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3 years ago

(25 points) Which list contains only rational numbers?

1 answer:

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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PLEASE I NEED HELP ASAP THANK YOU :) <3

Ainat [17]

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

Tom rolls 2 fair dice and adds the results from each. Work out the probability of getting a total that is a factor of 21.

nika2105 [10]

Answer:

3 plus 4. and 2 plus 1. or 4 plus 3 or 1 plus 2

Step-by-step explanation:

5 0

3 years ago

Solve by elimination method : x - y = 2 , x + y = 12.

aalyn [17]

Answer: (7,5) X=7 and Y=5

Explanation:

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

x-y=2 + x+y=12
= 2x = 14

Divide both sides by 2

x=7

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

(7)-y=2

Move all terms to one side to make it easier

-y=2-7

Subtract

y=5

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3 years ago

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saw5 [17]

Answer:

Step-by-step explanation:

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3 years ago