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
ioda
3 years ago
8

The probability density function of the time to failure of an electronic component in a copier (in hours) is f(x) = (e^-x/1076)/

(1076) for x>0. Determine the probability that
A) A component lasts more than 3000 hours before failure. (Round the answer to 3 decimal places.)
B) A component fails in the interval from 1000 to 2000 hours. (Round the answer to 3 decimal places.)
C) A component fails before 1000 hours. (Round the answer to 3 decimal places.)
D) Determine the number of hours at which 10% of all components have failed. (Round the answer to the nearest integer.)
Mathematics
1 answer:
kozerog [31]3 years ago
4 0

Answer:

(a) 0.06154

(b) 0.2389

(c) 0.6052

(d) 2478

Step-by-step explanation:

probability density function of the time to failure of an electronic component in a copier (in hours) is

P(x) = 1/1076e^−x/1076

λ = 1/1076

A) A component lasts more than 3000 hours before failure:

P(x>3000) = 1 − e^−3000/1076

= 0.06154

B) A component fails in the interval from 1000 to 2000 hours:

P(1000>x>2000) =1 − e^−2000/1076 − 1 +e^−1000/1076 = e^−1000/1076 − e^−2000/1076 = 0.3948 − 0.1559

= 0.2389

C) A component fails before 1000 hours:

P(x<1000) = 0.6052

D) The number of hours at which 10% of all components have failed:

e^−x/1076 = 0.1

= −x/1076

= ln(0.1)

x =(2.3026)×(1076)

x = 2478

You might be interested in
Find the product. Simplify your answer.<br> -5 • 9t<br> 7s 7
Sauron [17]

Answer:

-13            

 ——— = -0.20635  

 63            

Step-by-step explanation:

Step  1  :

           7

Simplify   —

           9

Equation at the end of step  1  :

 4    7

 — -  —

 7    9

Step  2  :

           4

Simplify   —

           7

Equation at the end of step  2  :

 4    7

 — -  —

 7    9

Step  3  :

Calculating the Least Common Multiple :

3.1    Find the Least Common Multiple

     The left denominator is :       7  

     The right denominator is :       9  

       Number of times each prime factor

       appears in the factorization of:

Prime  

Factor   Left  

Denominator   Right  

Denominator   L.C.M = Max  

{Left,Right}  

7 1 0 1

3 0 2 2

Product of all  

Prime Factors  7 9 63

     Least Common Multiple:

     63  

Calculating Multipliers :

3.2    Calculate multipliers for the two fractions

   Denote the Least Common Multiple by  L.C.M  

   Denote the Left Multiplier by  Left_M  

   Denote the Right Multiplier by  Right_M  

   Denote the Left Deniminator by  L_Deno  

   Denote the Right Multiplier by  R_Deno  

  Left_M = L.C.M / L_Deno = 9

  Right_M = L.C.M / R_Deno = 7

Making Equivalent Fractions :

3.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)2   and  (y2+y)/(y+1)3  are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

  L. Mult. • L. Num.      4 • 9

  ——————————————————  =   —————

        L.C.M              63  

  R. Mult. • R. Num.      7 • 7

  ——————————————————  =   —————

        L.C.M              63  

Adding fractions that have a common denominator :

3.4       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

4 • 9 - (7 • 7)     -13

———————————————  =  ———

      63            63  

Final result :

 -13            

 ——— = -0.20635  

 63            

8 0
3 years ago
Read 2 more answers
Wade has already spent $7 of his earnings. He could represent the total amount he has left using the expression a − 7 ⁢   .
valentinak56 [21]
The answer is b because 7 plus 2 equals 9 and a equals whole amount then his current amount is A-9
7 0
3 years ago
Read 2 more answers
Estimate the student's walking pace, in steps per minute, at 3:20 p.m. by averaging the slopes of two secant lines from part (a)
ehidna [41]

This question is incomplete, the complete question is;

A student bought a smart-watch that tracks the number of steps she walks throughout the day. The table shows the number of steps recorded (t) minutes after 3:00 pm on the first day she wore the watch.

t (min)       0          10          20         30         40

Steps   3,288    4,659    5,522    6,686    7,128

a) Find the slopes of the secant lines corresponding to the given intervals of t.

1) [ 0, 40 ]

11) [ 10, 20 ]

111) [ 20, 30 ]

b) Estimate the student's walking pace, in steps per minute, at 3:20 pm by averaging the slopes of two secant lines from part (a). (Round your answer to the nearest integer.)

Answer:

a)

1) for [ 0, 40 ], slope is 96

11) for [ 10, 20 ],  slope is 86.3

111) for  [ 20, 30 ], slope is 116.4

b) the student's walking pace is 101 per min

Step-by-step explanation:

Given the data in the question;

t (min)       0          10          20         30         40

Steps   3,288    4,659    5,522    6,686    7,128

SLOPE OF SECANT LINES

1) [ 0, 40 ]

slope =  ( 7,128 - 3,288 ) / ( 40 - 0

= 3840 / 40 = 96

Hence slope is 96

11)  [ 10, 20 ]

slope = ( 5,522 - 4,659 ) / ( 20 - 10 )

= 863 / 10 = 86.3

Hence slope is 86.3

111)  [ 20, 30 ]

slope = ( 6,686 - 5,522 ) / ( 30 - 20 )

= 1164 / 10 = 116.4

Hence slope is 116.4

b)

Estimate the student's walking pace, in steps per minute, at 3:20 pm by averaging the slopes of two secant lines from part .

Since this is recorded after 3:00 pm

{ 3:20 - 3:00 = 20 }

so t = 20 min

so by average;

we have ( [ 10, 20 ] + [ 20, 30 ] ) /2

⇒ ( 86.3 + 116.4 ) / 2

= 202.7 /2

= 101.35 ≈ 101

Therefore, the student's walking pace is 101 per minutes

3 0
3 years ago
This is hard and I need help
AleksAgata [21]
I think it is 40x16=640

Answer = 64:0
4 0
3 years ago
A sample of 40 batteries is taken from a case of 400. Thirty-seven of the batteries in the sample are good, and three are defect
barxatty [35]
The answer is option E i.e., 1 because we know that there are 3 defective batteries in the case so the probability will never be 1 for this case.
8 0
3 years ago
Other questions:
  • Solve for L.
    6·1 answer
  • Which number is divisible by both 2 and 4?<br> A. 1,022<br> B. 1,974<br> C. 2,836<br> D. 2,918
    10·2 answers
  • Sophie says that if the interior angle of a triangle is 65 degrees and the exterior one is 295 degrees. Comment on her thinking
    10·1 answer
  • 2^4⋅2^5−(2^2)^2<br><br> PLEASE HELP FAST!
    14·1 answer
  • maya cuts a piece of wood into two parts, the first part is 25 cm longer than the second part, .the original length of the wood
    8·1 answer
  • Tommy's salary increases by 4% each year. This year, Tommy's salaray was $42,250. How much will her salary be in 7 years?
    6·1 answer
  • Can someone answer ASAP
    14·1 answer
  • Submit Test
    15·1 answer
  • There are 10 apples for every 6 bananas how many bananas are there if there are 20 apples?
    13·2 answers
  • At a harvest 16 ears are being picked foot every 18 peppers. If 19 peppers have been picked, how many eats of corn have been pic
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!