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3 years ago

Quadrilateral CDEF is reflected across the x-axis and translated 3 units left to create quadrilateral GHJK .

Mathematics

1 answer:

PilotLPTM [1.2K]3 years ago

6 0

Answer- KG⎯∥JH⎯

the given figure is a trapezium in which CF||DE

Reflection of figure CDEF and shifting it by 3 units does not change the shape of the figure but changes only its position in the x-y plane.

so, the shape of the figure GHJK will be same as that of CDEF.

so sides, KG⎯∥JH⎯

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A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 380 babies were born, a

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Answer:

The 99% confidence interval estimate of the percentage of girls born is (86.04%, 93.96%). Considering the actual percentage of girls born is close to 50%, the percentage increased considerably with this method, which means that it appears effective.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

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This means that $n = 380, \pi = \frac{342}{380} = 0.9$

99% confidence level

So $\alpha = 0.01$ , z is the value of Z that has a p-value of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.575$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.9 - 2.575\sqrt{\frac{0.9*0.1}{380}} = 0.8604$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.9 + 2.575\sqrt{\frac{0.9*0.1}{380}} = 0.9396$

As percentages:

0.8604*100% = 86.04%.

0.9396*100% = 93.96%.

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