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djyliett [7]
3 years ago
5

The length of time between breakdowns of an essential piece of equipment is important in the decision of the use of auxiliary eq

uipment. An engineer thinks that the best model for time between breakdowns of a generator is the exponential distribution with a mean of 14 days. If the generator has just broken down, what is the probability that it will break down in the next 21 days
Mathematics
1 answer:
mina [271]3 years ago
5 0

Answer: The probability that it will break down in the next 21 days is 0.777

Step-by-step explanation:

Let the random variable x represent

time between breakdowns of a generator

Given that mean = 14 days,

Decay parameter, m = 1/14

The probability density function for exponential distribution is expressed as

F(x) = me-mx

It becomes

f(x) = 1/14e-(x × 1/14)

P(X < x) = 1 - e- mx

The probability that it will break down in the next 21 days is expressed as

P(x ≤ 21) = P(x < 21)

Therefore,

P(x < 21) = 1 - e-(1/14 × 21)

= 1 - e-1.5

= 1 - 0.223 = 0.777

P(x ≤ 21) = 0.777

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DanielleElmas [232]

Answer:

C) 100 m^2

Step-by-step explanation:

Area of a trapezoid= h*[(b1+b2)/2]

h=10

b1=8

b2=12

Therefore:

A=10*[(8+12)/2]

A=10*(20/2)

A=10*10

A=100

So the area of the trapezoid is 100 m^2

7 0
3 years ago
The revenue​ (in millions of​ dollars) from the sale of x units at a home supply outlet is given by ​R(x)equals=0.210.21x. The p
Natalka [10]

Answer: a) c(x) = 0.124x + 1.1, b) 13 units

Step-by-step explanation: Revenue function = R(x) = 0.21x

Profit function = p(x) = 0.086 - 1.1

Cost function = c(x) =?

A)

Recall that profit = total revenue - total cost

Hence, total cost = total revenue - profit

c(x) = 0.21x - (0.086x - 1.1)

c(x) = 0.21x - 0.086x + 1.1

c(x) = 0.124x + 1.1

B)

Break even point is the point where total revenue equals total cost

R(x) = c(x)

0.21x = 0.124x + 1.1

0.21x - 0.124x = 1.1

0.086x = 1.1

x = 1.1/0.086

x = 12.79 which is approximately 13 units

4 0
3 years ago
What times blank equal 90 and a 100
torisob [31]

Answer:

10x9=90

10x10=100

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
A rectangular prism with a volume of 101010 cubic units is filled with cubes with side lengths of \dfrac12
lawyer [7]
Given that the volume of the prism is given by:
10 cubic units and the the side length of cubes to fill the prism is 1/2 units. Then the number of cubes required to fill the prism will be given by:
(volume of rectangular prism)/(volume of cube)
but
volume of cube is:
volume=length*width*height
volume=1/2×1/2×1/2=1/8 cubic units
thus the number of cubes required to fill the prism will be:
10/(1/8)
=10×8/1
=80 cube
Answer: 80 cubes
4 0
3 years ago
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Algebra 2 - Grade 11
saveliy_v [14]

Answer:

for the first equation

f(-3) = 34

f(4) = 6

for the 2nd equation

f(-3) = -56

f(4) ÷ 70

Step-by-step explanation:

my work is attached in a picture.

all you do is substitute each x value into each equation

8 0
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