This is the concept of scale factors, we are required to calculate for the volume of the smaller solid if the larger solid has a volume of 1975.
Area scale factor=(linear scale factor)^2
thus;
Area scale factor=(area of larger solid)/(area of smaller solid)=1057/384
linear scale factor=√(1057/384)=5.7019
the volume scale factor=(linear scale factor)^3=[volume of larger solid]/[volume of smaller solid]
The volume scale factor=(5.7019)^3=185.3772
therefore;
volume of smaller solid=[volume of larger solid]/[volume scale factor]
=1795/185.3772
=9.683
The answer is 9.683 yd^3
Given
P(1,-3); P'(-3,1)
Q(3,-2);Q'(-2,3)
R(3,-3);R'(-3,3)
S(2,-4);S'(-4,2)
By observing the relationship between P and P', Q and Q',.... we note that
(x,y)->(y,x) which corresponds to a single reflection about the line y=x.
Alternatively, the same result may be obtained by first reflecting about the x-axis, then a positive (clockwise) rotation of 90 degrees, as follows:
Sx(x,y)->(x,-y) [ reflection about x-axis ]
R90(x,y)->(-y,x) [ positive rotation of 90 degrees ]
combined or composite transformation
R90. Sx (x,y)-> R90(x,-y) -> (y,x)
Similarly similar composite transformation may be obtained by a reflection about the y-axis, followed by a rotation of -90 (or 270) degrees, as follows:
Sy(x,y)->(-x,y)
R270(x,y)->(y,-x)
=>
R270.Sy(x,y)->R270(-x,y)->(y,x)
So in summary, three ways have been presented to make the required transformation, two of which are composite transformations (sequence).
Answer:
(1) 0.4207
(2) 0.7799
Step-by-step explanation:
Given,
Mean value,
Standard deviation,
(1) P(X ≥ 17.5) = 1 - P( X ≤ 17.5)
( By using z-score table )
= 0.4207
(2) P(14 ≤ X ≤ 18) = P(X ≤ 18) - P(X ≤ 14)
= 0.9918 - 0.2119
= 0.7799
ANSWER:
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