Lennox concluded: "It's not possible to map \triangle DCE△DCEtriangle, D, C, E onto \triangle ABE△ABEtriangle, A, B, E using a s
equence of rigid transformations and dilations, so the triangles are not similar."
1 answer:
Answer:
Lennox was curious if triangles \triangle ABE△ABEtriangle, A, B, E and \triangle DCE△DCEtriangle, D, C, E were similar, so she tried to map one figure onto the other using a reflection and a dilation. Lennox concluded: "It's not possible to map \triangle DCE△DCEtriangle, D, C, E onto \triangle ABE△ABEtriangle, A, B, E using a sequence of rigid transformations and dilations, so the triangles are not similar." What error did Lennox make in her conclusion?
Step-by-step explanation:
A rigid transformation is also called an isometry. The transformation of the plane has preserved the size of the triangle (object). So after transformation, the triangle size does not change.
A dilation is an enlargement or reduction of a triangle (object) by a scale factor and with a center of dilation. The scale factor refers to the change in size.
A dilation is a transformation that produces a triangle (object) that is the same shape as the original but is a different size. After dilation, the pre-triangle (pre-object) and triangle (object) have the same shape but not the same size.
Similar figures (object) means figures (object) that have the same shape but may have different sizes.
The figure is not similar, we can not map triangle DCE onto the triangle ABE, both shapes are different.
Line CD can not dilate to line AB with same scale factor.
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Answer:
- -2.2
- 1.4%
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The z-value is computed from ...
... z = (x -µ)/σ
... z = (184 -206)/10 = -2.2 . . . . for $184
... z = (200 -206)/10 = -0.6 . . . . for $200
You can look up these values in a normal distribution table, or you can use an appropriate calculator to find the corresponding percentiles.
... -2.2 corresponds to the 1.390 percentile. (That amount of area is below -2.2 standard deviations from the mean.)
... -0.6 corresponds to the 27.425 percentile.
Subtracting the two percentages gives the percentage of expenses between $184 and $200. That number is 26.035% ≈ 26%.
_____
<em>Comment on the calculator display</em>
The difference that got cut off from the display in the attachment is ...
... 0.2603496703
The <em>normalcdf( )</em> function requires a lower limit. Using -8 standard deviations is effectively equivalent to -∞ for this purpose, as any lower number has no effect on the least-significant digits of the result.
