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
Keith_Richards [23]
2 years ago
11

A boiler has five identical relief valves. The probability that any particular valve will open on demand is 0.93. Assume indepen

dent operation of the valves. Calculate P(at least one valve opens). (Round your answer to eight decimal places.)
Mathematics
2 answers:
matrenka [14]2 years ago
7 0

Answer:

0.930000

Step-by-step explanation:

noname [10]2 years ago
5 0

Answer:

There is a 99.99998% probability that at least one valve opens.

Step-by-step explanation:

For each valve there are only two possible outcomes. Either it opens on demand, or it does not. This means that we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinatios of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

In this problem we have that:

n = 5, p = 0.93

Calculate P(at least one valve opens).

This is P(X \geq 1)

Either no valves open, or at least one does. The sum of the probabilities of these events is decimal 1. So:

P(X = 0) + P(X \geq 1) = 1

P(X \geq 1) = 1 - P(X = 0)

So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{5,0}.(0.93)^{0}.(0.07)^{5} = 0.0000016807

Finally

P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0000016807 = 0.9999983193

There is a 99.99998% probability that at least one valve opens.

You might be interested in
Answer Question number 5 <br> Plzzzzzz
loris [4]

Answer:

Step-by-step explanation:

a = -4/3

d= -1 +4/3 =1/3

last term = 4 1/3 = 13/3

nth term = a +(n-1)d

\frac{-4}{3}+(n-1)*\frac{1}{3}=\frac{13}{3}\\\\(n-1)*\frac{1}{3}=\frac{13}{3}-\frac{-4}{3}\\\\(n-1)*\frac{1}{3}=\frac{13+4}{3}\\\\(n-1)*\frac{1}{3}=\frac{17}{3}\\\\n-1=\frac{17}{3}*\frac{3}{1}\\\\n-1=17\\\\n=17+1=18

Middle terms are 9the term and 10th term

t_{9}=\frac{-4}{3}+8*\frac{1}{3}=\frac{-4}{3}+\frac{8}{3}=\frac{4}{3}\\\\t_{10}=\frac{-4}{3}+9*\frac{1}{3}=\frac{-4}{3}+\frac{9}{3}=\frac{5}{3}\\\\ t_{9}+t_{10}=\frac{4}{3}+\frac{5}{3}=\frac{9}{3}=3\\\\t_{9}+t_{10}=3

3 0
3 years ago
The telephone company offers two billing plans for local calls. Plan 1 charges $36 per month for unlimited calls and Plan 2 char
Katyanochek1 [597]

Answer:

After 460 calls plan 1 is more economical than plan 2

Step-by-step explanation:

Plan 1: 36x + 0y

Plan 2: 13x + 0.05y

36x < 13x + 0.05y

36x - 13x < 0.05y

23x < 0.05y

23/0.05x < y

460x < y

5 0
2 years ago
A fair four-sided spinner has the numbers 1 to 4 marked on its sides. It is spun twice and the two scores are added together.
scZoUnD [109]

Answer:

Probability of getting doubles = 1/4

Step-by-step explanation:

Given - A fair four-sided spinner has the numbers 1 to 4 marked on its sides. It is spun twice and the two scores are added together.

To find - Using a sample space diagram, find the probability of getting a double.

Proof -

Given that,

A four-sided spinner is spin twice.

So,

The Sample Space becomes

S = { (1, 1), (1, 2), (1, 3), (1, 4)

       (2, 1), (2, 2), (2, 3), (2, 4)

       (3, 1), (3, 2), (3, 3), (3, 4)

       (4, 1), (4, 2), (4, 3), (4, 4) }

So,

n(S) = 16

Now,

Let A is the event Getting a double, So,

A = { (1, 1), (2, 2), (3, 3), (4, 4) }

and

n(A) = 4

So,

The Probability of getting doubles = n(A) ÷ n(S)

                                                         = 4 ÷ 16

                                                         = 1/4

∴ we get

Probability of getting doubles = 1/4

6 0
2 years ago
There are 360 people in a movie theater. Of these people, 35% bought student tickets, and 45% bought adult tickets. The rest bou
mafiozo [28]

Answer:

20%

Step-by-step explanation:

35+45 = 80

100-80=20

6 0
2 years ago
Read 2 more answers
SOMEONE PLZ HELP ME!!!!
zheka24 [161]

Answer:

I rlly don't know.

Step-by-step explanation:

Ask ur math teacher for help.

I hope this helps u out!

6 0
2 years ago
Other questions:
  • A sports club needs to raise at least $500 by selling chocolate bars for $2.50 each. Sebastian wants to know how many chocolate
    13·2 answers
  • It would take an apprentice house painter 1.5h longer than his supervisor to paint an apartment. If they work together they can
    12·1 answer
  • Hi I need this question please asap.
    15·1 answer
  • If i had 7 apples and someone took away 5 how many would i have left
    9·2 answers
  • What is the scale factor use to create this dilation?
    10·1 answer
  • Each of the four sides of a swimming pool measures 12 meters. The pool is 6 meters deep. How much water will be needed to fill i
    6·2 answers
  • Find the domain of the function. (Enter your answers using interval notation.) f(s, t) = square root of s^2+t^2.
    5·1 answer
  • Apply the Pythagorean Theorem to find the distance between points A and C.
    8·1 answer
  • HELP I WILL GIVE BRAINLIEST<br> The first picture with a bunch of numbers is the data set
    6·1 answer
  • Mr. van der westhuizen wants to visit his grandchildren In France. he has heard that it is very expensive for South Africans to
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!