1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Illusion [34]
2 years ago
15

Suppose lightning strikes at an average of 1.4 strikes per minute during a particular storm. You play the following game: if the

next strike occurs within the next minute, you win 3 dollars, if the next strike occurs between 1 minute and 2 minutes from now, you win 5 dollars, and if the next strike occurs more than 2 minutes from now, you win 1 dollar. How much should someone be charged to play this game, to make it a "fair game?"
Mathematics
1 answer:
ZanzabumX [31]2 years ago
4 0

Answer:

$3.25

Step-by-step explanation:

Given that:

Mean, λ = 1.4

Strike within next minute = $3 won

Strike between one and 2 minutes = $5

Strike more than 2 minutes = $1

Probability that next strike occurs within the next minute :

Using poisson :

P(x < 1) = 1 - e^-(λx) ;

P(x < 1) = 1 - e^-(1.4*1) = 1 - e^-1.4

P(x < 1) = 1 - 0.2465969

P(x < 1) = 0.7534030

Next strike occurs between 1 and 2 minutes :

(1 < x < 2) :

P(x < 2) - P(x < 1)

P(x < 2) = 1 - e^-(λx) ;

P(x < 2) = 1 - e^-(1.4*2) = 1 - e^-2.8

P(x < 2) = 1 - 0.0608100

P(x < 2) = 0.9391899

P(x < 2) - P(x < 1)

0.9391899 - 0.7534030 = 0.1857869

P(striking after 2 minutes)

P(x > 2) = e^-(λx) ;

P(x > 2) = e^-(1.4*2) = e^-2.8

P(x > 2) = 0.0608100

Amount charged :

(0.7534030 * 3) + (0.1857869 * 5) + (0.06081 * 1)

= 3.2499

= $3.25

You might be interested in
Find the missing angles in the following triangles.
Bezzdna [24]

Answer:

Step-by-step explanation:

angles in triangle = 180

1. 180 - (70+45) = x = 65

2. x = 35

180 - 110 = 70

70/2 = 35 (isosceles triangle)

3. x = 113, y = 67

180 - (62 + 51) = y = 67

Angles on a line = 180

180 - 67 = x = 113

4. x = 60, y = 50

x = 180 - 120 = 60

y = 180 - (60 + 70) = 50

answers in degrees.

8 0
2 years ago
F(x)=2x^2 -5 , simplify f(x+h)/h , where h≠0
7nadin3 [17]

Answer:

\huge\boxed{\dfrac{f(x+h)}{h}=\dfrac{2x^2+4xh+2h^2-5}{h}}

\huge\boxed{\dfrac{f(x+h)}{h}=\dfrac{2x^2-5}{h}+4x+2h}

Step-by-step explanation:

f(x)=2x^2-5\\\\\dfrac{f(x+h)}{h}=\dfrac{2(x+h)^2-5}{h}=\dfrac{2(x^2+2xh+h^2)-5}{h}\\\\\dfrac{f(x+h)}{h}=\dfrac{2x^2+4xh+2h^2-5}{h}\\\\h\neq0

4 0
2 years ago
Can some one help me with these questions thank you
lisov135 [29]
Positive and a positive, will always be a positive because theyre both the same. If two things are the same, theyre equal. ( this is from what ik,I read it as a common sense question)
3 0
3 years ago
Suppose you start with a full tank of gas (14 gallons) in your truck. After driving 4 hours, you now have 2
Alex73 [517]

Answer:

  a) -3 gallons per hour

  b) y = -3x +14

Step-by-step explanation:

Rate of change is computed by dividing the amount of change by the interval over which it occurred.

<h3>a)</h3>

Here the amount of gas decreased from 14 to 2 gallons, so a decrease of 14-2 = 12 gallons. That occurred over a 4-hour period, so the rate of change is (-12 gallons)/(4 hours) = -3 gallons/hour.

__

<h3>b)</h3>

The initial amount was 14 gallons, so the equation for the line describing remaining gas will be ...

  y = -3x +14 . . . . gas in the tank after x hours

4 0
2 years ago
Help I need to know plz
lana66690 [7]

Answer:

4 quarts

Step-by-step explanation:

3 gal = 12 quarts

4 pt = 2 quarts

24 cup = 6 quarts

2+6=8 12-8=4

7 0
3 years ago
Other questions:
  • How do I write this as a math equation: it's number 13
    12·1 answer
  • Colby worked three more hours on tuesday than he did on monday. on wednesday, he worked one hour more than twice the number of h
    11·1 answer
  • I don’t know how to find the inequalities
    13·1 answer
  • If coordinate (3,1) is translated down 2 and left 4 what will the new coornidate be
    5·1 answer
  • What is another word for translation?<br> A.flip<br> B.turn<br> C.slide<br> D.fall
    6·2 answers
  • 30b+53≥18b−83 please i end up with 11.33333333 but i need it as a fraction
    9·2 answers
  • What type of number is 2 2/3 ? whole number, integer, rational, irrational ?
    15·2 answers
  • Write the equation of a circle with a center at (-12, -11) and a radius of 7.​
    13·1 answer
  • Find the approximate area of a semicircle with a radius of 6 centimeters.
    8·1 answer
  • This is for today someone help me!!!
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!