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Juliette [100K]
3 years ago
13

(25 points) Which list contains only rational numbers?

Mathematics
1 answer:
Shkiper50 [21]3 years ago
8 0
A rational number is any number that can be wrote as a fraction (p/q). A rational number is the quotient or fraction of two integers. It is seen as a ratio of two integers as well. Repeating/terminating decimals are also rational numbers as they can be shown as the ratio of two integers. (p/q) the fraction, will have both the numerator and denominator being whole numbers.

what we can do: Look at each number in the sequences and see which will have only rational numbers. A: 0 is rational, 1/2 is rational because it is a ratio of two integers, 1.5 is rational because it can be written as 3/2, and 2.82843 is rational because it can be wrote over one as a ratio of two integers.

So A is the only list that contains only rational numbers.
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Answer: -3

Step-by-step explanation:

The rate of change in a graph is the same as the slope. To find the slope, divide the change in y by the change in x. In this case, it's -9/3, which gets you -3.

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3 years ago
A survey asked whether respondents favored or opposed the death penalty for people convicted of murder. Software shows the resul
pav-90 [236]

Answer:

95% confidence interval for the proportion of the adults who were opposed to the death penalty is (0.668, 0.704).

Step-by-step explanation:

We are given that a survey asked whether respondents favored or opposed the death penalty for people convicted of murder. Software shows the results below, where X refers to the number of the respondents who were in favor.

X = 1,790

N = 2,610

\hat p = Sample proportion = X/N = 0.6858

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 proportion = 0.6858

           n = sample of respondents = 2,610

           p = population proportion

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

So, 95% confidence interval for the population​ proportion, p is ;

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} }]

  = [ 0.6858-1.96 \times {\sqrt{\frac{0.6858(1-0.6858)}{2610} } , 0.6858+1.96 \times {\sqrt{\frac{0.6858(1-0.6858)}{2610} } ]

  = [0.668 , 0.704]

Therefore, 95% confidence interval for the population proportion of the adults is (0.668, 0.704).

3 0
3 years ago
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nika2105 [10]

Answer:

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Step-by-step explanation:

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Explanation:

Add the two equations together to eliminate y from the system.

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Substitute the value found for x into one of the original equations to solve for y

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Move all terms to one side to make it easier

-y=2-7

Subtract

y=5


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Answer:

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Step-by-step explanation:

7 0
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