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Harman [31]
3 years ago
11

Which biconditional is NOT a good definition?

Mathematics
2 answers:
Lady_Fox [76]3 years ago
8 0
The answer is D because and obtuse angle is 91 degrees or more
Vladimir79 [104]3 years ago
6 0
<h2>Answer:</h2>

Option: d is the correct answer.

  d.   An angle is obtuse if and only if its measure is greater than 180°      

<h2>Step-by-step explanation:</h2>

<u>Acute angle--</u>

An angle is acute if and only if the measure of the angle is strictly less than 90 degree.

<u>Right angle--</u>

An angle is right angle if and only if the measure of the angle is exactly equal to 90 degree.

<u>Obtuse angle--</u>

An angle is said to be obtuse if and only if the measure of the angle is strictly greater than 90 degree and strictly less than 180 degree.

<u>Congruent angles--</u>

Two angles are said to be congruent if and only if both the angles have the same measure.

Hence, the biconditional which is NOT a good definition is:

                                    Option: d

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I need help with this question
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<h2>C</h2>

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A newsgroup is interested in constructing a 90% confidence interval for the proportion of all Americans who are in favor of a ne
Leto [7]

Answer:

The 90% confidence interval for the proportion of all Americans who are in favor of a new Green initiative is (0.6247, 0.6923).

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}.

Of the 533 randomly selected Americans surveyed, 351 were in favor of the initiative.

This means that n = 533, \pi = \frac{351}{533} = 0.6585

90% confidence level

So \alpha = 0.1, z is the value of Z that has a p-value of 1 - \frac{0.1}{2} = 0.95, so Z = 1.645.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6585 - 1.645\sqrt{\frac{0.6585*0.3415}{533}} = 0.6247

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6585 + 1.645\sqrt{\frac{0.6585*0.3415}{533}} = 0.6923

The 90% confidence interval for the proportion of all Americans who are in favor of a new Green initiative is (0.6247, 0.6923).

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