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Mathematics

1 answer:

Ierofanga [76]2 years ago

6 0

Two linear equations can have no solutions, exactly one solution or infinitely many solutions. There will be no solution if the lines are parallel on a graph. There will be exactly one solution if the lines intersect each other on a single point. And finally, there will be infinite solutions if the lines overlap each other perfectly.

A single line however has infinite ordered pair solutions as the line travels infinitely in both directions on the coordinate plane. For example, using the equation y=3x, for any real value of x, we will get a real value for y.

Linear inequalities with two variables have infinitely many solutions. We can use the inequality y>3x as an example. For any real value of x, we will get a real value for y.

I hope this helps!

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Read 2 more answers

Cars arrive at a toll booth according to a Poisson process with mean 70 cars per hour. Suppose the attendant makes a phone call.

Alexxx [7]

Answer:

35.6 seconds

Step-by-step explanation:

The Poisson distribution has a probability model that follows the given relationship:

$P(X=x) = \frac{\lambda^xe^{-\lambda}}{x!}$

For x = zero calls at a probability of 50%, the arrival rate during the call is:

$P(X=0)=0.50 = \frac{\lambda^0e^{-\lambda}}{0!}\\e^{-\lambda}=0.50\\\lambda=0.6931\ cars/ n\ seconds$

Since cars arrive at a rate of 70 per hour, the length of call 'n' in seconds is:

$r = \frac{70}{h}*\frac{1h}{3,600s} = 0.019444\ cars/s\\n= \frac{\lambda}{r}=\frac{0.6931}{0.019444} =35.6\ seconds$

The call should be at most 35.6 seconds long to ensure a 50% probability that no cars arrive during the call.

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