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

What's the name of angle C thanks for the help :)

Answers

Answer:

Reflex angle

Step-by-step explanation:

Properties of reflex angles:

1). Any angle measuring between 180° and 360°.

2). Other side of the reflex angle is either acute or obtuse angle.

By these properties,

Since, angle C measures more than 180° but less than 360° and opposite angle is an acute angle.

By these properties angle C and angle D are the reflex angles.

how do you solve an equation that looks like this?

Answers

Answer:

x = 11

Step-by-step explanation:

5x - 8 + 43 = 90

5x = 55

x = 11

Step-by-step explanation:

5x - 8° + 43° = 90° (right Angle)

5x + 35° = 90°

5x = 90° - 35°

5x = 55°

x = 55°/5

x = 11°

5x - 8 = 5 × 11 - 8 = 47°

The first angle is 47° and second one is 43°.

Write a sentence containing a gerund which functions as the subject of the verb.

Answers

Answer:

Swimming can improve your health.

Step-by-step explanation:

Gerunds are nouns which derive from verbs and take the -ing form. In the sentence, the noun swimming functions as the subject of the verb can.

Gerunds are usually used as subjects of sentences, after certain verbs (such as enjoy and look forward to) and after prepositions.

(11–6)÷6. Solve this and show your work.

Answers

brackets first
(11-6) divide by 6
(5) divide by 6 = 0.83

Step-by-step explanation:

5/6 was 0.833333333333333

Dylan records whether people prefer to drink milk, tea, coffee, or smoothie in the morning. He
separates the responses by which of three eastern United States regions they live in the Northeast,
the Mid-Atlantic, or the South. What is the conditional frequency of people from the Mid-Atlantic
who prefer smoothie, relative to the total number of respondents? Round to the nearest hundredth
if necessary

Answers

Dylan has a butt full of poop

Please please please help

Answers

Answer:

the answer is more than 6 rides

Answer:

The answer is more than 6 rides.

Step-by-step explanation:

Plan A has the same cost of $15 no matter the number of rides. It stays the same. However, Plan B has an increasing price depending on how many rides you ride. Once you reach 6 rides, which is the exact same price for both of the plans, Plan A will stay at $15 for more rides, while Plan B will continue to increase in price for more rides.

x:y=5:3 and x+y=56 work ouy the value of x and y​

Answers

Answer:

x=35, y=21

Step-by-step explanation:

A way to rewrite the first equation is  [tex]\frac{x}{y} =\frac{5}{3}[/tex]

after cross-multiplying, we get 3x=5y.

If we solve for one variable, we can substitute it into the other equation.

Let's solve for x.

3x=5y

x=(5/3)y

Now, we can substitute x=(5/3)y in the equation x+y=56.

(5/3)y+y=56

(8/3)y=56

y=21

Going back to x+y=56, we can now plug back in y, knowing that it is 21.

x+21=56

x=35.

Which retirement plan is managed by an insurance company?

a Fixed Annuity
b Pension Plan
c Roth IRA
d Traditional IRA

Answers

Answer:

Fixed Annuity

Step-by-step explanation:

Fixed annuity is the most common annuity

During the accumulation phase, the individual makes a lump-sum payment or multiple payments over time to the insurance company

The insurance company invests the money as it sees fit, along with the money of other participants, forming a pool of invested funds

Answer Is A Because A fixed annuity is a type of insurance contract that promises to pay the buyer a specific, guaranteed interest rate on their contributions to the account. By contrast, a variable annuity pays interest that can fluctuate based on the performance of an investment portfolio chosen by the account's owner.

What is the area of this rectangle ?

Answers

Answer:

1x

Step-by-step explanation:

Area is length times width. Because there isnt a value for x, the area is just 1x. Let me know in the comments if it was right!

Please help me, I will mark as brainliest.

Answers

I think it is student 1

Necesito ayuda con está pregunta por favor. :)​

Answers

La respuesta es la segunda

B.

One acre is equivalent to 43,560 square feet. If an acre is also equivalent to 4,840 square yards, how many square feet are equal to one square yard? Add an explanation and a step by step answer.
Help please thank you so much! (Math has never really been my strongest subject)

Side Note: I'd rather not have the answer in a file thank you very much.

Answers

Answer:

9 square feet

Step-by-step explanation:

1 acre = 43,560 ft²

1 acre = 4,840 yd²

Since both values are equal to 1 acre, we can set them equal to each other via the property of equality:

43,560 ft² = 4,840 yd²

The question is asking us to find the ft²/yd² ratio, which is found by dividing.

43,560 ft² / 4,840 yd² = 9 ft²/yd² (or 9 square feet is equal to one square yard.)

(If it helps to grasp the concept, we can add a variable representing this ratio to solve for.)

43,560 = 4,840x

43,560 / 4,840 = 9

what's the opposite of -3.9

Answers

positive 3.9

negative is the opposite of positive

positive it the opposite of negative

Can someone provide some assistance.​

Answers

Answer:

m<E=120°

m<T=60°

Step-by-step explanation:

10m+4m+12=180

14m=168

m=12

m<E=10m=10(12)=120

m<T=4m+12=4(12)+12=48+12=60

Answer:

Solution given:

10m+4m+12=180°[sum of opposite angle of cyclic quadrilateral is supplementary]

14m=180-12

m=168/14=12

m<E=10×12=120°

m<T=4×12+12=60°

What is the area of the figure?
15in.
30in
-50in.
The area of the figure is

Answers

Answer:

2,250

Step-by-step explanation:

During a recent drought, a water utility in a certain town sampled 100 residential water bills and found that 75 of the residences had reduced their water consumption over that of the previous year. Find a 95% confidence interval for the proportion of residences that reduced their water consumption. Round the answers to three decimal places.

Answers

Answer:

The 95% confidence interval for the proportion of residences that reduced their water consumption is (0.665, 0.835).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

Sampled 100 residential water bills and found that 75 of the residences had reduced their water consumption over that of the previous year.

This means that [tex]n = 100, \pi = \frac{75}{100} = 0.75[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.75 - 1.96\sqrt{\frac{0.75*0.25}{100}} = 0.665[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.75 + 1.96\sqrt{\frac{0.75*0.25}{100}} = 0.835[/tex]

The 95% confidence interval for the proportion of residences that reduced their water consumption is (0.665, 0.835).

Jina is pumping water into a tank at a rate of 15 liters per minute. Since she started pumping water, 13 liters has splashed out of the tank. Her goal is given by
15x-13 < 77, where x is the number of minutes she pumps water into the tank.
First, solve the given inequality and graph the solution on the number line below.
Then, choose and complete the statement that best describes the solution

Answers

Step-by-step explanation:

subtract-13 from -13 get zero

then, subtract 13 from 77 =64

then do divide 15 from 15

then divide 15 from 64 = 4.26 repeat

-87 8g = 56
I need help please

Answers

G = 8

-8 + 8g = 56

Add 8 to both sides

8g = 64

Divide by 8

g = 8

Can someone help me? I’ll reward brainalist + points

Answers

Answer:

B, -25

Step-by-step explanation:

3-4 = -1

-1(3 + 3^2 + 13) = -1(25), the answer is -25

Answer:

-25

Step-by-step explanation:

-25 is the answer...........

Owner investment: $8,000
Revenue: $15,000
Equity: $21,000
Expenses: $3,000

Based on this data, the net profit or loss on the income statement should be:

Answers

Answer: $12,000

Step-by-step explanation:

The Income statement shows the Net Profit or Loss for a company in a given period. That Net income is calculated by subtracting expenses from the revenue for the period:

= Revenue - Expenses

= 15,000 - 3,000

= $12,000

which of the following box plot has the greatest median F. G. H. J.

Answers

Step-by-step explanation:

hmph................

A rocket is fired directly upwards with a velocity of 80 ft/sec. The equation for its height, H, as a function of time, t, is
given by the function
H (t) = -1612 + 80+
Find the time at which the rocket reaches its maximum height, and its maximum height.
5
a) O time =
22
sec, max height = 200 ft
b) O time = 80 sec, max height = 100 ft
5
c) O time =
2
sec, max height = 100 ft
d) O time = 5 sec, max height = 200 ft
5
e) Otime = sec, max height = 400 ft
23
Revie

Answers

Answer:

(c).

Step-by-step explanation:

h(t) = - 16 t² + 80 t

Coordinates of the vertex are:

t = - [tex]\frac{80}{2(-16)}[/tex] = [tex]\frac{5}{2}[/tex] = 2.5 sec.

h = - 16(2.5)² + 80(2.5) = - 100 + 200 = 100 ft.

What is the greatest
common factor of 4 and 34?

Answers

Answer:

2

Step-by-step explanation:

The Greatest Common Factor (GCF) is the number that both numbers share. In this case, 4 and 34 can both be divided by 2 evenly to produce an answer. However, no other number can be used to divide both numbers, making 2 the final answer.

norma had 3/8 birthday cake left over from her party she ate 3/4 of the cake for lunch. how much did she eat at lunch?

Answers

Answer:

1/12

Step-by-step explanation:

Fraction is the representation of the parts of a whole number. The amount of cake ate by Norma in the lunch is 9/32 parts.

Given-

Total cake left over by the Norma after the party is 3/8.

Total cake she ate for the lunch is 3/4.

The value of the whole cake is given in the fraction parts. To solve this the fraction should be understood.

What is fraction?

Fraction is the representation of the parts of a whole number.

As the one whole of cake was there earlier. The 3/8 part of the cake is,

[tex]=\dfrac{3}{8}[/tex]

As she ate the 3/4 part of the left over cake in the lunch. Suppose the part of cake she ate is x. Therefore the part of cake she ate at lunch is,

[tex]x=\dfrac{3}{8} \times\dfrac{3}{4}[/tex]

[tex]x=\dfrac{9}{32}[/tex]

Hence, the amount of cake ate by Norma in the lunch is 9/32 parts.

Learn more about the fraction here;

https://brainly.com/question/1301963

round 38.68 to the nearest hundred​

Answers

38.68 is rounded to the nearest hundredth

2
10 m
5 m

what is the hypotenuse

Answers

10 m cause it’s the largest.

Answer:

i don't know  the answer sorry

Step-by-step explanation:

FIND THE AREA OF THE SHAPE

Answers

32 ezzz work so ezzz

Chang knows one side of a triangle is 13 cm. Which set of two sides is possible for the lengths of the other two
sides of this triangle?

5 cm and 8 cm

D cm and 7 cm
O
7 cm and 2 cm

8 cm and 9 cm
Hurry

Answers

Uodidufufufifijuduxxjdififfi

Answer:

8 and 9

Step-by-step explanation:

I can't tell what the second option is, though but I think 8 and 9 should be a valid answer

lmk if you want me to explain

What's greater? 18% or 11/55?

Answers

Answer:

11/55

Step-by-step explanation:

11/55 = 20%

18% = 18%

Answer:

11/55 is greater

Step-by-step explanation:

18% is less because divided by 100 it will be 0.18 and if you multiply 11/55 the answer is 0.20

PLZ HELP I GIVE BRAINLIEST!!!

Answers

Answer:

800 × ( 3.87÷ 100 ) × 1

= 30.96

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