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1 answer:
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Answer:
The rule of dilation is .
The vertices of the dilated triangle are ,
and
, respectively.
Step-by-step explanation:
From Linear Algebra, we define the dilation by the following definition:
(1)
Where:
- Center of dilation, dimensionless.
- Scale factor, dimensionless.
- Original point, dimensionless.
- Dilated point, dimensionless.
If we know that ,
,
,
and
, then dilated points of triangle ABC are, respectively:
(2)
(3)
(4)
The rule of dilation is:
(5)
The vertices of the dilated triangle are ,
and
, respectively.
Answer:
Percentage of scores that fall between 70 and 80 = 24.34%
Step-by-step explanation:
We are given a test with a population mean of 75 and standard deviation equal to 16.
Let X = Percentage of scores
Since, X ~ N()
The z probability is given by;
Z = ~ N(0,1) where,
= 75 and
= 16
So, P(70 < X < 80) = P(X < 80) - P(X <= 70)
P(X < 80) = P( <
) = P(Z < 0.31) = 0.62172
P(X <= 70) = P( <
) = P(Z < -0.31) = 1 - P(Z <= 0.31)
= 1 - 0.62172 = 0.37828
Therefore, P(70 < X < 80) = 0.62172 - 0.37828 = 0.24344 or 24.34%