15. What is the number?
Your answer

Answers

Answer:

I think it is 24

Step-by-step explanation:

15÷5=3

3×8=24

Answer:

24

Step-by-step explanation:

divide 15 by 5 to get 3 which is equal to 1/8 of the number. then just multiply 3 by 8 to get 24.

PLEASEEEEEEEEEEEE HELPPPPPPPPPP :(
will give brainliest

32,300 is 85% of what

Answers

Answer:

27455

Step-by-step explanation:

32300per of 85

is 27455

How do you use Trigonometric Ratios to solve Real-world problems

Answers

9514 1404 393

Explanation:

Obviously, the way you use trig ratios will depend on the problem. The problems you see in algebra and trig courses are a good sampling of the kinds of problems you run across in the real world. Some of them include ...

  finding height or widths based on a measure and an angle (SOH CAH TOA)

  finding areas based on side lengths and an angle (area formula)

  finding unknown sides or angles of a triangle (law of sines/cosines)

  finding bearing and/or distance (spherical trig relations, law of cosines)

__

As with solving problems of any kind, you choose the appropriate formula(s), fill in the known values, and solve for the unknown values. Sometimes a real-world problem will require solution of intermediate problems before the answer to the original question is found.

A quality-control engineer samples 100 items manufactured by a certain process, and finds that 15 of them are defective. True or False:
a) The probability that an item produced by this process is defective is 0.15.
b) The probability that an item produced by this process is defective is likely to be close to 0.15, but not exactly equal to 0.15.

Answers

Answer: b) The probability that an item produced by this process is defective is likely to be close to 0.15, but not exactly equal to 0.15.

Step-by-step explanation:

Given that:

Number of samples = 100

Number of defective samples = 15

Proportion =number defective samples / total samples

P = 15 / 100 = 0.15

Hence, the probability that an item produces is defective is 0.15.

However, due to sampling Variations, the probability will be corrected for these variations. Hence, probability that an item produced by this process is defective is likely to be close to 0.15, but not exactly equal to 0.15.


An equation for a line is 3x + 3y = 18.
What are the slope and Y -intercept point?

Answers

Answer:

y = -1x + 6

slope ^   ^ y-intercept

Step-by-step explanation:

3x + 3y = 18

3y = -3x + 18

y = -1x + 6

hope this helps

Answer:

y int: 6 slope: -1

Step-by-step explanation:

Convert to y=mx+b format

3x + 3y - 18 = 0

3x - 18 = -3y

-1x + 6 = y

in mx+b format, m is the slope and b is the y-int:

m = -1

b = 6

Determine if the described set is a subspace. Assume a, b, and c are real numbers. The subset of R3 consisting of vectors of the form a b c , where abc

Answers

This question is incomplete, the complete question is;

Determine if the described set is a subspace. Assume a, b, and c are real numbers.

The subset of R³ consisting of vectors of the form [tex]\left[\begin{array}{ccc}a\\b\\c\end{array}\right][/tex] , where abc = 0

The set is a subspaceThe set is not a subspace

Answer:

Therefore; The set is not a subspace

Step-by-step explanation:

Given the data the question;

the subset R³;

S = {  [tex]\left[\begin{array}{ccc}a\\b\\c\end{array}\right][/tex] , where abc = 0 }

we know that a subset of R³ is a subspace if it stratifies the following properties;

it contains additive identityit is closed under additionit is closed under scales multiplication

Looking at the properties, we can say that it is not a subspace

As;

         u = [tex]\left[\begin{array}{ccc}1\\1\\0\end{array}\right][/tex] ∈ S       and v = [tex]\left[\begin{array}{ccc}0\\1\\1\end{array}\right][/tex]  ∈ S

As    1×1×0=0                          0×1×1=0

But   u+v = [tex]\left[\begin{array}{ccc}1+0\\1+1\\0+1\end{array}\right] =[/tex] [tex]\left[\begin{array}{ccc}1\\2\\1\end{array}\right][/tex]  ∉  S     as 1×2×1 ≠ 0

Hence, it is not closed under addition.

Therefore; The set is not a subspace

A utility company might offer electrical rates based on time-of-day consumption to decrease the peak demand in a day. Enough customers need to accept the plan for it to be successful. Suppose that among 50 major customers, 15 would accept the plan. The utility selects 10 major customers randomly (without replacement) to contact and promote the plan. a. What is the probability that exactly two of the selected major customers accept the plan

Answers

Answer:

0.2406 = 24.06% probability that exactly two of the selected major customers accept the plan

Step-by-step explanation:

The customers are chosen without replacement, which means that we use the hypergeometric distribution to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

50 major customers, 15 would accept the plan.

This means that [tex]N = 50, k = 15[/tex]

The utility selects 10 major customers randomly (without replacement) to contact and promote the plan.

This means that [tex]n = 10[/tex]

a. What is the probability that exactly two of the selected major customers accept the plan

This is P(X = 2).

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,50,10,15) = \frac{C_{15,2}*C_{35,8}}{C_{50,10}} = 0.2406[/tex]

0.2406 = 24.06% probability that exactly two of the selected major customers accept the plan

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