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3 years ago

Please help 10 points

Mathematics

1 answer:

Margarita [4]3 years ago

6 0

Answer:

The value of x is -2 and 2.

Step-by-step explanation:

When solve an expression, you have to make the expression equals to 0 by moving all the terms to one side :

x² - 3x - 1 = -3x + 3

x² - 3x - 1 + 3x - 3 = 0

x² - 4 = 0

Next, you have to factorize and solve it :

x² - 4 = 0

x² + 2x - 2x - 4 = 0

x(x + 2) - 2(x + 2) = 0

(x + 2)(x - 2) = 0

x + 2 = 0

x = -2

x - 2 = 0

x = 2

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Step-by-step explanation:

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3 years ago

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.

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3 years ago

Read 2 more answers

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Then, using the circle area formula, the area of the 1/9 circle would be:
full circle area= pi * r^2
full circle area= 22/7 * 6^2
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Step-by-step explanation: