Answer:
A solution curve pass through the point (0,4) when .
There is not a solution curve passing through the point(0,1).
Step-by-step explanation:
We have the following solution:
Does any solution curve pass through the point (0, 4)?
We have to see if P = 4 when t = 0.
A solution curve pass through the point (0,4) when .
Through the point (0, 1)?
Same thing as above
No solution.
So there is not a solution curve passing through the point(0,1).
First, find the slope (m) = =
=
=
Now plug in ONE of the points and the slope into the point-slope equation:
y - y₁ = m(x - x₁); where (x₁, y₁) is the chosen point.
y - 5 = (x - 1) (I used (1,5) as the chosen point)
3(y - 5) = x - 1
3y - 15 = x - 1
3y -14 = x
-14 = x - 3y → x - 3y = -14
Answer: x - 3y = -14
Answer:
A. 13.9 and 14.1 inches
See explanation below.
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 outside diameters of a population, and for this case we know the distribution for X is given by:
Where and
If we want the middle 68% of the data we need to have on the tails 16% on each one
For this part we want to find a value a, such that we satisfy this condition:
(a)
(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 0.16 of the area on the left and 0.84 of the area on the right it's z=-0.994. On this case P(Z<-0.994)=0.16 and P(z>-0.994)=0.84
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
And since the distribution is symmetrical for the upper limit we can use z = 0.994 and we have:
And if we solve for a we got
So the correct answer for this case would be:
A. 13.9 and 14.1 inches