What is 2/3 dividend by 1/2?<br><img src="https://tex.z-dn.net/?f=%20%5Cdiv%20" id="TexFormula1" title=" \div " alt=" \div " ali

How large a sample should be selected to provide a 95% confidence interval with a margin of error of 6? Assume that the populati

marshall27 [118]

Using the z-distribution, it is found that a sample of 171 should be selected.

<h3>What is a z-distribution confidence interval?</h3>

The confidence interval is:

$\overline{x} \pm z\frac{\sigma}{\sqrt{n}}$

The margin of error is:

$M = z\frac{\sigma}{\sqrt{n}}$

In which:

$\overline{x}$ is the sample mean.

z is the critical value.

n is the sample size.

$\sigma$ is the standard deviation for the population.

For this problem, the parameters are:

$z = 1.96, \sigma = 40, M = 6$

Hence we solve for n to find the needed sample size.

$M = z\frac{\sigma}{\sqrt{n}}$

$6 = 1.96\frac{40}{\sqrt{n}}$

$6\sqrt{n} = 40 \times 1.96$

$\sqrt{n} = \frac{40 \times 1.96}{6}$

$(\sqrt{n})^2 = \left(\frac{40 \times 1.96}{6}\right)^2$

n = 170.7.

Rounding up, a sample of 171 should be selected.

More can be learned about the z-distribution at brainly.com/question/25890103

#SPJ1

4 0

2 years ago

Find angle D if angle B = 50

Mariana [72]

<h3>Answer: 80 degrees</h3>

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Explanation:

I'm assuming that segments AD and CD are tangents to the circle.

We'll need to add a point E at the center of the circle. Inscribed angle ABC subtends the minor arc AC, and this minor arc has the central angle AEC.

By the inscribed angle theorem, inscribed angle ABC = 50 doubles to 2*50 = 100 which is the measure of arc AC and also central angle AEC.

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Focus on quadrilateral DAEC. In other words, ignore point B and any segments connected to this point.

Since AD and CD are tangents, this makes the radii EA and EC to be perpendicular to the tangent segments. So angles A and C are 90 degrees each for quadrilateral DAEC.

We just found angle AEC = 100 at the conclusion of the last section. So this is angle E of quadrilateral DAEC.

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Here's what we have so far for quadrilateral DAEC

angle A = 90
angle E = 100
angle C = 90
angle D = unknown

Now we'll use the idea that all four angles of any quadrilateral always add to 360 degrees

A+E+C+D = 360

90+100+90+D = 360

D+280 = 360

D = 360-280

D = 80

Or a shortcut you can take is to realize that angles E and D are supplementary

E+D = 180

100+D = 180

D = 180-100

D = 80

This only works if AD and CD are tangents.

Side note: you can use the hypotenuse leg (HL) theorem to prove that triangle EAD is congruent to triangle ECD; consequently it means that AD = CD.

5 0

3 years ago

The junior and senior classes at Central High School were asked to choose a destination for a field trip. The results are shown

Ann [662]

Solution:

We are given below frequency table:

Amusement-Park Museum Broadway-Show Total

Juniors 57 21 42 120

Seniors 64 44 58 166

Total 121 65 100 286

We have to find the percentage of surveyed students who chose the amusement park.

From the table, we see there are total 121 students who chose amusement park out of total 286 students.

Therefore, the percentage of surveyed students who chose the amusement park is given below:

$\frac{121}{286}\times 100=42.3\%$

Hence, the option A. 42.30% correct.

3 0

3 years ago

HELPPPPPPPPP PLEASEEEEE<br><br> Write the perimeter of the triangle as a polynomial

GuDViN [60]

It’s either B or D. I’m sorry I’m not so sure but I think it’s either one of those.

6 0

3 years ago

Alicia, Malik, Joey, and Hailey had some pencils. Alicia gave 18 pencils to Malik. She received 10 pencils from Joey and 23 penc

strojnjashka [21]

Answer:

61

Step-by-step explanation:

subtract the ones she got add the ones she gave away

6 0

2 years ago

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