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AveGali [126]
2 years ago
14

Choose the graph which represents the solution to the inequality: 3x + 8 ≥ 11

Mathematics
1 answer:
Mashutka [201]2 years ago
8 0

The solution of the inequality is x ≥ 1.

Solution:

Given inequality:

3 x+8 \geq 11

To find the solution of the inequality:

3 x+8 \geq 11

Subtract 8 from both sides.

3 x+8-8 \geq 11-8

3 x \geq 3

Divide by 3 on both sides.

$\frac{3 x}{3} \geq \frac{3}{3}

On simplifying this, we get

x \geq 1

The solution of the inequality is x ≥ 1.

The graph of the solution is attached below.

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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
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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.

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2 years ago
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P(factor of 30 chosen is a 2-digit number) = number of two-digit factors ÷ number of factors

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