Answer:

Step-by-step explanation:
Given:
Center of circle is at (5, -4).
A point on the circle is 
Equation of a circle with center
and radius 'r' is given as:

Here, 
Radius of a circle is equal to the distance of point on the circle from the center of the circle and is given using the distance formula for square of the distance as:
Using distance formula for the points (5, -4) and (-3, 2), we get

Therefore, the equation of the circle is:

Now, rewriting it in the form asked in the question, we get

Answer:
a) Q(-2,1) is false
b) Q(-5,2) is false
c)Q(3,8) is true
d)Q(9,10) is true
Step-by-step explanation:
Given data is
is predicate that
then
. where
are rational numbers.
a)
when 
Here
that is
satisfied. Then

this is wrong. since 
That is 
Thus
is false.
b)
Assume
.
That is 
Here
that is
this condition is satisfied.
Then

this is not true. since
.
This is similar to the truth value of part (a).
Since in both
satisfied and
for both the points.
c)
if
that is
and
Here
this satisfies the condition
.
Then 
This also satisfies the condition
.
Hence
exists and it is true.
d)
Assume 
Here
satisfies the condition 
Then 
satisfies the condition
.
Thus,
point exists and it is true. This satisfies the same values as in part (c)
Answer:
Negative Association.
Step-by-step explanation:
Association between variables:
Association between variables can be classified as positive or negative.
Positive: Both move in the same direction, that is, either both increase or both decrease.
Negative: The variables move in opposite directions, one increases and the other decreases.
In this question:
As the first increases the second decreases, that is, they move in opposite directions, so it is a Negative Association.
Since you are given that the student registered early, the total number you deal with is all students who registered early.
211 + 329 = 540
number of undergraduates who registered early = 211
Among students who registered early:
p(undergraduate) = 211/540