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Murljashka [212]
3 years ago
7

A survey of 85 families showed that 36 owned at least one DVD player. Find the 99% confidence interval estimate of the true prop

ortion of families who own at least one DVD player. Place your limits, rounded to 3 decimal places, in the blanks. Place the lower limit in the first blank and the upper limit in the second blank
Mathematics
1 answer:
attashe74 [19]3 years ago
8 0

Answer:

0.424 - 2.58\sqrt{\frac{0.424(1-0.424)}{85}}=0.286

0.424 + 2.58\sqrt{\frac{0.424(1-0.424)}{85}}=0.562

The 99% confidence interval would be given by (0.286;0.562)

Step-by-step explanation:

Information given:

X= 36 represent the families owned at least one DVD player

n= 85 represent the total number of families

\hat p=\frac{36}{85}= 0.424 represent the estimated proportion of families owned at least one DVD player

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by \alpha=1-0.99=0.01 and \alpha/2 =0.05. And the critical value would be given by:

z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58

The confidence interval for the mean is given by the following formula:  

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

If we replace the values obtained we got:

0.424 - 2.58\sqrt{\frac{0.424(1-0.424)}{85}}=0.286

0.424 + 2.58\sqrt{\frac{0.424(1-0.424)}{85}}=0.562

The 99% confidence interval would be given by (0.286;0.562)

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The limit of the given function if \lim_{x \to 0} f(x)=4 is 64

<h3>Limit of a function</h3>

Given the following limit of a function expressed as;

\lim_{x \to 0} f(x)=4

We are to determine the value of the function

\frac{1}{4}  \lim_{x \to 0} [f(x)]^4


This can also be expressed as

\frac{1}{4}  \lim_{x \to 0} [f(x)]^4\\ = \frac{1}{4}(4)^4 \\=1/4\times 256\\=64

Hence the limit of the given function if \lim_{x \to 0} f(x)=4 is 64

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2 years ago
-13.9+(-12.8) evaluate the answer
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Answer:

<u>=-26.7</u>

Step-by-step explanation:

=-13.9+(-12.8)

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<u>=-26.7</u>

8 0
2 years ago
Read 2 more answers
What is the value of x, the side length of the smallest square (please show work) Thanks!
Ratling [72]

Answer:

8 cm

Step-by-step explanation:

Ok lets on the biggest square we have 17 cm

17cm is the hypotenuse for the right triangle

The second largest's area is 225 cm^2

Sq root of 225 cm^2, is 15

To find x, lets plug the info we have to the pythagorean theorom

a^2 + b^2 = c^2\\a^2 + 15^2 = 17^2\\a^2 + 225 = 289\\\\289 - 225 = a^2\\64=a^2\\a = 8 cm

The side length of the smallest Square is 8 cm

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Present a picture of an object (TV, Ipad Screen, Book Cover) that contains a right angle (it could be something in nature or tha
myrzilka [38]

The measure of hypotenuse using the ruler is 25.5 cm and using the formula is 23.43 cm, they are not same, and formula can be used to in the real life problems as well.

<h3>What is a right-angle triangle?</h3>

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

The question is incomplete:

The complete question is:

Present a picture of an object (TV, Ipad Screen, Book Cover) that contains a right angle (it could be something in nature or that is man-made). Use a ruler or measuring tape to measure the two sides that make the right angle and measure the distance from the end of one side to the end of the other side (hypotenuse). Draw a diagram of the object including the measurements. Use your leg measurements on your diagram to calculate a theoretical hypotenuse. (Show all steps).

  • Does the hypotenuse that measured with a ruler/measuring tape equal the hypotenuse you calculated?
  • Why do you think they are or are not exactly the same?
  • What did you learn from developing this presentation?

We are assuming the length of one side x:

x = 18 cm

Length of other side y:

y = 15 cm

And length of the hypotenuse z:

z = 23.5 cm

From the Pythagoras theorem:

z² = x² + y²

z² = 18² + 15²

z² = 549

z = √54 = 23.43 cm

The measure of hypotenuse is:

Using ruler: x = 25.5 cm

Using formula: x = 23.43 cm

They are not equal due to the reading in the ruler.

The formula can be used to in the real life problems as well.

Thus, the measure of hypotenuse using the ruler is 25.5 cm and using the formula is 23.43 cm, they are not same, and formula can be used to in the real life problems as well.

Learn more about the right angle triangle here:

brainly.com/question/3770177

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