Children arrive at a house to do Halloween trick-or- treating according to a Poisson process at the unlucky rate of 13/hour. What is the probability that the time between the 15th and 16th arrivals will be more than 4 minutes ? (Hint: Think exponential.)
a) e e-2 = 0.1353
b) e-13/15 = 0.4204
c) e-1 = 0.3679
d) 1-2-1 = 0.6321

Answers

Answer 1

Answer:

0.4204 probability, option b.

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

Children arrive at a house to do Halloween trick-or- treating according to a Poisson process at the unlucky rate of 13/hour

13 arrivals during an hour, which means that the mean time between arrivals, in minutes is of [tex]\mu = \frac{13}{60} = 0.2167[/tex]

What is the probability that the time between the 15th and 16th arrivals will be more than 4 minutes ?

This is P(X > 4). So

[tex]P(X > 4) = e^{-0.2167*4} = 0.4204[/tex]

So the correct answer is given by option b.


Related Questions

The average of two numbers is 5x. If one of the numbers is 2x + 3, find the other number.

Answers

Answer:

8x-3

Step-by-step explanation:

Average of 2 numbers means add the two numbers and divide by 2

(y+z)/2 = 5x

Let z = 2x+3

(y+2x+3)/2 = 5x

Multiply each side by 2

y+2x+3 = 10x

Subtract 2x from each side

y+3 = 10x-2x

y+3 = 8x

Subtract 3

y = 8x-3

The other number is 8x-3

how many feet is in one centimeter and how many inches is in 1 feet?​

Answers

Answer:

12 inches r in a foot

0 feet r in a centimeter

Step-by-step explanation:

Answer:

0.032 feet in a centimeter and 12 inches in 1 foot

Step-by-step explanation:

hope it helps pls mark as brainliest!

A baseball team plays in a stadium that holds 58000 spectators. With the ticket price at $12 the average attendance has been 25000. When the price dropped to $9, the average attendance rose to 29000. Assume that attendance is linearly related to ticket price.

Required:
a. Find the demand function p(x), where x is the number of the spectators.
b. How should ticket prices be set to maximize revenue?

Answers

Answer:

We need to assume that the relationship is linear.

a) Remember that a linear relation is written as:

y = a*x + b

then we will have:

p(x) = a*x + b

where a is the slope and b is the y-intercept.

If we know that the line passes through the points (a, b) and (c, d), then the slope can be written as:

y = (d - b)/(c - a)

In this case, we know that:

if the ticket has a price of $12, the average attendance is 25,000

Then we can define this with the point:

(25,000 , $12)

We also know that when the price is $9, the attendance is 29,000

This can be represented with the point:

(29,000, $9)

Then we can find the slope as:

a = ($9 - $12)/(29,000 - 25,000) = -$3/4,000 = -$0.00075

Then the equation is something like:

y = (-$0.00075)*x + b

to find the value of b we can use one of the known points.

For example, the point (25,000 , $12) means that when x = 25,000, the price is $12

then:

$12 = (-$0.00075)*25,000 + b

$12 = -$18.75 + b

$12 + $18.75 = b

$30.75 = b

Then the equation is:

p(x) = (-$0.00075)*x + $30.75

b) We want to find the ticket price such that it maximizes the revenue.

The revenue will be equal to the price per ticket, p(x) times the total attendance, x.

Then the revenue can be written as:

r(x) = x*p(x) = x*( (-$0.00075)*x + $30.75 )

r(x) =  (-$0.00075)*x^2 + $30.75*x

So we want to find the maximum revenue.

Notice that this is a quadratic equation with a negative leading coefficient, thus the maximum will be at the vertex.

Remember that for an equation like:

y = a*x^2 + bx + c

the x-value of the vertex is:

x = -b/2a

Then in our case, the x-value will be:

x = -$30.75/(2*(-$0.00075)) = 20,500

Then the revenue is maximized for x = 20,500

And the price for this x-vale is given by:

p( 20,500) =  (-$0.00075)*20,500 + $30.75 = $15.375

which should be rounded to $15.38

what is the area of triangle JHK?​

Answers

9514 1404 393

Answer:

  4.18 square units

Step-by-step explanation:

The area is given by the formula ...

  A = 1/2bh

where b is the length of the base, and h is the perpendicular distance from the base to the opposite vertex.

  A = 1/2(2.2)(3.8) = 4.18 . . . square units

Please help I will mark brainliest to who ever is rigjt

Answers

Answer:

(1,0) and (0,4)

Step-by-step explanation:

Crosses the x axis

When f(x) will cross the x axis, the y coordinate will turn 0, so 0=-5^(x)+5, 5=5^(x) Which is possible when x=1. So (1,0)

Crosses the y axis

When f(x) will cross the y axis, the x coordinate will turn 0, so f(0)=-5^(0)+5, f(0)=-1+5=4. So (0,4)

Find the volume of the figure. If necessary, round the answer to the nearest whole number.

Answers

Answer:

V = 108 ft³

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Geometry

Volume of a Rectangular Prism Formula: V = lwh

l is lengthw is widthh is height

Step-by-step explanation:

Step 1: Define

Identify variables

l = 4 ft

w = 3 ft

h = 9 ft

Step 2: Find Volume

Substitute in variables [Volume of a Rectangular Prism Formula]:               V = (4 ft)(3 ft)(9 ft)Evaluate [Order of Operations]:                                                                      V = 108 ft³

Polynomials with odd degrees typically make a "u-shaped graph" and polynomials with even degrees typically make an "s-shaped" graph.
True
False

Answers

the answer is True :)

The statement that odd degree polynomials have a u-shaped graph and even degree polynomials have an s-shaped graph is FALSE.

What do odd degree polynomials look like on a graph?

Odd degree polynomials have branches that go in opposing directions which means that they will form an s-shaped graph.

Even degree polynomials on the other hand, have graphs that go in the same direction which is why they form u-shaped graphs.

In conclusion, the above statement is false.

Find out more on polynomials at https://brainly.com/question/9696642.

A dodgeball team at Lincoln Elementary School needs a team of 4 in order to compete against other schools. If there are 9 kids that want to be part of the team, how many different ways can you pick a team of 4

Answers

Answer:

3 ways

Step-by-step explanation:

You flip a coin that is not fair, the prbability of heads on each flip is 0.7. if the coin shows heads, you draw a marble from urn h with 1 blue and 4 red marbles. if the coin shows tails, you draw a marble from urn t with 3 blue and 1 red marble. Find the following probabilities:

a. The probability of choosing a red marble.
b. The probability of choosing a blue marble, given that the coin showed heads.
c. The probability that the coin showed tails, given that the marble was red.

Answers

Solution :

P(H) = 0.7  ;  P(T) = 0.3

If heads, then Urn H,  1 blue and 4 red marbles.

If tails, then Urn T ,  3 blue and 1 red marbles.

a).

P ( choosing a Red marble )

= P (H) x P( Red from Urn H) + P (T) x P( Red from Urn T)

[tex]$=0.7 \times \frac{4}{5} + 0.3 \times \frac{1}{4}$[/tex]

= 0.56 + 0.075

= 0.635

b).  If P (B, if coin showed heads)

If heads, then marble is picked from Urn H.

Therefore,

P (Blue) [tex]$=\frac{1}{5}$[/tex]

             = 0.2

c). P (Tails, if marble was red)

[tex]$=P (T/R) = \frac{P(R/T)}{P(R)} \ P(T)$[/tex]

Where P (R/T) = P ( red, if coin showed tails)

                        [tex]$=\frac{1}{4}$[/tex]

                        = 0.25 (As Urn T is chosen)

P (R) =  P (Red) = 0.635 (from part (a) )

P (T) = P (Tails) = 0.3

∴ [tex]$P(T/R) = \frac{0.25 \times 0.3}{0.635}$[/tex]

                = 0.118

                 

The perimeter of a triangle is 83 centimeters. If two sides are equally long and the third side is 8 centimeters longer than the others, find the lengths of the three sides.

Answers

Answer:

25, 33

Step-by-step explanation:

let the length of the one with equal sides be x

third side = x+8

x+x+x+8 = 83

3x+8 = 83

3x = 75

x = 25

x+8 = 25+8 = 33

If 2^x=3^y=12^z then prove it 2/x = 1/z -1/y.​

Answers

SOLUTION:

[tex] \begin{array}{l} 2^x = 3^y = 12^z \\ 2^x = 3^y = 2^{2z} \cdot 3^z \\ \Rightarrow 3 = 2^{\frac{x}{y}} \\ \Rightarrow 2^x = 2^{2z} \cdot 2^{\frac{xz}{y}} \\ \Rightarrow x = 2z + \frac{xz}{y} \\ \Rightarrow xy = 2zy + xz \\ \Rightarrow 2zy = xy - xz \\ \text{Dividing both sides by }xyz,\text{ we get:} \\ \dfrac{2}{x} = \dfrac{1}{z} - \dfrac{1}{y} \end{array} [/tex]

A bakery owner asked 150 customers to taste a new type of cookie and found that 60 people liked its taste.

Which of these is an example of descriptive statistics?

a.)
40% of the people in the city where the bakery is located like the taste of the cookie.
b.)
40% of the surveyed customers like the taste of the cookie.
c.)
40% of all the bakery's customers like the taste of the cookie.
d.)
40% of all people like the taste of the cookie.

Answers

Answer:[ 40% of the surveyed customers like the taste of the cookie is an example of descriptive statistics. ]

A bakery owner asked 150 customers to taste a new type of cookie and found that 60 people liked its taste. [ 40% of the surveyed customers like the taste of the cookie is an example of descriptive statistics. ]

An example of the disruptive statistics is  40% of the surveyed customers like the taste of the cookie is an example of descriptive statistics.

We have given that,

A bakery owner asked 150 customers to taste a new type of cookie and found that 60 people liked its taste.

We have to determine the

an example of descriptive statistics

What are the descriptive statistics?

Descriptive statistics is a set of brief descriptive coefficients that summarize a given data set representative of an entire or sample population.

A bakery owner asked 150 customers to taste a new type of cookie and found that 60 people liked its taste. 40% of the surveyed customers like the taste of the cookie is an example of descriptive statistics.

An example of the disruptive statistics is  that 40% of the surveyed customers like the taste of the cookie is an example of descriptive statistics.

To learn more about the statistics visit:

https://brainly.com/question/3493733

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A driveway is 2/5 kilometers long. Omar walks 1/3 of the driveway. How far does Omar walk?

Answers

Answer:

2/15 kilometers

Step-by-step explanation:

Multiply the distance by the fraction walked

2/5 kilometers * 1/3

2/5 * 1/3

2/15 kilometers

Find the value of this expression

Answers

Answer:

[tex] \frac{(3) ^{2} + 3}{3 - 1} [/tex]

[tex] \frac{9 + 3}{3 - 1} [/tex]

[tex] \frac{12}{2} [/tex]

= 6

Answer: 6

Replace the x with 3

3^2

=3x3

=9

9+3=

3-1=2


(12/2) =( 6/1)

= 6

What is A11 for the geometric sequence 3,072, −1,536, -768, −384...?

Answers

Answer:

3

Step-by-step explanation:

The general formula of the series is 3072/(-2)^(n-1). A11=3072/(-2)^10=3

Which equation is represented by the graph below?

Answers

Answer:

Hello,

Answer C

Step-by-step explanation:

Since ln(1)=0

if x=1 then y=4 ==> y=ln(x)+4

y=ln(x) is translated up for 4 units.

10. (30-i)-(18+6i)+30i

Answers

Answer:

[tex]12+23i[/tex]

Step-by-step explanation:

[tex](30−i)−(18+6i)+30i[/tex]

[tex]30−i−18−6i+30i[/tex]

[tex]12−i−6i+30i[/tex]

[tex]12−7i+30i[/tex]

[tex]12+23i[/tex]

Hope it is helpful....

Probability that a person is chosen at random

Answers

Answer:

152 / 370

Step-by-step explanation:

Total number of people

152+218 = 370

P( own a dog) = people said yes / total

                       = 152 / 370

A 230 pound man, a 140 pound woman, a 750 pound crate of equipment, an 80 pound bag of concrete. What percent of the total weight was concrete?
What percent of the total weight was human?

Answers

Concrete percent: 80/1200 = .0666666 = 6.7%
Human percent: 370/1200 = .308333 = 30.8 %

what is the slope and point

Answers

Answer:

Step-by-step explanation:

x = either 100 , 140 , or 120

Answers

ANSWER EXPLANATION: 140

The circle is split into halves, so we know that the degree for the circumference is 180°. Then to find x, you add 30° and 10° which is 40° and subtract from 180° to get 140°.

If the terminal side of an angle (θ) goes through the point (4 , -3) what is (θ)?

Answers

Answer:

The family of directions of the given vector is represented by [tex]\theta = 323.130^{\circ} \pm 360\cdot i[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex].

Step-by-step explanation:

According to the given information, vector stands in the 4th Quadrant ([tex]x > 0[/tex], [tex]y < 0[/tex]) and direction of the vector ([tex]\theta[/tex]) in sexagesimal degrees, is determined by following definition:

[tex]\theta = 360^{\circ} - \tan^{-1} \left(\frac{|y|}{|x|} \right)\pm 360\cdot i[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex]

Please notice that angle represents a function with a periodicity of 360°.

If we know that [tex]x = 4[/tex] and [tex]y = -3[/tex], then the direction of the vector is:

[tex]\theta = 360^{\circ}-\tan^{-1}\left(\frac{|-3|}{|4|} \right)\pm 360\cdot i[/tex]

[tex]\theta = 323.130^{\circ} \pm 360\cdot i[/tex]

The family of directions of the given vector is represented by [tex]\theta = 323.130^{\circ} \pm 360\cdot i[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex].

The percent of data between z=0.23 and z = 1.27 is
(Round to two decimal places as needed.)

Answers

Answer:

0.40905 - 0.10204 = .30701 = 30.7 %

Step-by-step explanation:

0.23 0.40905

1.27 0.10204

if point B is the midpoint of points A and C, find the value of x and AC. AB= 5x - 2, BC= 9x -10

Answers

9514 1404 393

Answer:

x = 2AC = 16

Step-by-step explanation:

The midpoint divides the segment into two equal lengths:

  AB = BC

  5x -2 = 9x -10

  8 = 4x

  2 = x

  AB = 5(2) -2 = 8

  AC = 2AB = 2(8) = 16

plzzzzz helppp i will give brainlyist

Answers

Answer:

C. (2)

Step-by-step explanation:

an integer is a WHOLE NUMBER

have an amazing day :)

Answer:

2 is an integer

Step-by-step explanation:

An integer is a whole number, it does not have a fractional part

WORTH 100 POINTS!
The function h(x) is quadratic and h(3) = h(-10) = 0. Which could represent h(x)?

1) h(x) = x2 - 13x - 30
2) h(x) = x2 - 7x - 30
3) h(x) = 2x2 + 26x - 60
4) h(x) = 2x2 + 14x - 60

Answers

Answer:

h(x) = 2x^2 +14x -60

Step-by-step explanation:

A quadratic is of the form

h(x) = ax^2 + bx +c

h(3) = h(-10) = 0

This tells us that the zeros are at x=3 and x = -10

We can write the equation in the form

h(x) = a( x-z1)(x-z2) where z1 and z2 are the zeros

h(x) = a(x-3) (x- -10)

h(x) = a(x-3) (x+10)

FOIL

h(x) = a( x^2 -3x+10x-30)

h(x) = a(x^2 +7x -30)

Let a = 2

h(x) = 2x^2 +14x -60

It means

zeros are 3 and -10

Form equation

y=x²-(3-10)x+(-10)(3)y=x²+7x-30

Multi ply by 2

y=2x²+14x-60

Option D

A tour bus is traveling along a triangular path. The three straight lines form a right triangle. One leg of the triangle represents a distance of 8 miles. The other leg of the triangle is 4 miles shorter than the hypotenuse. What is the length of the hypotenuse of this​ triangle? Of the other​ leg?

Answers

Answer:

Hypotenuse=10 miles.

Short leg=6 miles.

Step-by-step explanation:

Set up triangle, leg 8 miles, hypotenuse x miles, short leg x-4 miles.Input into Pythagoras theorem.Simplify.

How to divided 245 by 70
Show your work

Answers

Answer:

Step-by-step explanation:

Hello!

          2          4              5          ∟ 70

        -2           1                                 3, 5

------------------------

                      3              5        0

                      3              5       0

                -   --------------------------------

                     0                0        0

Translate this phrase into an algebraic expression.
61 less than twice Jenny's age
Use the variable j to represent Jenny's age.

Answers

ANSWER: 2j-61
j = Jenny's age

find the area of the triangle

Answers

9514 1404 393

Answer:

  108 cm²

Step-by-step explanation:

The area of a triangle is given by the formula ...

  A = 1/2bh

where b represents the base length, and h represents the height--the perpendicular distance from the base to the opposite vertex. The area of this triangle is ...

  A = 1/2(12 cm)(18 cm) = 108 cm²

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