Enter the system represented on the graph below. Find and explain the meaning of the point of intersection of the lines.

Mathematics

1 answer:

myrzilka [38]3 years ago

5 0

Answer:

y = -2x+4

y = (3/2)x -3

The point of intersection is (2, 0), or x=2 and y=0.

Step-by-step explanation:

The downward-sloping line drops 2 grid squares for each 1 it goes to the right, so its slope is -2. It intersects the y-axis at +4. In slope-intercept form, its equation is ...

y = slope · x + (y-intercept)

y = -2x + 4

Similarly, the upward-sloping line rises 3 grid squares for each 2 it goes to the right, so its slope is 3/2. It intersects the y-axis at -3. Its equation is ...

y = (3/2)x -3

The two lines intersect at the point where x=2 and y=0, so the coordinates are (2, 0). These are the values of x and y that satisfy both equations, so are the solution to the system.

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A machine making computer chips isn't working correctly, and 5% of the computer chips it makes are defective. If an inspector ch

Rainbow [258]

Answer:

0.25% probability that they are both defective

Step-by-step explanation:

For each computer chip, there are only two possible outcomes. Either they are defective, or they are not. The probability of a computer chip being defective is independent of other chips. So we use the binomial probability distribution to solve this question.

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 combinations 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.

5% of the computer chips it makes are defective.

This means that $p = 0.05$

If an inspector chooses two computer chips randomly (meaning they are independent from each other), what is the probability that they are both defective?

This is P(X = 2) when n = 2. So

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

$P(X = 2) = C_{2,2}.(0.05)^{2}.(0.95)^{0} = 0.0025$