Approximately 297 million guests visit the 400 American amusement parks annually, and take 1.7 billion safe rides. The National Safety Council publishes a report titled "Fixed-Site Amusement Ride Injury Survey" for the International Association of Amusement Parks and Attractions. The number of injuries per million patron-rides, X, has a Poisson distribution with parameter 0.8. In one million patron-rides, what is the probability that there are
a) No injuries?
b). More than TWO injuries?

Answers

Answer 1

The probabilities are given as follows:

a) No injuries: 0.4493 = 44.93%.

b) More than two injuries: 0.0474 = 4.74%.

What is the Poisson distribution?

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following equation:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

x is the number of successes that we want to find the probability of.e = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval or range of values of the input parameter.

The mean for this problem is of:

[tex]\mu = 0.8[/tex]

The probability of no injuries is of P(X = 0), hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-0.8}(0.8)^{0}}{(0)!} = 0.4493[/tex]

The probability of more than two injuries is of:

P(X > 2) = 1 - P(X <= 2)

In which:

P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2)

Hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-0.8}(0.8)^{0}}{(0)!} = 0.4493[/tex]

[tex]P(X = 1) = \frac{e^{-0.8}(0.8)^{1}}{(1)!} = 0.3595[/tex]

[tex]P(X = 2) = \frac{e^{-0.8}(0.8)^{2}}{(2)!} = 0.1438[/tex]

Then:

P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.4493 + 0.3595 + 0.1438 =  0.9526.P(X > 2) = 1 - P(X <= 2) = 1 - 0.9526 = 0.0474.

More can be learned about the Poisson distribution at https://brainly.com/question/7879375

#SPJ1


Related Questions

I'm going to try this one more time...

Which of these characteristics of a star make it most likely to become a black hole? Select the TWO!!!! correct answers.

A. Its mass is equal to that of the sun.

B. It has an abundant supply of hydrogen.

C. Its mass is greater than 20 times the mass of the sun.

D. It is dying.

Answers

Answer and Step-by-step explanation:

C and D  is the answer.

It needs a lot of mass so that it can collapse on itself to form a black hole, and when it dies, it also collapses on itself, forming a black hole.

A is incorrect because the mass of our sun hasn't made it to collapse, and it still has some billions of years before the mass increases.

B is incorrect because the hydrogen needs to be depleted in order for the sun/star to start the nuclear process.

#teamtrees #PAW (Plant And Water)

Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.

Answers

Answer:

u can download the gauthmath app it's very helpful i PROMISE :)

Answer: Answer: −9±√−255/ 24

Step-by-step explanation:

12a2+9a+7=0

a=12, b=9, c=7

12a^2+9a+7=0

a=12, b=9, c=7.

−b±√b2−4ac/ 2a

−(9)±√(9)2−4(12)(7)/ 2(12)

Help.....ASP Please help right now

Answers

The triangle with side lengths given in the question can be classified as a scalene triangle.

What is a scalene triangle?

A scalene triangle is a type of triangle in which none of its three given length of sides are equal. It can be differentiated from other types with respect to  this property.

A triangle is a plane shape which can be described by three sides and three measure of internal angles. Some other types of triangle are: equilateral, obtuse, isosceles etc. The sum of all internal angles of a triangle is 180^o

Considering the given length of sides in the question, it can be proven the the only type of triangle that can be formed is a scalene triangle. Therefore, the triangle can be classified as a scalene triangle.

Learn more about scalene triangle at https://brainly.com/question/16589630

#SPJ1

Can you let me know the answer please

Answers

Answer:

The answer is A

Step-by-step explanation:

When looking at this image, look at A, notice how it says y and the equal to symbol is facing it? then notice at the end of answer a is -4, look at the graph and the line intercepts -4, remeber, the end number, whether positive or negative will always be the on the y axis

Pls help me I’ll give thxs and brainiest if you answer correctly to both exercises

Answers

Answer:

Activity 1

1. a.8, b.4, c.8, d.12

2. a.10, b.8, c.20, d.40

3. a.16, b.9, c.40, d.27

Activity 2

1. a.10, b.40, c.15

2. a.4, b.35, c.14

3. a.80, b.20, c.2.5

150 people went to see "Ode to Algebra" performed in the school auditorium. If the number of children that attended the performance was c, how many adults attended?​

Answers

Answer:

150-c

Step-by-step explanation:

150= total

c= children

adults=x

x=150-c

Mrs. Avery is going to randomly select one student from her class to read a poem out loud. There are 15 boys and 13 girls in her class.
What is p (boy)?
If necessary, round your answer to 2 decimal places.

Answers

Answer:

53.57%

Step-by-step explanation:

P(boy) = 15/28 which is 53.57%

Answer:

1.87

Step-by-step explanation:

I found another brainly answer to this question.

Carl wants to find the product 30×56.
Which of the following best explains how he can find the product mentally?
A.


He knows that 30÷5 is 6. He then multiplies 6 by 6 to get 36.
B.


He knows that 30×66is 30. He then subtracts 1 from 30 to get 29.
C.


He knows that 3×6=18. He then adds 18 and 5 to get 23.
D.


He knows that 30×16is 5. He then multiplies 5 by 5 to get 25.

Answers

Answer:

Your answer will be D. He knows that 30 × 16 is 5 then multiples 5 by 5 to get 25.

URGENT!! 50 POINTS!!! based on the linear table of ordered pairs, what is the y intercept?

Answers

Answer:

y- intercept = 0

Step-by-step explanation:

the linear function can be expressed in slope- intercept form, that is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁ , y₁ ) = (4, - 4) and (x₂, y₂ ) = (- 2, 2) ← 2 ordered pairs from the table

m = [tex]\frac{2-(-4)}{-2-4}[/tex] = [tex]\frac{2+4}{-6}[/tex] = [tex]\frac{6}{-6}[/tex] = - 1

the line crosses the y- axis at (0, 0 ) ⇒ c = 0

y = - x + 0, that is

y = - x ←  is the linear function defining the ordered pairs in the table

Pythagorean Theorem & irrational Numbers Question
Which of the following could not be the lengths of sides of a
right triangle?
Select one:

8, 10, 12

6, 8, 10

9, 12, 15

8, 15, 17

Answers

Answer:

2nd

Step-by-step explanation:


I’ll give brainliest

Answers

Answer:

Step-by-step explanation:

P of red or green = (40 red+ 10 green)/ (40 red +50 yellow+10 green)

= 50/ 100= 1/2

97 = 10x + 27 need help!!

Answers

Answer:

x=7

Step-by-step explanation:

97 = 10x + 27

97 - 27 = 10x

70 = 10x

70/10 = x

7=x

Answer:

X=7

HOPE THIS HELPS

-Todo ❤️

Step-by-step explanation:

97=10x+27

-27. -27

70=10x

/10. /10

X=7

I am giving away 10 points to anybody who provides correct answers with explanations.

Answers

Answer:

[tex]5)\ f(n) = 4v[/tex]

[tex]6)\ \frac{1}{4}n[/tex]

[tex]7)\ True[/tex]

This might not be correct though. I'm only in middle school lol. I am sure about the last one.

Mhanifa please help! This is due soon

Answers

Answer:

1) x²=256-64

x=8√3

2). x²=200+81

x=√281

3). x²=169+36

x=√205

3).

Step-by-step explanation:

here's your solution

==> in figure 1,

= perpendicular^2 = hypotenuse^2 - base^2

= x^2 = 16^2 - 8^2

= x^2 = 256 - 64

= x^2 = 192

= x = √192

= x = 13.85

==> in figure 2,

= hypotenuse^2 = Perpendicular^2 + base^2

= x^2 = 40^2 + 9^2

= x^2 = 1600 + 81

= x^2 = 1681

= x = √1681

= x = 41

==> in figure 3,

= hypotenuse^2 = Perpendicular^2 + base^2

= x^2 = 13^2 + 6^2

= x^2 = 169 + 36

= x^2 = 205

= x = √205

= x = 14.31

[tex]hope \: it \: helps.....[/tex]

heh help please my bootiful people lol

Answers

Answer:

x = 52

Step-by-step explanation:

128 + x = 180

180 - 128 = x

x = 52

Have a nice day!

How do I solve these problems?

Answers

Answer:

1.) The 1ˢᵗ three term is (-32), (-7) and 18

2.) The 1ˢᵗ three term is 127, 106 and 85

Step-by-step explanation:

1.)

Here,

First Term = a₁ = - 32

Common Difference = (d) = 25

Now, For 1ˢᵗ three term,

n = 1

a₁ = - 32

n = 2

aₙ = a + (n - 1)d

a₂ = (-32) + (2 - 1) × 25

a₂ = (-32) + 1 × 25

a₂ = (-32) + 25

a₂ = -7

n = 3

aₙ = a + (n - 1)d

a₃ = (-32) + (3 - 1) × 25

a₃ = (-32) + 2 × 25

a₃ = (-32) + 50

a₃ = 18

Thus, The 1ˢᵗ three term is (-32), (-7) and 18

2.)

Here,

First Term = a₁ = 127

Common Difference = (d) = -21

Now, For 1ˢᵗ three term,

n = 1

a₁ = 127

n = 2

aₙ = a + (n - 1)d

a₂ = 127 + (2 - 1) × (-21)

a₂ = 127 + 1 × (-21)

a₂ = 127 - 21

a₂ = 106

n = 3

aₙ = a + (n - 1)d

a₃ = 127 + (3 - 1) × (-21)

a₃ = 127 + 2 × (-21)

a₃ = 127 - 42

a₃ = 85

Thus, The 1ˢᵗ three term is 127, 106 and 85

-TheUnknownScientist

A bakery sells chocolate cupcakes and vanilla cupcakes. It sold 400 cupcakes in a day,
and 17% of them were vanilla. How many of the cupcakes sold that day were
chocolate?

Answers

Answer:

332 chocolate cupcakes.

Step-by-step explanation:

17% of 400 = 68

400 - 68 = 332

Write 1 and 3/8 as an improper fraction.

Answers

1 3/8 as an improper fraction is 11/8

Answer:

1 3/8 = 11/8 as a improper answer

Step-by-step explanation:

You have to make your whole number into a numerator along with your original numerator.

Improper fraction: When your numerator is greater than your denominator.

Show that f is continuous on (−[infinity], [infinity]). f(x) = 1 − x2 if x ≤ 1 ln(x) if x > 1
On the interval
(−[infinity], 1),
f is function; therefore f is continuous on
(−[infinity], 1).
On the interval
(1, [infinity]),
f is function; therefore f is continuous on
(1, [infinity]).

Answers

The function [tex]$$f(x)= \begin{cases}1-x^2 & x \leqslant 1 \\ \ln (x) & x \geqslant 1\end{cases}$$[/tex]  is continuous on (-∞, ∞).

As per the given data the function f(x) is given by:

[tex]$$f(x)= \begin{cases}1-x^2 & x \leqslant 1 \\ \ln (x) & x \geqslant 1\end{cases}$$[/tex]

Here we have to determine that the function f(x) is continuous on (-∞, ∞)

If we show that f(x) is continuous at x = 1 then f(x) is continuous on (-∞, ∞)

What are continuous function?

A continuous function in mathematics is one where changes in the parameter cause constant changes in the function's value (i.e., a change without a leap). This shows that there are no abrupt changes in value or discontinuities.

To show f(x) is continuous at x = 1

[tex]\lim _{x \rightarrow 1^{-}} f(x)=\lim _{x \rightarrow 1^{+}}[/tex] f(x)

[tex]\rightarrow \lim _{x \rightarrow 1^{-}} f(x) & =\lim _{x \rightarrow 1^{-}}\left(1-x^2\right) \\[/tex]

= 1 - 1

= 0

[tex]\lim _{x \rightarrow 1^{+}} f(x) & =\lim _{x \rightarrow 1^{+}} \ln (x) \\[/tex]

= ln 1

= 0

Therefore  [tex]\lim _{x \rightarrow 1^{+}} f(x) & =\lim _{x \rightarrow 1^{-}} f(x)-0[/tex].

Hence f(x) is continuous on (-∞, ∞)

For more questions on Limits

https://brainly.com/question/20067425

#SPJ4

What should be added to 7x^2 5x 1 to get 3x^2 4x 7?

Answers

The value should be added will be [tex]y = -4x^{2} +9x+6[/tex]

Now, According to the question:

Let the value y be added to  [tex]7x^2-5x+1[/tex] to give [tex]3x^2+4x+7[/tex]

y =  [tex]3x^2+4x+7[/tex] - ( [tex]7x^2-5x+1[/tex])

y = [tex]3x^{2} +4x+7-7x^{2} +5x-1[/tex]

Combine like terms:

y = [tex]3x^{2} -7x^{2} +4x+5x+7-1[/tex]

Calculate the subtraction and addition.

[tex]y = -4x^{2} +9x+6[/tex]

Hence, The value should be added will be [tex]y = -4x^{2} +9x+6[/tex].

Learn more about Addition at:

https://brainly.com/question/24289893

#SPJ4

The complete question is this:

What should be added to  [tex]7x^2-5x+1[/tex] to get [tex]3x^2+4x+7[/tex] ?

A scale drawing of a square has a side length of 8 inches. The drawing has a scale of 1 in. : 6 mi. Find the actual perimeter and area of the square.

Perimeter $=$
mi

Area $=$
mi $^2$

Answers

Answer:

192 mi

2,304 mi²

Step-by-step explanation:

actual side length = 8×6 = 48 mi

so, perimeter of square = 4 × 48 = 192 miles

the area of square = 48×48 = 2,304 sq miles

b. Consider a circle with centre O and radius of 4 units. The distance of point P is 2 units from centre. Find the distance of inverse of point P' from the centre O.​

Answers

The distance of the inverse of point P' from the centre O is also 4 units. This is because the inverse of a point is the point on the opposite side of the circle from the original point, and the radius of the circle is 4 units. Therefore, the distance of the inverse of point P' from the centre O is also 4 units.

Find the missing lengths.

Answers

Answer:

x = 5√2

Step-by-step explanation:

The triangle on the right is a special right triangle, so we know that the adjacent side to 60° is 5. Since the left triangle is a 45-45-90, the hypotenuse is the leg times √2, so the value of x is 5√2

Please answer the question in the picture and show your work! I got tan= square root of 2 but I’m not sure if that’s right and if there’s more answers since it wants all values of tan. This is due tomorrow please help!

Answers

Answer:

tan(θ) is undefined.

Step-by-step explanation:

Recall that tan(θ) = sin(θ) / cos(θ). We are given that sin(θ) = -1. Hence:

[tex]\displaystyle \tan\theta=\frac{\sin\theta}{\cos\theta}=-\frac{1}{\cos\theta}[/tex]

Since 1 / cos(θ) = sec(θ):

[tex]\tan\theta=-\sec\theta[/tex]

We can square both sides:

[tex]\tan^2\theta=\sec^2\theta[/tex]

From the Pythagorean Identity:

[tex]\tan^2\theta+1=\sec^2\theta[/tex]

Substitute:

[tex]\tan^2\theta+1=\tan^2\theta[/tex]

So:

[tex]1\neq0[/tex]

Since we acquire an untrue statement, no solutions exist.

If needed, refer to the unit circle. Recall that sin(θ) only equals -1 when θ = 3π/2 (on the interval [0, 2π)). At 3π/2, cos(θ) = 0. Since tan(θ) = sin(θ) / cos(θ), tan(θ) is undefined whenever sin(θ) = -1 (or 1).

What is an unsolvable problem?

Answers

As a result, it may be shown that the answer to the algorithm problem at hand is a halting problem, which is indecidable and thus impossible to solve.

Algorithm : what is it ?

No matter the circumstance, algorithms are fundamentally problem solvers of expression ; they exist to identify, resolve, and frequently automate of solution to a specific problem. Algorithms are frequently introduced in area introductory textbooks by characterizing them as "a series of steps to complete a problem."

Here,

one of the most common problems that hasn't been solved is the stopping problem. It asks the following question:

Does M come to a standstill when given the input w for any Turing machine with the parameters alphabet = a, b, and any string w over

It can be shown that the halting problem cannot be resolved since it is indecisive.

As a result, it may be shown that the answer to the algorithmic problem at hand is a halting problem, which is indecidable and thus impossible to solve.

To know more about algorithm , visit:

brainly.com/question/29289479

#SPJ4

What are the 3 types of trigonometry?

Answers

the main three types of trigonometry are ,

1- sine angle (sin Q)

2- cosine angle (cos Q)

3- tangent angle (tan Q)

all the other types of trigonometry are related to these three types only.

sine angle

we can find out the sine angle by taking perpendicular of the triangle divided by hypotenuse of the triangle. sine angle is a acute angle.

cosine angle

we can find out the cosine angle by taking base of the triangle divided by hypotenuse of the triangle. cosine angle is a acute angle.

tangent angle

we can find out the sine angle by taking perpendicular of the triangle divided by base of the triangle.

Learn more about trigonometric ratios here :-

https://brainly.com/question/25122825

#SPJ4

In 2010, the population of a city was 237,000. From 2010 to 2015, the population grew by 7.6%. From 2015 to 2020, it fell by 4.7%. To the nearest whole number, by what percent did the city grow from 2010 to 2020?

Answers

The population of the city grew from 2010 to 2020 by 13.37 %

What is percentage?

A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.

Given that, In 2010, the population of a city was 237,000. From 2010 to 2015, the population grew by 7.6%. From 2015 to 2020, it fell by 4.7%.

The population in 2015 =

A = P (1+r)ⁿ

A = final population.

P = Initial population.

r = rate

n = time

The population in 2015 =

A = 237,000(1+0.076)⁵

A = 341829.629

The population in 2020 =

A = P (1-r)ⁿ

A = 341829.629(1-0.047)⁵

A = 268704.047

Percent grow = 268704.047 - 237,000 / 237,000 × 100

= 31704.047 / 237,000 × 100

= 13.37 %

Hence, the population of the city grew from 2010 to 2020 by 13.37 %

Learn more about percentage, click;

https://brainly.com/question/29306119

#SPJ1

PLS WHAT IS THE VALUE OF X SOMEONE

Answers

Answer:

It would be 166 degrees.

Step-by-step explanation:

Do 180-97 to get 83 degrees

Since the triangle is a isosceles triangle, the opposite side of it would also be 83 degrees, so 83+83

With this, do 180-83-83 to get 14 degrees for the third interior angle

Last, subtract this from 180 to get the value of x, 166 degrees.

Hope that helps.

( 1/2 ) ^2
HELP!
ME!

Answers

Answer:

1/4 is the answer

just multiply 1/2 x 1/2

hope this helps

have a good day :)

Step-by-step explanation:

1/2 x 1/2 =1/4 ^2 to just multiply the inside by itself twice.

I NEED HELPPPPPPPPPPPPP

Answers

Answer:

y= 12

Step-by-step explanation:

3(-12)-24

-36-24

-12

Other Questions
Click to review the online content. Then answer the question(s) below, using complete sentences. Scroll down to view additional questions.Online Content: Site 1How did artists influence the financial success of Florence? Describe the method some artists used during the 14th century. What is meant by workforce trends? IMPORTANTAnswer the two questions below please. Will wants to buy a new TV for $900. What is the minimum payment that she must pay each month to avoid paying interest on her credit card? There are two chords AB and CD in a circle. |AB| = 10 cm, |CD| 10 cm, |CD| = 8 cm and the radius of the circle is 12 cm. What is the distance of each chord from the centre of the circle? PLEASE SOMEONE HELP. Im FAILING MATH . WILL NAME BRAINLIEST AND ITS WORTH 30 points!! Classify the reaction in each of the following equations. a. FeCl2 (aq) + Mg MgCl2 (s) + Fe(s) b. NH3 (g) N2 (g) + H2 (g) What is the DNA test examining specifically? It is comparing the protein enzymes. It is looking for matching patterns of alleles. It is trying to find a mutation. It is examining the lipid level of the cells. What are the 3 parts of a quadratic equation? Amelia just received a $9000 bonus. She has been advised to invest hei bonus in two accounts, one yielding 3% per annum and the other 8% per annum. If Amelia wants to earn $580 in interest, how much should she put in each account Help againnnnnnnnnnnnnnnnnnnnnnnnn Your campaign about chest pains is complete, and research shows that you were most successful at reaching people who were already well-informed about heart attack warning signs. Unfortunately, low-income individuals are at the highest risk for heart attacks, and these individuals were not as influenced by the campaign message. The occurrence of this scenario in campaign efforts is an example of: Find the work done by a force of 200 pounds acting in the direction in moving an object 75 feet from (0, 0) to (-75, 0). What role did WW1 play in the current Israeli crisis? A family made three trips to the grocery store in one month. What was the total amount of money spent on groceries for the month? Max's living room is 4 meters wide and 7 meters long. He wants to put a border around the top of the room. The cost of the border is $0.84 per meter. How much will it cost to buy enough of the border to go around the room? A screw has _____ over the cylinder. What is (3/2) raised to the power of -3?What is (3/2)^-3? Which of the following is not a complete sentence Why do the graduate students create UbiSketch? (This is an i-Ready question) Describe how you would identify mutations that are dominant. Describe how you would identify mutations that are dominant. To identify dominant mutations, breed the mutant individual to a mutant individual. Dominant mutations will be visible in the F1 generation. To identify dominant mutations, breed the wild-type individual to a wild-type individual. Dominant mutations will be visible in the F1 generation. To identify dominant mutations, breed the mutant individual to a mutant individual. Dominant mutations will be visible in the F2 generation. To identify dominant mutations, breed the mutant individual to a wild-type individual. Dominant mutations will be visible in the F2 generation. To identify dominant mutations, breed the mutant individual to a wild-type individual. Dominant mutations will be visible in the F1 generation.