<span>In order to use a normal distribution to calculate confidence intervals for proportion, p, by the central limit theorem, the sample has to be sufficiently large.
This condition is determine by ensuring that np and nq > 5.
Therefore, the condition that must be satisfied is </span><span>np and nq must be > 5. (option d).</span>
Answer:
The slope of the line perpendicular to the given line is 2/3
Step-by-step explanation:
step 1
Find the slope of the given line
we have
3x+2y=6
isolate the variable y
2y=-3x+6
y=-(3/2)x+3
The slope of the given line is m=-(3/2)
step 2
Find the slope of the line perpendicular to the given line
Remember that
If two lines are perpendicular, their slopes are opposite reciprocal of each other ( the product of their slopes is equal to -1)
so
m1*m2=-1
we have
m1=-3/2
so
m2=2/3
therefore
The slope of the line perpendicular to the given line is 2/3
Answer:
(-8, -4) is the solution
Step-by-step explanation:
Determine whether or not (-8, -4) is a solution to this system. It is a solution if we can substitute -8 for x and -4 for y in both equations and find that both equations are true:
2(-8) = 5(-4) + 4 TRUE
3(-8) - 2(-4) = -16 TRUE
So (-8, -4) is a solution to the given system.
Check out the second possible solution in the same way:
2(8) = 5(4) + 4 FALSE
Check out the third possible sol'n in the same way:
2(-4) = 5(4) + 4 FALSE
Check out the fourth in the same way:
2(4) = 5(8) + 4 FALSE
So we conclude that (-8, -4) is the sole solution to the given system.
Answer:
(2,-5)
Step-by-step explanation:
See attachment
One can also solve this by calculation:
y=2x-9
y=-2x-1
-
Rearrange either equation to find x. I'll use the first:
y=2x-9
2x = y+9
x = (y+9)/2
Now use this value of x in the second equation:
y = -2x-1
y =-2((y+9)/2)-1
y = (-2y-18)/2)-1
y = -y -9 - 1
2y = -10
y = -5
Now use -5 for y in the rearranged equation:
y = -2x-1
-5 = -2x-1
-2x = -4
x = 2
Solution is (2,-5)
But the question wants a graph solution, which is also fun when you use DESMOS.