Mathematics College

The time in hours required to repair a machine is an exponential distributed random variable with the average repair time of 2 hours, what is the probability that the repair time takes between 2 to 4 hours

Answers

Answer 1

Answer:

0.4968 = 49.68% probability that the repair time takes between 2 to 4 hours

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]

Average repair time of 2 hours

This means that [tex]m = 2, \mu = \frac{1}{2} = 0.5[/tex]

What is the probability that the repair time takes between 2 to 4 hours

More than 2:

[tex]P(X > 2) = e^{-0.5*2} = 0.3679[/tex]

Less than 4:

[tex]P(X \leq 4) = 1 - e^{0.05*4} = 0.8647[/tex]

Between two and four:

[tex]P(2 \leq x \leq 4) = 0.8647 - 0.3679 = 0.4968[/tex]

0.4968 = 49.68% probability that the repair time takes between 2 to 4 hours

Related Questions

HELP PLEASE

ARM SPAM (INCHES) HEIGHT (INCHES)
58 60
49 47
51 55
19 25
37 39
44 45
47 49
36 35
41 40
46 50
58 61
65 68

1. Which variable did you plot on the x-axis and which variable did you plot on the y-axis? Explain why you assigned the variables in that way.

2. Write the equation of the line of best fit using the slope-intercept formula y = mx + b. Show all your work, including the points used to determine the slope and how the equation was determined.

3. What does the slope of the line represent within the context of your graph? What does the y-intercept represent?

4. Test the residuals of two other points to determine how well the line of best fit models the data.

5. Use the line of best fit to help you to describe the data correlation.

6. Using the line of best fit that you found in Part Three, Question 2, approximate how tall is a person whose arm span is 66 inches?

7. According to your line of best fit, what is the arm span of a 74-inch-tall person?

Answers

Step-by-step explanation:

we have to write all things by which which x-axis is viraivil with you and y axis is variable with you and spleen in our right one formula X is equals to X is equals to y y - behind honey bunny i y is equals to x minus b right and right that formula and write if you don't know and I will tell you another this video is it was thank you so much

What is the surface area of this design ?

please help!!!!!!!!!!

Answers

The surface area of the design is 5

Answer: 392.

Step-by-step explanation:

Please help please please

Answers

Answer:

C. y = 2x + 8

Step-by-step explanation:

✔️First, find the slope of the line that goes through points (-2, 4) and (6, 20):

Slope (m) = ∆y/∆x = (20 - 4) / (6 - (-2))

Slope (m) = 16/8

m = 2

✔️Find the y-intercept (b):

To do this, substitute (x, y) = (6, 20) and m = 2 into y = mx + b

Thus:

20 = 2(6) + b

20 = 12 + b

20 - 12 = b

8 = b

b = 8

✔️Write the equation by substituting m = 2 and b = 8 into y = mx + b

Thus:

y = 2x + 8

5.7 is increased to 7.8
What is the percentage of increase?

Answers

Answer:

7.8%

Step-by-step explanation:

Answer:

The percentage of increase is 37%

Step-by-step explanation:

The way to find the percentage of increase is to divide The difference between the two numbers by the number before the increase

7.8 - 5.7 = 2.1

The difference between 7.8 and 5.7 is 2.1

So now we divided 2.1 by the number before the increase, in this case, 5.7

2.1 ÷ 5.7 = 0.3684

0.3684 rounded to the nearest hundredth is 0.37

Thus the percentage of increase is 37%

If the sum of 20 numbers is 440, find the mean of the numbers.

Answers

Answer:

Step-by-step explanation:

mean= sum of observations/no: of observations

mean=440/2=22

please mark me brainliest

The mean is 22. You divide 440(the sum) by 20(the amount of numbers) to get the answer.

The first four terms of a sequence are shown below:
8, 5, 2, -1
Which of the following functions best defines this sequence?
O f(1) = 8, f(n + 1) = f(n) + 3; forn
O f(1) = 8, f(n + 1) = f(n) - 5; for n 1
O f(1) = 8, f(n + 1) = f(n) + 5; for n 1
Of(1) = 8, f(n + 1) = f(n) -3; for n 1

Answers

Answer:

Step-by-step explanation:

Since each term is decreased by three [tex]f(n+1)=f(n)-3[/tex]

Consider the box plot.
A+++ ++ +
+
1 2 3 4 5 6 7 8 9 10
Which could be the data set for this box plot?
O {1, 2, 3, 7, 9, 10}
o {1, 2, 4, 5, 8, 10}
o {1, 3, 4, 6, 8, 10}
• {1, 3, 6, 6, 9, 10

Answers

Answer:

Step-by-step explanation:

The box plot explains the right numbers in order

The correct option is (d) {1,3,6,6,9,10}

According to the box plot,

the median must be 6.the lower quartile must be 3.the upper quartile must be 9.the smallest value must be 1.and the largest value must be 10.

Now looking at the data sets we can see that there are 6 values in each data set. So to satisfy all the conditions above regarding the given box plot, the correct option must be {1,3,6,6,9,10}.

Learn more about box plots:

https://brainly.com/question/14750698

ice cream is served for dessert if Gio serves himself and 3 friends half a cup of ice cream how many total pints did Gio and his friends eat?

Answers

Answer:

0.25 pints

Step-by-step explanation:

To find how many pints they ate, find the number of pints in half a cup.

In 1 cup, there are 0.5 pints.

This means in half a cup, there will be 0.25 pints.

So, Gio and his friends ate 0.25 pints

Drew bakes a casserole for 25 5/12 minutes. He decides it needs to bake longer. He bakes it for another 2 3/6 minutes. How long does the casserole bake altogether?

Answers

Answer:

add more detail then i can answer

Step-by-step explanation:

I think the answer is 27 11/12 minutes.

Hello, happy Friday, I am just here with some geometry questions.

Please only answer this if you know the answer. If you have a comment, please add it to the comment box. Only answer the question if you can explain your answer and why you think it is accurate. Thanks, good luck!

What is x? and how did you get it?

Answers

Answer:

x = 16

Step-by-step explanation:

step 1 - 64 + 100 + x = 180 (all triangles equals 180)

step 2 - 164 + x = 180

step 3 - 164 + x = 180

-164. -164

step 4 - 180 - 164 = 16

step 5 - 100 + 64 + 16 = 180

(I do this part to double check my work)

step 6 - x = 16

Answer:

x = 48

Step-by-step explanation:

The ratio:

x/64 = (100 - 64)/xx² = 64*36x = 48

HELP MEH PLEASEEEEE!!!!!!!!

Answers

Answer: A = w l

Step-by-step explanation:

Answer:

A = lw

Step-by-step explanation:

[tex]A = \frac{1}{2} bh[/tex] - Area of a triangle

[tex]A = lw[/tex] - Area of a rectangle

[tex]A= \frac{1}{2} bh^2[/tex] - Area of a triangle

[tex]A =\pi r^2[/tex] - Circumference of a circle

I’ll give the brainliest What can we conclude about the triangles on the line shown below?

Answers

Answer:

I believe the answer is C.

Step-by-step explanation:

Answer:

Step-by-step explanation:

It would be B. since both triangles are right triangles. They also are on the same line. So neither of them are at a different angle.

Now to verify that this is correct, we need to eliminate some of the other answers.

Let's start with A.. Congruent means that they are the same shape and size and can be mirrored/backwards. These triangles are the same shape and mirrored but it IS NOT the same size. This means we can eliminate answer A..

Now answer C.. As originally stated, the triangles are similar because they are both right triangles, but they have the same slope since they are on the same line. The line is not changing so the slope will not change either.

And finally answer D.. Answer D. has been proven wrong from the answers B. and C., so we can eliminate it.

This means all the answers are eliminated but B.

a license plate that has 3 numbers from 0 to 9 and 2 letters

Answers

Answer:

what's the question there

Given the functions flx) = 3x2, g(x) = x2 - 4x + 5, and h(x) = -2x2 + 4x + 1, rank them from leasrto greatest based on their axis of symmetry.

Answers

9514 1404 393

Answer:

f(x), h(x), g(x)

Step-by-step explanation:

For a quadratic in standard form, ...

ax² +bx +c

the axis of symmetry is ...

x = -b/(2a)

For the various functions, the axes of symmetry are ...

f(x): x = 0/(2·3) = 0

g(x): x = -(-4)/(2·1) = 2

h(x): x = (-4)/(2(-2)) = 1

From least to greatest axis of symmetry the functions are ...

f(x), h(x), g(x)

Is a triangle with sides 5 feet, 10 feet, and 12 feet a right, acute or obtuse
triangle?

Answers

Answer:

acute angles

Step-by-step explanation:

non of the angles are of the same lenght

How many ways are there to place 3 indistinguishable red chips, 3 indistinguishable blue chips, and 3 indistinguishable green chips in the squares of a 3 x 3 grid so that no two chips of the same color are directly adjacent to each other, either vertically or horizontally?
A. 12,
B. 18,
C. 24,
D. 30 ,
E. 36

Answers

Answer:

E. 36

Step-by-step explanation:

Let:

[tex]C_1 =[/tex] color 1

[tex]C_2 =[/tex] color 2

[tex]C_3 =[/tex] color 3

Case I

C₂ C₃ C₂

C₃ C₁ C₃

C₁ C₂ C₁

Since C₁ has 3 choices, then C₂ has 2 choices and C₁ has 1 choice