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3 years ago

What is the next number in the series? 83 79 75 71 67

2 answers:

7 0

This is an arithmetic sequence with a common difference of -4, meaning that each term is four less than the previous term. So the next term in that sequence (technically the term "series" should be reserve for infinite sequences) will be 67-4=63.

Brilliant_brown [7]3 years ago

3 0

83-79 =4

79-75 = 4

the numbers are decreasing by 4

so the next number would be 67-4 = 63

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

noname [10]

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:

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

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

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

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

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.

5 0

3 years ago

Read 2 more answers

Can you help me plss!

Ksivusya [100]

(1/3) × the cone's volume = The cylinder's volume.

Step-by-step explanation:

Step 1:

The volume of any cone is obtained by multiplying $\frac{1}{3}$ with π, the square of the radius ( $r^{2}$ ) and the height ( $h$ ).

So the volume of the cone, $V=\pi r^{2} \frac{h}{3}$ .

Step 2:

The cylinder's volume is nearly the same as the cone but instead by multiplying $\frac{1}{3}$ we multiply with 1.

So the cylinder's volume is determined by multiplying π with the square of the radius of the cylinder ( $r^{2}$ ) and the height of the cylinder ( $h$ ).

So the the cone's volume, $V = \pi r^{2} h$ .