Write the equation of the line through each point.

Mathematics

1 answer:

Leya [2.2K]3 years ago

5 0

Answer:

The equation would be y = -1/3x + 4

Step-by-step explanation:

The first step to finding this equation needs to be solving the first equation for y so that we can find the slope.

-3x + y = 1

y = 3x + 1

Now that we have the slope of 3, we know the slope of a perpendicular line would be -1/3. This is because perpendicular lines have opposite and reciprocal slopes. We can then use this and the point to solve in point-slope form.

y - y1 = m(x - x1)

y - 2 = -1/3(x - 6)

y - 2 = -1/3x + 2

y = -1/3x + 4

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A machine fills containers with a particular product. Assume the filling weights are normally distributed with a variance of 0.1

Ghella [55]

Answer:

$z=-0.674$

And if we solve for $\mu$ we got

$\mu=12 +0.674*0.4=12.270$

So then the mean is $'mu = 12.270$ for this case.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

$X \sim N(\mu,\sqrt{0.16}= 0.4)$

For this part we want to find a value a, such that we satisfy this condition:

$P(X>12)=0.85$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.25 of the area on the left and 0.85 of the area on the right it's z=-0.674. On this case P(Z<-0.674)=0.25 and P(z>-0.674)=0.85

If we use condition (b) from previous we have this:

$P(X$