A randomized telephone survey of adults in the United States determines that a certain number out of 504 respondents have one or more pets. They use p^ to construct a 95% confidence interval to estimate the proportion p of American adults who have pets to be (0.56137,0.60529). How many respondents said they have one or more pets?
283
294
305
290

The critical value for 95% of confidence is

And since we know the total and the proportion is defined as:

If we solve for X (number of people who say yes) we got:

And the best answer would be:

294

Step-by-step explanation:

We know that the confidence interval for the proportion is given by:

The margin of error for the proportion interval is given by this formula:  

   (a)  

The margin of error can be calculated with this formula:

And the estimation for the true proportion is:

The critical value for 95% of confidence is

And since we know the total and the proportion is defined as:

If we solve for X (number of people who say yes) we got:

And the best answer would be:

294

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

answer

step-by-step explanation: