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2 years ago

What is the value of x?

Mathematics

2 answers:

andrey2020 [161]2 years ago

3 0

Answer:

91 degrees

Step-by-step explanation:

Don't count mine someone fixed it for me

sergejj [24]2 years ago

3 0

<h3>Answer</h3>

X=91

<h3>Step -by Step explanation</h3>

or,X+32+57=180

or,X+89=180

or,X=180-89

or,X=91

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A programmer plans to develop a new software system. In planning for the operating system that he will use, he needs to estimat

Vedmedyk [2.9K]

Using the z-distribution, we have that:

a) A sample of 601 is needed.

b) A sample of 93 is needed.

c) A. Yes, using the additional survey information from part (b) dramatically reduces the sample size.

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $\alpha$ , 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 $\frac{1+\alpha}{2}$ .

The margin of error is:

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

95% confidence level, hence $\alpha = 0.95$ , z is the value of Z that has a p-value of $\frac{1+0.95}{2} = 0.975$ , so $z = 1.96$ .

For this problem, we consider that we want it to be within 4%.

Item a:

The sample size is <u>n for which M = 0.04.</u>

There is no estimate, hence $\pi = 0.5$

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

$0.04 = 1.96\sqrt{\frac{0.5(0.5)}{n}}$

$0.04\sqrt{n} = 1.96\sqrt{0.5(0.5)}$

$\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.04}$

$(\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.04}\right)^2$

$n = 600.25$

Rounding up:

A sample of 601 is needed.

Item b:

The estimate is $\pi = 0.96$ , hence:

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

$0.04 = 1.96\sqrt{\frac{0.96(0.04)}{n}}$

$0.04\sqrt{n} = 1.96\sqrt{0.96(0.04)}$

$\sqrt{n} = \frac{1.96\sqrt{0.96(0.04)}}{0.04}$

$(\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.96(0.04)}}{0.04}\right)^2$

$n = 92.2$

Rounding up:

A sample of 93 is needed.

Item c:

The closer the estimate is to $\pi = 0.5$ , the larger the sample size needed, hence, the correct option is A.

For more on the z-distribution, you can check brainly.com/question/25404151

8 0

2 years ago

Which congruence statements are true? Choose all answers that are correct?<br><br> A: B: C: D:

tester [92]

Answer:

Correct choices are A and C

Step-by-step explanation:

Inscribed angles property: The inscribed angles subtended by the same arc are equal.

1. Angles EFH and EGH are both inscribed angles subtended by the arc EH. Therefore, these angles are congruent (option A is true).

2. Angles GHF and GEF are both inscribed angles subtended by the arc GF. Therefore, these angles are congruent (option C is true).

3. Angles EGH and FHG are interior angles of the triangle KGH and can be congruent (if triangle is isosceles) or can be not congruent (in general). Thus, option B is false.

4. Angles EFH and FHG in general are not congruent. They can be congruent only when arcs EH and FG have the same measure. In general, option D is false.

4 0

3 years ago

Find the vertices and foci of the hyperbola with equation quantity x plus 1 squared divided by 225 minus the quantity of y plus

miss Akunina [59]

Answer:

The vertices are (-16,-5) and (14,-5)

The foci are (-26,-5) and (24,-5)