Answer:
a) P(X∩Y) = 0.2
b) 
= 0.16
c) P = 0.47
Step-by-step explanation:
Let's call X the event that the motorist must stop at the first signal and Y the event that the motorist must stop at the second signal.
So, P(X) = 0.36, P(Y) = 0.51 and P(X∪Y) = 0.67
Then, the probability P(X∩Y) that the motorist must stop at both signal can be calculated as:
P(X∩Y) = P(X) + P(Y) - P(X∪Y)
P(X∩Y) = 0.36 + 0.51 - 0.67
P(X∩Y) = 0.2
On the other hand, the probability that he must stop at the first signal but not at the second one can be calculated as:
= P(X) - P(X∩Y)
= 0.36 - 0.2 = 0.16
At the same way, the probability 
that he must stop at the second signal but not at the first one can be calculated as:
= P(Y) - P(X∩Y)
= 0.51 - 0.2 = 0.31
So, the probability that he must stop at exactly one signal is:
How are you? Ok so It probably B but I’m not sure so just wait a few minutes till someone else answers because I’m not sure
D. -2p + q - 5 - you have to multiply, then distribute parentheses and apply plus or minus rules.
The answer to this question is letter B
Answer: Let's assume that the pig pens need to be fenced in the way shown in the diagram above.
Then, the perimeter is given by
4
x
+
3
y
=
160
.
4
x
=
160
−
3
y
x
=
40
−
3
4
y
The area of a rectangle is given by
A
=
L
×
W
, however here we have two rectangles put together, so the total area will be given by
A
=
2
×
L
×
W
.
A
=
2
(
40
−
3
4
y
)
y
A
=
80
y
−
3
2
y
2
Now, let's differentiate this function, with respect to y, to find any critical points on the graph.
A
'
(
y
)
=
80
−
3
y
Setting to 0:
0
=
80
−
3
y
−
80
=
−
3
y
80
3
=
y
x
=
40
−
3
4
×
80
3
x
=
40
−
20
x
=
20
Hence, the dimensions that will give the maximum area are
20
by
26
2
3
feet.
A graphical check of the initial function shows that the vertex is at
(
26
2
3
,
1066
2
3
)
, which represents one of the dimensions that will give the maximum area and the maximum area, respectively.
Hopefully this helps!
Step-by-step explanation: hope this helps
