M=32
Hope it helps!!!!!
Hope it helps!!!!!
A.) Describe a transformation sequence that will transform quadrilateral ABCD into quadrilateral A’B’C’D’.
1 answer:
a.) The orientation of ABCD is clockwise, as is the orientation of A'B'C'D'. This means the transformation involves a even number of reflections (may be 0). The orientation of AB is North, and the orientation of A'B' is West, so a rotation of 90° CCW (or equivalent) is involved. We can find the point of intersection of the perpendicular bisectors of AA' and BB' (at (-1, -1)) to determine a suitable center of rotation.
ABCD can be transformed to A'B'C'D' by ...
- rotation 90° CCW about the point (-1, -1)
b.) Rotation by 90° can also be accomplished by reflection across a diagonal line. Since we want the orientation to remain unchanged, we need another reflection to put the figure into its final position. A suitable alternate sequence for mapping ABCD to A'B'C'D' is ...
- reflection across the line y=x
- reflection across the line x=-1
You might be interested in
Answer:
We conclude that the actual percentage of households is equal to 30%.
Step-by-step explanation:
We are given that a consumer group suspects that the proportion of households that have three cell phones NOT known to be 30%.
Their marketing people survey 150 households with the result that 43 of the households have three cell phones.
Let p = <u><em>proportion of households that have three cell phones NOT known.</em></u>
So, Null Hypothesis, : p = 30% {means that the actual percentage of households is equal to 30%}
Alternate Hypothesis, : p
30% {means that the actual percentage of households different from 30%}
The test statistics that would be used here <u>One-sample z-test for proportions;</u>
T.S. = ~ N(0,1)
where, = sample proportion of households having three cell phones =
= 0.29
n = sample of households = 150
So, <u><em>the test statistics</em></u> =
= -0.27
The value of z test statistic is -0.27.
<u>Also, P-value of the test statistics is given by;</u>
P-value = P(Z < -0.27) = 1 - P(Z 0.27)
= 1 - 0.6064 = <u>0.3936</u>
<u>Now, at 1% significance level the z table gives critical value of -2.58 and 2.58 for two-tailed test.</u>
Since our test statistic lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <em><u>we fail to reject our null hypothesis</u></em>.
Therefore, we conclude that the actual percentage of households is equal to 30%.