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3 years ago

You just looked at the graph of this system of equations. Why will the lines never intersect? y = –x + 5 y = –x – 3

Mathematics

2 answers:

Serjik [45]3 years ago

7 0

Answer:

The lines are parallel

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - x + 5 is in this form with m = - 1

y = - x - 3 is in this form with m = - 1

Parallel lines have equal slopes

The 2 lines are parallel and never intersect.

IceJOKER [234]3 years ago

4 0

Sample Response:

The linear equations have the same slope, so the rate of change for each is the same. As long as the rate of change is the same, the lines will stay the same distance apart and not intersect.

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There is approximately 17% chance of a person not having a disease if he or she has tested positive.

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The information provided is:

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Compute the missing probabilities as follows:

$P(D) = 1- P(D^{c})=1-0.95=0.05\\\\P(-|D)=1-P(+|D)=1-0.98=0.02\\\\P(-|D^{c})=1-P(+|D^{c})=1-0.01=0.99$

The Bayes' theorem states that the conditional probability of an event, say A provided that another event B has already occurred is:

$P(A|B)=\frac{P(B|A)P(A)}{P(B|A)P(A)+P(B|A^{c})P(A^{c})}$

Compute the probability that a random selected person does not have the infection if he or she has tested positive as follows:

$P(D^{c}|+)=\frac{P(+|D^{c})P(D^{c})}{P(+|D^{c})P(D^{c})+P(+|D)P(D)}$

$=\frac{(0.01\times 0.95)}{(0.01\times 0.95)+(0.98\times 0.05)}\\\\=\frac{0.0095}{0.0095+0.0475}\\\\=0.1666667\\\\\approx 0.1667$

So, there is approximately 17% chance of a person not having a disease if he or she has tested positive.

As the false negative rate of the test is 1%, this probability is not unusual considering the huge number of test done.

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