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?"

Answers

Answer 1

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


Related Questions

x – 1/4=1/2 what is x?

Answers

Answer:

x= 3/4

Step-by-step explanation:

x-1/4=1/2

 +1/4  +1/4

x=3/4

x is 3/4 ; 3/4-1/4=1/2

Together, Dien and Jane can eat 2/3 of a pizza in 4 seconds. How long would it take each of them to eat the whole pizza alone if Jane can eat a pizza 5 seconds faster than Dien?

Answers

Answer:

Dien - 15 seconds, Jane - 10 seconds

Step-by-step explanation:

Together:

2/3 of pizza ⇒ 4 secondsFull pizza ⇒ 4 ÷ 2/3 = 6 seconds

Dien needs  x seconds to eat pizza

Jane needs  x - 5 seconds to eat pizza

In one second, Dien can eat 1/x, Jane can eat 1/(x - 5), together 1/6 of a pizza

1/x + 1/(x - 5) = 1/6x(x - 5) = 6(x + x - 5)x² - 5x - 12x + 30 = 0x² - 17x + 30 = 0(x - 15)(x - 2) = 0x = 15 (x = 2 is discounted as not realistic)

Dien can eat a pizza in 15 seconds, Jane can eat a pizza in 10 seconds

23, 75, 79, 99, 105, 110, 110, 142, 149, 168, 168, 170, 183, 195, 202
Find the IQR, show your work.

HELP!

Answers

Answer:

the IQR is 71

Step-by-step explanation:

the Xl is 99 and the Xu is 170. Xu-Xl=71

I need help with this question please, if anyone would be kind enough to give me the correct answer, in return I would gladly rate a 5 star and give brainliest (:

Answers

-4(3n + 5) is the answer

Kareem borrowed money from a credit union for 6 years and was charged simple interest at an annual rate of 8%. The total interest that he paid was $240 . How much money did he borrow?

Answers

Answer:

I think 220.8

  Step-by-step explanation:

math come help plese

Answers

Answer:

74

Step-by-step explanation:

36 is 18% of what number

Answers

Answer:

200

Step-by-step explanation:

Do 36/0.18

200

200 because 100% divided by 18 = 5.55555556 and 5.55555556x36=200

What was the temperature in the city with an elevation of -9?

Answers

Answer:

7(u will trace the _9 in x axis to y axis where the blue dot is the value there will be our answer and that is 7)

Which number line shows the solution to the inequality?

Answers

the answer is c
hope this helps :)

Answer:

C

Step-by-step explanation:

I was taking the test and finished an hour ago

Please help is for noww

Answers

Answer:

25¢

Step-by-step explanation:

Answer: Answer: $0.25

Step-by-step explanation:

Let x be the total money was in her wallet and m be the cost of each petunia,

From the given table , the money left in wallet after purchasing 2 petunia =$6.50

Then we have the following equation: 6.50 = x - 2m - - - - - ( 1 ) Also, the money left in wallet after purchasing 8 petunia =$5 Then, we have 5 = x - 8m - - - - - - - - - ( 2 ) Subtracting (2) from (1) , we get 6.50 - 5 = -2m - (8m) then -2m + 8m = 1.50 then we 6m = 1.50. m = 1.50/6 = 0.25 hope this helped.

Plz help if correct ill give brailiest

Answers

Answer:

At most 5

At least 0

Step-by-step explanation:

22 - 17 = 5

You can't have no more than 5, and you can have none join at all.

Answer:

At the most, it will be 5

At least  it will be 0

You can't have anymore than 5, and you can have none join at all.

Step-by-step explanation:

22 - 17 = 5

You can't have anymore than 5, and you can have none meet at all.

A raffle is going to be held in which the winner will get $200. If 1000 tickets are to be sold, what is the fair
price for a ticket?

Answers

Answer:

$5

Step-by-step explanation:

1000/200=5

Answer:

20 cents.

Step-by-step explanation:

A fair price would be 200/1000 = 1/5 of a dollar which is 20 cents. But this does not allow for the people putting on the raffle to make any money for doing it. It would be better if the raffle went for a dollar. Most people would think that is fair and would not begrudge a dollar.

Sally told Joe that if you are reducing an image, the scale factor is less than 1, and if you are enlarging an image, the scale factor is greater than 1. Is Sally correct? Explain.

Answers

Answer:

YES!

Step-by-step explanation:

if its less than 1, then ur reducing

ex. = 1 x 0.5 = 0.5

If its greater than 1, then ur increasing

1  1.5 = 1.5

Works with any number

i dont know how do i delete this

I’ll give 35 points and brainliest answer asap please it’s due tomorrow

Answers

Answer:

try 72.2

Step-by-step explanation:

surface area is 3.8x3.8x6

but minus one side is 3.8x3.8x5 = 72.2

Answer:

72.2 square meters

Step-by-step explanation:

multiply the length by the width

3.8 x 3.8 = 14.44

in a cube there are 6 sides; however, it says Sarah is painting all the sides except for one so she is only painting 5 sides

14.44 x 5 = 72.2

in a school of 40 students 10% are boys. How many boys are there

Answers

Answer:

4boys

Step-by-step explanation:

40 of 10% 40×10/100 =4 remember percentage is always over 100

Find the slope of the line that passes through (1, 11) and (9, 10).

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answers

Answer:

i think it would be negative. -1/8

For every hour of exercise, Tina drinks 8 ounces of water. What is the ratio of hours to water

Answers

Answer:

1:8

Step-by-step explanation:

1 hour for every 8 ounces gives a 1:8 ratio

Answer:

8:3 would be the ratio

The formula for the circumference, C, of a circle with given radius, r, is C = 2πr. meters? what is the circumference of a circle with a radius of 3 1/2 meters? (use 22 as an estimate for it.)
A. 7 meters
B. 11 meters
C. 22 meters
D. 44 meters​

Answers

Answer:

22

actual answer was 21.99

I need this fast pls

Answers

Answer:

D

Step-by-step explanation

-2 1/2 is less than -1 1/2, s -2 1/2<-1 1/2

Find the area of the rhombus. Each indicated distance is half the length of it’s respective diagonal.
(image included)

Answers

Answer:

384 ft²

Step-by-step explanation:

12x16x2=384

Help

solve 2x+4=10

Brainliest

Answers

❤️ The answer is attached

achievements.

Answer:

x=3

Step-by-step explanation:

2x+4=10

subtracting both side by 4.

2x+4-4=10-4

2x=6

x=6/2=3

PLSSSS ANSWER 10 POINTS AND BRAINLIEST

Answers

Answer:

[tex]x=20[/tex]

Step-by-step explanation:

we know that

[tex]x+100+3x=180[/tex]

so solve for x

[tex]4x+100=180\\\\4x=80\\\\x=\frac{80}{4}=20[/tex]

Answer: x = 20

Step-by-step explanation:

180 - 100 = 80

4x = 80

x = 20

This Question: 1 pt
17 of 29
Emma has $160 cash to spend at a music store. How much can she spend on items if there is a 7% sales tax?
Emma can spend on items.
(Round to the nearest cent as needed.)

Answers

Answer:

i would say $148.80

Step-by-step explanation:

tax would amount to 11.20 so when you subyract that from the total then the rest is what she can spend.

What 3d shape does this
net make?

a. rectangular prism
b. triangular prism
c. triangular pyramid
d. rectangular pyramid

Answers

Triangular prism will be your answer

Answer:

B) A triangular prism

Step-by-step explanation:

Br0 yk this is easy l.o.l

A water balloon was launched into the top of the hill 38 feet above the ground

Answers

Answer: -71.104 ft/sec

Step-by-step explanation:So you need to know how fast the balloon is moving when it hits this person's head. velocity is based on time. So you need the time that it hits this person's head. You can get time from the position equation. Because the balloon hits this person's head 6 feet from the ground, you know that the final position is at 6 so you plug that into the position equation and solve for t. You look and see what the appropriate t value is and plug it into the velocity equation and see what the answer is.

6=-16t^2+40t+60

0=-16t^2+40t+54

plug in those values into the quadratic formula or your calculator and you get:

t = -.972

or

t = 3.472

since you can't have negative time, the other answer must be it.

So you then plug it in and solve.

v(3.472) = -32(3.472) + 40

which is approximately -71.104 ft/sec

or if they just want speed, 71.104 ft/sec. (remember, speed is velocity without direction)

Which list shows the runners in order by their completion times from fastest to slowest

Answers

Answer:

answer is D

Step-by-step explanation:

12+1/2=12.5          12+2/5=12.4

Can someone help please, please no dirty links you will be reported.

Answers

Answer:

3.25

nskkdbskaxmxbshlmsg

A cookie jar contains 3 vanilla, 2 chocolate chip, and 7 gingersnap cookies. If one cookie is taken at random from the jar, what is the probability that it will be a vanilla cookie?

Answers

Answer:

3/12= 1/4

Step-by-step explanation: because you would add the all up for 12 and you have a 3 vanilla's so 3/12= 1/4

After school Philippe spent 1 3/4 hours at baseball practice, 2 1/4 hours on homework, and 1/4 hour getting ready for bed. About how many hours after school will he be ready for bed. Explain

Answers

Answer:

4 hours. 1 3/4 is about 2, and 2 1/4 rounds to 2. 1/4 would round to 0, but it would not affect the estimate's accuracy much because we rounded up by 1/4 on 1 3/4 already. Philipe spent about 4 hours on activities.  

Step-by-step explanation:

Branliest to correct answer explain how to solve it please

Answers

In general, nCr = n! / r! (n-r)!

Here, 7C3 = 7! / 3!(7-3)!

=7 x 6 x 5 x 4 x 3 x 2 x 1 /3 x 2 x 1 ( 4 x 3 x 2 x 1)

=7x6x5x4 / 4x3x2

=7x5x6x4 / 24

=35x24 / 24

=35

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