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4 years ago

Which functions are the same as their inverse functions

Mathematics

1 answer:

11Alexandr11 [23.1K]4 years ago

8 0

Answer:

we need to so the functions

Step-by-step explanation:

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A boiler has five identical relief valves. The probability that any particular valve will open on demand is 0.95. Assuming indep

Gre4nikov [31]

Answer:

a) There is a 99.99997% probability that at least one valve opens.

b) There is a 22.62% probability that at least one valve fails to open.

Step-by-step explanation:

For each valve, there are only two possible outcomes. Either it open, or it does not. So 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 combinations 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:

$p = 0.95, n = 5$

(a) What is the probability that at least one valve opens?

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

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

We want $P(X \geq 1)$

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

$P(X = 0) = C_{5,0}.(0.95)^{0}.(0.05)^{5} = 0.0000003$

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0000003 = 0.9999997$

There is a 99.99997% probability that at least one valve opens.

(b) What is the probability that at least one valve fails to open?

Either all valves open, or at least one does not open. The sum of the probabilities of these events is decimal 1. So

$P(X = 5) + P(X \leq 4) = 1$

We want $P(X \leq 4)$

$P(X \leq 4) = 1 - P(X = 5)$

$P(X = 5) = C_{5,5}.(0.95)^{5}.(0.05)^{0} = 0.7738$

$P(X \leq 4) = 1 - P(X = 5) = 1 - 0.7738 = 0.2262$

There is a 22.62% probability that at least one valve fails to open.

5 0

3 years ago

The quotient of a number and - 2/3 is -9/10.

Ad libitum [116K]

It would be: -2/3 * -9/10 = 18/30 = 3/5

So, option B is your answer.

Hope this helps!

6 0

3 years ago

Read 2 more answers

Can someone help, please ;)

8090 [49]

Answer:

7/12 would be ur answer

Step-by-step explanation:

6 0

3 years ago

Joel can run around a 14– mi track in 81 sec, and Jason can run around the track in 69 sec. If the runners start at the same poi

Alenkasestr [34]

Answer:37.2 sec

Step-by-step explanation:

Given

Joel takes 81 sec for 14 mile long track

speed of joel $\frac{14}{1.35}$ mi/min=10.37 mi/min

Jason takes 69 sec for 14 mi track

so jason speed is $\frac{14}{1.15} mi/min=12.17 mi/min$

if both starts from same spot in opposite direction then

$\frac{x}{10.37}=\frac{14-x}{12.17}$

where x is distance covered by Joel

then x=6.44 miles

therefore time required

$t=\frac{6.44}{10.37}=0.621 min\approx 37.2 sec$

8 0

4 years ago

If n=3 then what is (4n-2) (7-2)

babymother [125]

The value of equation when n = 3 is 50

Solution:

Given equation is:

$(4n -2)(7-2)$

We have to find the value of equation when n = 3

By plugging in n = 3 in given equation we can find the value of given equation

Substitute n = 3 in given equation

$\rightarrow (4(3) -2)(7-2)\\\\Solve\ the\ above\ equation\\\\\rightarrow (12-2)(7-2)\\\\\rightarrow (12 - 2)(5)\\\\Simplify\ the\ above\ equation\\\\\rightarrow 10 \times 5 = 50$

Thus the value of equation when n = 3 is 50

7 0

3 years ago