(a) X follows a Poisson distribution with parameter lambda = 273 = 81.
(b) We would expect 81 red trucks to pass through the tunnel between 7am and 10am next Monday.
(c) The number of red trucks passing through the tunnel between 8am and 10am follows a Poisson distribution with parameter lambda = 272 = 54.
The probability that 8 red trucks pass through the tunnel between 8am and 10am is P(X = 8) = 0.0634.
(d) The appropriate distribution is a geometric distribution with parameter [tex]p = e^{-1} = 0.3679.[/tex]
The probability that the truck will be the only one in the tunnel is P(X = 1) = 0.3679.
(e) The expected time of arrival for the first red truck can be modeled by an exponential distribution with parameter lambda = 27/3 = 9.
We expect the red truck to arrive at the tunnel around 7:06 am.
(a) Since the red trucks arrive independently at a constant rate, the number of red trucks passing through the tunnel between 7am and 10am follows a Poisson distribution with parameter λ = 27, denoted as X ~ Poisson(λ=27).
(b) The expected value of a Poisson distribution is equal to its parameter. Therefore, we would expect 27 red trucks to pass through the tunnel between 7am and 10am next Monday.
(c) Let Y be the number of red trucks that pass through the tunnel between 7am and 8am.
Since the red trucks arrive independently at a constant rate, Y follows a Poisson distribution with parameter λ = 27/3 = 9, denoted as Y ~ Poisson(λ=9).
We want to find the probability that 8 red trucks pass through the tunnel between 8am and 10am.
Let Z be the number of red trucks that pass through the tunnel between 8am and 10am.
Since Y and Z are independent Poisson random variables, the distribution of Z is also Poisson with parameter λ = 27-9 = 18, denoted as Z ~ Poisson(λ=18).
Therefore, we want to find P(Z=8), which can be calculated as:
P(Z=8) = (e^(-18) * 18^8) / 8!
= 0.0948 (rounded to four decimal places)
Therefore, the probability that 8 red trucks pass through the tunnel between 8am and 10am is 0.0948.
(d) Let T be the time in hours that the red truck spends in the tunnel. Since the time it takes for a red truck to pass through the tunnel is exponentially distributed with parameter λ = 2 (since it takes 0.5 hours to pass through the tunnel, the rate parameter is 1/0.5 = 2), we have T ~ Exp(λ=2).
We want to find the probability that the red truck is the only one in the tunnel for the entire time it spends in the tunnel, given that there are no other red trucks in the tunnel when it enters at 7:35am.
Let t be the time in hours from 7:35am that the red truck enters the tunnel.
Then, the probability that the red truck is the only one in the tunnel for the entire time it spends in the tunnel is:
[tex]P(T > 2 - t) = e^{-2(2-t)})[/tex]
[tex]= e^{-4+2t}[/tex]
[tex]= e^{(2t-4) }[/tex]
Therefore, we want to find P(T > 2 - t | T > t) using conditional probability:
P(T > 2 - t | T > t) = P(T > 2 - t) / P(T > t)
[tex]= e^{2t-4} / e^{(-2t)}[/tex]
[tex]= e^{(4t-4)}[/tex]
Since we know that the red truck entered the tunnel at 7:35am, we have t = 0.25.
Substituting this value, we get:
[tex]P(T > 1.75 | T > 0.25) = e^{(4(0.25)}-4)[/tex]
[tex]= e^{(-3)[/tex].
= 0.0498 (rounded to four decimal places)
Therefore, the probability that the red truck is the only one in the tunnel for the entire time it spends in the tunnel, given that there are no other red trucks in the tunnel when it enters at 7:35am, is 0.0498.
(e) Let W be the time in hours that it takes for the g-th red truck to arrive at the tunnel.
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Correct answers of the following are:
(a) The distribution of X is 81.
(b) 81 trucks would pass through the tunnel between 7am and 10am next Monday.
(c) Probability that 8 red trucks pass through the tunnel between 8am and 9am is 0.048.
(d) Probability it will be the only red truck in the tunnel the whole time it spends in the tunnel is 0.0067.
(e) A red truck would arrive at the tunnel on Monday morning at around 7:06:40am.
In this problem, we are given information about the arrival of red trucks at a tunnel from 7am to 10am on Monday mornings. We are asked to find the distribution of the number of trucks that pass through the tunnel, the expected number of trucks, the probability that 8 trucks pass through the tunnel between 8am and 9am, the probability that a single truck entering at 7:35am will be the only truck in the tunnel, and the expected arrival time of a red truck on Monday morning.
(a) The distribution of X, the number of red trucks passing through the tunnel, is a Poisson distribution, since the arrivals are independent and occur at a constant rate. The parameter λ of the Poisson distribution is equal to the average number of red trucks that enter the tunnel per hour times the number of hours the tunnel is open. Therefore, λ = 27*3 = 81.
(b) The expected number of red trucks passing through the tunnel is equal to the parameter of the Poisson distribution, which is λ = 81.
(c) To find the probability that 8 red trucks pass through the tunnel between 8am and 9am, we can use a Poisson distribution with parameter λ = 27*1 = 27, since we are only considering the arrivals between 8am and 9am. The probability can be calculated as:
P(X=8) = (e^-27)*(27^8)/8!
= 0.048
(d) The distribution that models the number of red trucks in the tunnel at any given time is a Poisson distribution with parameter λ = 27/2, since the trucks arrive at a constant rate of 27 per hour and each truck takes half an hour to pass through the tunnel. The probability that a single truck entering the tunnel at 7:35am will be the only truck in the tunnel for its entire time in the tunnel can be calculated as:
P(X=0) = e^(-27/2)
= 0.0067
(e) To find the expected arrival time of a red truck on Monday morning, we can use an exponential distribution with parameter λ = 27/3 = 9, since the red trucks arrive at a constant rate of 27 per hour and we are interested in the time between arrivals. The expected arrival time can be calculated as:
E(W) = 1/λ
= 1/9 hours
= 6.67 minutes
Therefore, we would expect a red truck to arrive at the tunnel on Monday morning at around 7:06:40am (7:00am + 6.67 minutes = 7:06:40am).
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Write the equation of the line that passes through the points (-4,8) and (-2, -1).
Put your answěr in fully reduced point-slope form, unless it is a vertical or horizontal
line.PLEASEEE HELPPP MEE I’ll give you BRAINLEST
Step-by-step explanation:
find the slope
-1 - 8/ -2 - -4 = -9/2
y - -1 = -9/2(x - -2)
y +1 = -9/2(x+2)
y = -9/2x -10
Answer:
y=-9/2x-10
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-1-8)/(-2-(-4))
m=-9/(-2+4)
m=-9/2
y-y1=m(x-x1)
y-8=-9/2(x-(-4))
y-8=-9/2(x+4)
y=-9/2x-36/2+8
y=-9/2x-18+8
y=-9/2x-10
Which of the following is not a true statement? *
a. The boundary line of y > x + 1 is a solid line.
b. The boundary line of y < 2x - 3 is not a solid line.
c. 3x + y < 2 is an example of linear inequality
d. (1, 1) is a solution of x + 3y > 2
Answer:
b. The boundary line of y < 2x - 3 is not a solid line.
Step-by-step explanation:
It's a linear inequality thus its boundary line must be a solid line.
If you have 100$ and then lose 25$ ,what is the percent change
Answer:
75 %
Step-by-step explanation:
100$= 100%
1$= 1%
75$ (left)= 75%
#2 Find the value of x. Round to the nearest degree.
Answer:
49°
Step-by-step explanation:
arccos x = 15/23
Help po plss
1.jane read 10books in one year,while huan rrad 8books.find the ratio jane's to juan's finished books .
2.nadine has 860 female followers out of a total of 1260followes in the social photosharing site find the ratio of female to male followers.
3.a public school has 4415 students and 1200 teachers.what is the ratio of the students to each other teacher.
Answer:
1. 10:8 = 5:4 (simplest form)
2. 860:400 = 43:20 (simplest form)
3. 4415:1200 = 883:240 (simplest form)
I need help with everything but A. assignment is worth 150 points
LOOK IF YOU DONT KNOW HOW TO PARAPHRASE JUST USE THIS WEBSITE AND TEACHERS NEVER NOTICE BOOK MARK IT IT WILL HELP YOU
What amount of tax will be owed on an income of 63,280 if city income tax rate is 1.5% of all income
Answer:
multiply 63280 by 1.5% (.015). The answer is $949.20
Step-by-step explanation:
Paula is going to hire a makeup artist for a fashion show and is comparing prices. Shelley charges $40 as a booking fee and an additional $30 per hour. Ezra charges $35 per hour, plus a booking fee of $30. Depending on the length of the show, the cost could end up being the same for either artist. What would the cost be?
Answer:70
Step-by-step explanation:
The cost of booking was $100 as obtained by the length of the show.
What are linear and non-linear functions?A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane.
Any function whose graph is not a straight line is said to be nonlinear. Any curve other than a straight line can be a graph of it.
An example of a non-linear function is a quadratic function.
From the given information the two linear equations can be formed as,
30x + 40 and 35x + 30.
The cost would be the same when we'll equate these two equations.
30x + 40 = 35x + 30.
30x - 35x = 30 - 40.
- 5x = - 10.
5x = 10.
x = 10/5.
x = 2, So at two hours the cost would be the same and the total cost is,
$30(2) + 40.
$60 + 40.
= $100.
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PLZ help me i will give u many points
Answer:
im pretty sure its the last one
Step-by-step explanation:
Answer:
be
Step-by-step explanation:
Im giving brainiest to the person who answers it first. Thank you!
Answer: Oscer
Step-by-step explanation:
A figure is shown
9 in.
3 in.
2 in.
3 in.
Which expression shows how to find the area of the figure?
A. 9x2 + 3x3
O C. 9+3+2+3
B. 9x 3 + 3 x 2
OD. 9 X5
What is the area of the figure? Enter the answer in the box.
Answer:
C. 9×3 + 3×2
The area of the figure is 33 in.
Step-by-step explanation:
Area is:9x5
Hope i could help u
Write a ratio in three different forms.
Shawn biked 5 miles and ran 2 miles. What is the ratio of the distance Shawn ran to the distance he biked?
Answer:
2:5 is the answer
Step-by-step explanation:
Why is because it says What is the ratio of the distance Shawn ran to the distance he biked shawn ran 2 miles the ratio is 2: and comparing how he rode 5 miles is 2:5
Answer:
2:5
Step-by-step explanation:
im in k12 LOL
Joe determined the mass of 2 boxes using a scale. Since the cost of each box is the same, Joe would like to choose the box with the larger mass. Box A Box B 32.012 kg 32.02 kg Place the correct symbol between the 2 masses to help Joe decide. 32.012 Response area 32.02
Answer:
32.012 kg < 32.02 kg
Step-by-step explanation:
32.012 kg < 32.02 kg
please help me if you can please
Answer:
hello! :) have a good day!
Exact Form:
x= 87/35
Decimal Form:
x= 2.48571428
Mixed Number Form:
x= 2 17/35
Graph and then find the perimeter of this shape. H(3, 0), I(3, 7), J(6, 7), K(6, 0)
Answer:
20 unitsStep-by-step explanation:
Graphed the points to find out it is a rectangle with sides 3 and 7.
Vertical segments with distance 7 - 0 = 7Horizontal segments with the distance 6 - 3 = 3The perimeter is:
P = 2(3 + 7) = 20 unitsAnswer:
50 points
Step-by-step explanation:
I did it and got an A
Which of the following values are solutions to the inequality 6≥4x−5?
Answer:
The solution to the inequality is:
[tex]6\ge \:4x-5\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \frac{11}{4}\:\\ \:\mathrm{Decimal:}&\:x\le \:2.75\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:\frac{11}{4}]\end{bmatrix}[/tex]
-5 and -6 are the solution values.
Step-by-step explanation:
Given the inequality
[tex]6\ge \:4x-5[/tex]
Let us solve the inequality
[tex]6\ge \:4x-5[/tex]
switch sides
[tex]4x-5\le \:6[/tex]
Add 5 to both sides
[tex]4x-5+5\le \:6+5[/tex]
Simplify
[tex]4x\le \:11[/tex]
Divide both sides by 4
[tex]\frac{4x}{4}\le \frac{11}{4}[/tex]
Simplify
[tex]x\le \frac{11}{4}[/tex]
Thus, the solution to the inequality is:
[tex]6\ge \:4x-5\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \frac{11}{4}\:\\ \:\mathrm{Decimal:}&\:x\le \:2.75\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:\frac{11}{4}]\end{bmatrix}[/tex]
In our case, we are given the values -6, 8, and -5
We have already determined that the solution is x ≤ 2.75.
Since the solution is x ≤ 2.75, so -5 and -6 come under the solution set because -5 and -6 are less than 2.75.
Hence, -5 and -6 are the solution values.
The graph of the solution of the inequality is also attached below.
The solutions to the inequality 6 ≥ 4x − 5 is x ≤ 11/4.
What is inequality?A statement of an order relationship-greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.
Now the given inequality is,
6 ≥ 4x − 5
Adding 5 both the side we get,
6 + 5 ≥ 4x − 5 + 5
⇒ 11 ≥ 4x
Dividing both the side by 4 we get,
11/4 ≥ 4x/4
⇒ 11/4 ≥ x
or, x ≤ 11/4
this is the required solution of the given inequality.
Thus, the solutions to the inequality 6 ≥ 4x − 5 is x ≤ 11/4.
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in order to use an expert from a movie in your history class you must pay a royalty fee. the base fee is 50 and an additional .25 cents per minute of the film. the equation for this is?
Answer:
.50=.25x x= Minutes of watching the film.
Step-by-step explanation:
A student needs 23 pound of modeling clay for a project. If each package has 18 pound of clay, how many packages of clay does the student need for his projec
Answer:
First from 18, you count to 23. So, 19, 20, 21, 22, 23. There were only 5 more pounds needed, so it would be, 1 full package of 18 pounds and 1 quarter of a package (I think), because it is not a full package, another full package of 18 would be 36 pounds. I hope this helped! [It might not]
can u guys please help! tysmmmmmm
it's 88.1 x 10 to the power negative 2
and
0,0881
Step-by-step explanation:
88.1÷1000=0,0881
FIND THE AREA
WORK PLEASEEE and thank you
Answer:
Some ways on how to solve the questions:
Use formulas as given by your teacher.
Application of the Pythagorean Theorem would be useful for 5 and 6.
For 7-10 use a formula as given by your teacher (just basic operations like plugging in the formula for those questions)
For 11 and 12 draw it out.
please help asap!!!!
Answer:
The area is 60. Thats all I know TwT
Step-by-step explanation:
a block that is 2 inches wide,3 inches long, and 2 inches tall. what is the volume of a tower that is built by 3 blocks?
Answer:
36
Step-by-step explanation:
length*Width*height
3*2*2=12
12*3=36
Please help!! Given that triangle ABC is congruent to triangle DEF, the measure of angle A = 70°, the measure of angle B = 60°, the measure of angle C = 50°, the measure of angle D = (3x + 10)°, the measure of angle E = (y/3 + 20)°, and the measure of angle F = (z^2 + 14)°, find the values of x, y, and z.
Answer:
Ok so since the triangles are congruent, that means that the corresponding angles are congruent. This means angle A = angle D, angle B = angle E, and angle C = angle F.
So:
angle A = angle D
70 = 3x + 10
3x + 10 = 70
3x = 60
x = 20
angle B = angle E
60 = y/3 + 20
y/3 + 20 = 60
y/3 = 40
y = 120
angle C = angle F
50 = z^2 + 14
z^2 + 14 = 50
z^2 = 36
z = 6 (or -6)
Answer:
Step-by-step explanation:
2a+3b=5
b=a-5 help please
Answer:
2a + 3b = 5
b = a - 5
Step-by-step explanation:
2a + 3b = 5
b = a - 5
You can write this another way:
2a + 3(a-5) = 5 ( I added the second formula in the first one )
Now you gotta factor out:
2a + 3a - 15 = 5
Here im gonna do plus 15
2a + 3a = 20 ==> 5a = 20
Now if you divide by 5, you get: a = 4
Now you can fill in the second formula again
b = a - 5 (ill fill this in now)
b = 4 - 5 = -1
So, this makes:
a = 4 , b = -1
Answer:
a = -2
b = -7
Step-by-step explanation:
the best method to solving this system of equations would be substitution since you are given an expression that equals one of the variables you're solving for (which is b = a - 5)
to begin, plug in a - 5 for b in the equation 2a + 3b = 5.
2a + 3b = 5 ⇒ 2a + 3(a - 5) = 5
the next step is to distribute 3 to a - 5. start with distributing 3 to a, which is just multiplying 3 · a. after that, you're left with a minus sign and 5, so that sign gets attached to the 5 and makes it a -5. distribute 3 to -5, which is just multiplying 3 · -5.
2a + 3(a - 5) = 5 ⇒ 2a + 3a - 15 = 5
since you have two terms with the variable a on one side of the equation (2a and 3a), combine the two like terms.
2a + 3a - 15 = 5 ⇒ 5a - 15 = 5
add 15 to both sides of the equation. on the left side, -15 and 15 cancel each other out because -15 + 15 = 0, leaving you with only 5a. on the right side of the equation, you have 5 - 15, which equals -10.
now your equation is 5a = -10.
divide both sides of the equation by 5. on the left side of the equation, you have 5a/5, which equals 1a, or a. on the right side, you have -10/5, which equals -2.
therefore a = -2.
now plug in -2 for a in b = a - 5 in order to solve for b!
b = a - 5 ⇒ b = -2 - 5
subtract -2 - 5.
b = -2 - 5 ⇒ b = -7
therefore b = -7.
your solutions are a = -2 and b = -7 :) i hope this helps! have a great day <3
A metallic cylinder of diameter 14 cm and height 49 cm is melted and cast into cubes with side 22 7 cm. How many cubes will be formed
Answer:
22 cubes are formed.
Step-by-step explanation:
Given that,
The diameter of the cylinder, d = 14 cm
Height of the cylinder, h = 49 cm
The side of the cube, a = 7 cm
Let there are n cubes formed. So,
[tex]n=\dfrac{\text{volume of cylinder}}{\text{side of cube}^3}\\\\=\dfrac{\pi r^2 h}{a^3}\\\\=\dfrac{\dfrac{22}{7}\times (7)^2 \times 49}{(7)^3}\\\\n=22[/tex]
Hence, there are 22 cubes that are formed.
fine the equation of the line that goes through the point (2,-9) that is parallel to the line with equation y=-3/4x
Answer:
y=6x
Step-by-step explanation:
g=-9/2
c=0
y=-9/2x
3/4x*-9/2
y=6x
How much water do you add to make 75% sugar syrup using 99g sugar?
Answer: You will need 33ml of water added
Step-by-step explanation:
The side lengths of a square are each 4p. By adding 3 to the length and subtracting 3 from the width, a rectangle is made. What is the area of the rectangle?
Answer: [tex]16p^{2} -9[/tex]
The area of the rectangle is [tex]16p^{2} -9[/tex].
What is a rectangle?A rectangle is one of the types of quadrilaterals in which all four angles are right angles or equal to 90 degrees. It is four-sided polygon in which the opposite sides are parallel and equal to each other.
For the given situation,
The side length of square = 4p
The length of rectangle, l = 4p+3
The width of rectangle, w = 49-3
The formula of area of rectangle is
[tex]A=lw[/tex]
⇒ [tex]A=(4p+3)(4p-3)[/tex] [∵ [tex](a+b)(a-b)=a^{2}-b^{2}[/tex] ]
⇒ [tex]A=(4p)^{2} -3^{2}[/tex]
⇒ [tex]A=16p^{2} -9[/tex]
Hence we can conclude that the area of the rectangle is [tex]16p^{2} -9[/tex].
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1. Bella and Caiden each bought a 12-oz can of soda. They are drinking their sodas at the
rates shown. Who is drinking their soda the fastest?
BELLA
CAIDEN
Min
Oz
0
12.
Ounces
20
18
16
14
12
10
8
6
4
2
2
3
4.5
4
2.
1 2 3 4 5 6 7 8 9 10
Minutes
Answer:
The question is incorrect. Please use a table or a diagram.