Answer:
-320................................
Answer:y=-y
Step-by-step explanation:
Answer




Explanation:
Given
See attachment for proper data presentation
--- Sample
A = Supplier 1
B = Conforms to specification
Solving (a): P(A)
Here, we only consider data in sample 1 row.
Here:
and 



P(A) is then calculated as:



Solving (b): P(B)
We only consider data in the Yes column.
Here:
and 



P(B) is then calculated as:



Solving (c): P(A n B)
Here, we only consider the similar cell in the yes column and sample 1 row.
i.e. [Supplier 1][Yes]
This is represented as: n(A n B)

The probability is then calculated as:



Solving (d): P(A u B)
This is calculated as:

This gives:

Take LCM




First, turn
into an improper fraction with a denominator of 4, which matches
.

Now, just add the numerators.


is conservative if we can find a scalar function
such that
. This would require



Integrating both sides of the first equation wrt
gives

Differentiating both sides of this wrt
gives

but we assumed
was a function of
and
, independent of
. So there is no such
and
is not conservative.
To find the work, first parameterize the path (call it
) by

for
. Then

and the work is given by the line integral,

