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Zepler [3.9K]
3 years ago
6

The figure below shows a rectangle ABCD having diagonals AC and DB: A rectangle ABCD is shown with diagonals AC and BD. Anastasi

a wrote the following proof to show that the diagonals of rectangle ABCD are congruent: Anastasia's proof: Statement 1: Statement 2: AB = DC (opposite sides of a rectangle are congruent) Statement 3: AC2 = DB2 (from statements 1 and 2) Statement 4: AC = DB (taking square root on both sides of AC2 = DB2) Which statement below completes Anastasia's proof? In triangle ADC and BCD, AB = DC (opposite sides of a rectangle are congruent) In triangle ADC and BCD, AB = DC (opposite sides of a rectangle are parallel) In triangle ADC and BCD, AD = BC (opposite sides of a rectangle are congruent) In triangle ADC and BCD, AD = BC (opposite sides of a rectangle are parallel)
Mathematics
1 answer:
erica [24]3 years ago
7 0

Answer:In triangle ADC and BCD, AD = BC (opposite sides of a rectangle are congruent)


Step-by-step explanation:

As congruent means shapes having the same length and same internal angles.  In the given figure the two statements are already written. The only information about sides AD and BC are missing to complete the proof of congruent diagonals.


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Out of 100 people sampled, 42 had kids. Based on this, construct a 99% confidence interval for the true population proportion of
maksim [4K]

Answer:

The 99% confidence interval for the true population proportion of people with kids is (0.293, 0.547).

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}.

Out of 100 people sampled, 42 had kids.

This means that n = 100, \pi = \frac{42}{100} = 0.42

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}} = 0.42 - 2.575\sqrt{\frac{0.42*0.58}{100}} = 0.293

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.42 + 2.575\sqrt{\frac{0.42*0.58}{100}} = 0.547

The 99% confidence interval for the true population proportion of people with kids is (0.293, 0.547).

7 0
3 years ago
Find the equation of a line parallel to −x+5y=1 that contains the point (−1,2)
arsen [322]

Answer:

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Step-by-step explanation:

Find the slope of the original line and use the point-slope formula  y-y^1=m(x-x^1) to find line parallel to -x+5y=1

Hope this helps

6 0
3 years ago
Read 2 more answers
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Feliz [49]

Answer:

The answer to your question are letters A, C and D.

Step-by-step explanation:

To factor this polynomial we need to look for the common factor of the three terms.

To find it, get the greatest common factor

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                            7     7      7     7

                             1     1       1    

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Factor the polynomial

140c + 28 - 14a = 14 ( 10c + 2 - a)

Factor only 7          7(20c + 4 - 2a)

Factor only 2          2 (70c + 14 - 7a)

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Complete the following direct proof:
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B. I hope this help please let me know if it's correct.
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1678-1463/1463 * 100 = -12.8128

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