The labor bureau wants to estimate, at a 90% confidence level, the proportion of all households that receive welfare. a preliminary sample showed that 17.5% of households in this sample receive welfare. the sample size that would limit the margin of error to be within 0.025 of the population proportion is:

Sample size should be atleast 625

Step-by-step explanation:

Given that the  Labor Bureau wants to estimate, at a 90% confidence level, the proportion of all households that receive welfare

Sample proportion = 17.5%

Let n be the sample size

Standard error of sample proportion=

Z critical for 90% = 1.645

Margin of error = 1.645 * std error

Since margin of error<0.025 we have

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.