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Vitek1552 [10]
3 years ago
15

What is the circumcenter

Mathematics
2 answers:
dolphi86 [110]3 years ago
7 0
The center of a circumference
34kurt3 years ago
6 0

The circumcenter is the center of a triangle's circumcircle. It can be found as the intersection of the perpendicular bisectors.

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95% confidence interval for the percentage of all U.S. public high school students who are obese is [0.110 , 0.190].

Step-by-step explanation:

We are given that 15% of a random sample of 300 U.S. public high school students were obese.

Firstly, the pivotal quantity for 95% confidence interval for the population proportion is given by;

                        P.Q. = \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }  ~ N(0,1)

where, \hat p = sample % of U.S. public high school students who were obese = 15%

           n = sample of U.S. public high school students = 300

           p = population percentage of all U.S. public high school students

<em>Here for constructing 95% confidence interval we have used One-sample z proportion statistics.</em>

<u></u>

<u>So, 95% confidence interval for the population proportion, p is ;</u>

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                             of significance are -1.96 & 1.96}  

P(-1.96 < \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } } < 1.96) = 0.95

P( -1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } < {\hat p-p} < 1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } ) = 0.95

P( \hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } < p < \hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } ) = 0.95

<u>95% confidence interval for p</u> = [\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } , \hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }]

  = [ 0.15-1.96 \times {\sqrt{\frac{0.15(1-0.15)}{300} } } , 0.15+1.96 \times {\sqrt{\frac{0.15(1-0.15)}{300} } } ]

  = [0.110 , 0.190]

Therefore, 95% confidence interval for the percentage of all U.S. public high school students who are obese is [0.110 , 0.190].

6 0
3 years ago
Caleb will be going to college next year. He would like to save some money for living expenses. Select the goal that would be th
Rina8888 [55]

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Step-by-step explanation:

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Which of the following could represent the graph of f(x)=x^3-x^2-6x?
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I think it's the first one

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