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
Nataly_w [17]
3 years ago
7

(a) A lamp has two bulbs, each of a type with average lifetime 1400 hours. Assuming that we can model the probability of failure

of these bulbs by an exponential density function with mean μ = 1400, find the probability that both of the lamp's bulbs fail within 1700 hours. (Round your answer to four decimal places.)
Mathematics
1 answer:
Temka [501]3 years ago
8 0

Answer:

For first lamp ; The resultant probability is 0.703

For both lamps; The resultant probability is 0.3614

Step-by-step explanation:

Let X be the lifetime hours of two bulbs

X∼exp(1/1400)

f(x)=1/1400e−1/1400x

P(X<x)=1−e−1/1400x

X∼exp⁡(1/1400)

f(x)=1/1400 e−1/1400x

P(X<x)=1−e−1/1400x

The probability that both of the lamp bulbs fail within 1700 hours is calculated below,

P(X≤1700)=1−e−1/1400×1700

=1−e−1.21=0.703

The resultant probability is 0.703

Let Y be a lifetime of another lamp two bulbs

Then the Z = X + Y will follow gamma distribution that is,

X+Y=Z∼gamma(2,1/1400)

2λZ∼

X+Y=Z∼gamma(2,1/1400)

2λZ∼χ2α2

The probability that both of the lamp bulbs fail within a total of 1700 hours is calculated below,

P(Z≤1700)=P(1/700Z≤1.67)=

P(χ24≤1.67)=0.3614

The resultant probability is 0.3614

You might be interested in
Do you work At nasa? I think your beauty is out of this world.
viva [34]

Answer:

Huh?

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
The reference angle for 5pi/4 is 1, which has a terminal point of
maxonik [38]

Answer:

D

Step-by-step explanation:

8 0
2 years ago
Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the co
jeka57 [31]

Answer:

<h2>A. The series CONVERGES</h2>

Step-by-step explanation:

If \sum a_n is a series, for the series to converge/diverge according to ratio test, the following conditions must be met.

\lim_{n \to \infty} |\frac{a_n_+_1}{a_n}| = \rho

If \rho < 1, the series converges absolutely

If \rho > 1, the series diverges

If \rho = 1, the test fails.

Given the series \sum\left\ {\infty} \atop {1} \right \frac{n^2}{5^n}

To test for convergence or divergence using ratio test, we will use the condition above.

a_n = \frac{n^2}{5^n} \\a_n_+_1 = \frac{(n+1)^2}{5^{n+1}}

\frac{a_n_+_1}{a_n} =  \frac{{\frac{(n+1)^2}{5^{n+1}}}}{\frac{n^2}{5^n} }\\\\ \frac{a_n_+_1}{a_n} = {{\frac{(n+1)^2}{5^{n+1}} * \frac{5^n}{n^2}\

\frac{a_n_+_1}{a_n} = {{\frac{(n^2+2n+1)}{5^n*5^1}} * \frac{5^n}{n^2}\\

aₙ₊₁/aₙ =

\lim_{n \to \infty} |\frac{ n^2+2n+1}{5n^2}| \\\\Dividing\ through\ by \ n^2\\\\\lim_{n \to \infty} |\frac{ n^2/n^2+2n/n^2+1/n^2}{5n^2/n^2}|\\\\\lim_{n \to \infty} |\frac{1+2/n+1/n^2}{5}|\\\\

note that any constant dividing infinity is equal to zero

|\frac{1+2/\infty+1/\infty^2}{5}|\\\\

\frac{1+0+0}{5}\\ = 1/5

\rho = 1/5

Since The limit of the sequence given is less than 1, hence the series converges.

5 0
3 years ago
The equation f = v + at represents the final velocity of an object, f, with an initial velocity, v, and an acceleration rate,
Veronika [31]
Um not to sure about that
7 0
3 years ago
Finished the first one don´t understand these.
Mashutka [201]

Answer:

Let "x" be the number of people who can go to the amusement park.

So we have: 19 + 14x ≤ 180. This inequality basically means that the parking cost plus the cost of the tickets for every person cannot cost more than 180 dollars.

Solving this inequality, we get:

19 + 14x ≤ 180

14x ≤ 161

x ≤ 11.5

Obviously, we know that we can't have "half" a person, so the most people who can come to the amusement park would be 11 people, and the answer would be: x ≤ 11

Hope this helps!

4 0
2 years ago
Other questions:
  • What is the value of x in a &amp; b?
    7·1 answer
  • I NEED HELP PLEASE !!!!
    13·1 answer
  • A radio station spends 1/4 of each 24 hours on public service announcements. How much time is spend on public service announceme
    5·1 answer
  • Which of the following illustrates the inverse property of addition?
    12·1 answer
  • I don’t get it I need hey
    11·2 answers
  • Max has 4/5 qt of apple juice. He drinks 1/2 qt of it. How many apple juice does he have left? (Give your answer in quarts)
    5·1 answer
  • Colvert the decimal to percent: 0.272
    8·1 answer
  • What kind of cell is made of only DNA, ribosomes, cytoplasm and a cell membrane?(A)amoeba
    14·1 answer
  • Let f(x) = −x2 + ax + b. Determine the constants a and b such that f has a relative maximum at x = 3 and the relative maximum va
    7·1 answer
  • At a farm the ratio of cows to horses was 8 : 3. If there were 24 cows at the farm, how many horses were there?
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!