Answer:
Step-by-step explanation:
<u>a)</u>
- Given that ; X ~ N ( µ = 65 , σ = 4 )
From application of normal distribution ;
- Z = ( X - µ ) / σ, Z = ( 64 - 65 ) / 4, Z = -0.25
- Z = ( 66 - 65 ) / 4, Z = 0.25
Hence, P ( -0.25 < Z < 0.25 ) = P ( 64 < X < 66 ) = P ( Z < 0.25 ) - P ( Z < -0.25 ) P ( 64 < X < 66 ) = 0.5987 - 0.4013
- P ( 64 < X < 66 ) = 0.1974
b) X ~ N ( µ = 65 , σ = 4 )
From normal distribution application ;
- Z = ( X - µ ) / ( σ / √(n)), plugging in the values,
- Z = ( 64 - 65 ) / ( 4 / √(12)) = Z = -0.866
- Z = ( 66 - 65 ) / ( 4 / √(12)) = Z = 0.866
P ( -0.87 < Z < 0.87 )
- P ( 64 < X < 66 ) = P ( Z < 0.87 ) - P ( Z < -0.87 )
- P ( 64 < X < 66 ) = 0.8068 - 0.1932
- P ( 64 < X < 66 ) = 0.6135
c) From the values gotten for (a) and (b), it is indicative that the probability in part (b) is much higher because the standard deviation is smaller for the x distribution.
<u>Answer:
</u>
The point-slope form of the line that passes through (1,-5) and is parallel to a line with a slope of 1 is y + 5 = x – 1
<u>Solution:
</u>
The point slope form of the line that passes through the points 
and parallel to the line with slope “m” is given as
---- equation 1
Where “m” is the slope of the line. 
and 
are the points that passes through the line.
From question, given that slope “m” = 1
Given that the line passes through the points (1,-5). Hence we get 
and 
By substituting the values in eqn 1, we get the point slope form of the line which is parallel to the line having slope 1 can be found out.
y – (-5) = 1(x – 1)
y + 5 = x – 1
hence the point slope form of given line is y + 5 = x – 1
Answer:
y=-5/4x-4.
Step-by-step explanation:
parallel lines have to have the same slope so they don't intersect each other
original equation with the same slope and rewrite it using point slope form:
y-y1=-5/4(x-x1) now Substitute the point(-4,1)
y-1=-5/4(x-(-4))
y-1=-5/4(x+4)
Now we can distribute the -5/4 and add 1 to the right to get our final slope-intercept form:
y-1=-5/4x-5
y=-5/4x-4.
The parallel line of y=-5/4x+7 that passes through point (-4,1) is y=-5/4x-4.
Answer:
s = 4.579 mm
Step-by-step explanation:
The volume of a cube is side * side * side. We know the volume, so plug it in to find side length.
V = s^3
96 = s^3
<u>s = 4.579 mm</u>
The answer is (x-4)(x-12)
