Answer: 0.0238
Step-by-step explanation:
Given : Proportion of politicians are lawyers: p= 0.56
Sample size : n= 787
Let be th sample proportion.
The the probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by greater than 4% will be :-
Hence, the required probability = 0.0238
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
Answer:
B
Step-by-step explanation:
False
Equation 1) -4x + 7y = 1
Equation 2) 25 = 2x + 5y
For both equations, move the variables all onto one side, preferably the left side.
To do so, for equation 2, subtract 2x from both sides, as well as subtracting 5y from both sides, and then subtracting 25 from both sides.
2) -2x - 5y = -25
1) -4x + 7y = 1
Multiply all of equation 2 by 2.
2) 2(-2x - 5y = -25)
2) -4x - 10y = -50
1) -4x + 7y = 1
Subtract the equations from each other.
-17y = -51
Divide both sides by -17.
y = 51/17
y = 3
Plug in 3 for y in the first equation.
-4x + 7y = 1
-4x + 7(3) = 1
-4x + 21 = 1
-4x = 1 - 21
-4x = -25
x = -25/-4
x = 25/4
x = 6 1/4
(6 1/4, 3)
~Hope I helped!~
Answer:
y = -14
Step-by-step explanation:
7y - 8y - 28 = -14
- y = -14 + 28
- y = 14
y = -14
hope it helps!