Find the direct algebraic relationship between x and y and determine whether this parametric relationship is a function. Simplify as much as possible. x= t^2 − 4t and y = √t + 1

Step-by-step explanation:

Given:

x = t^2 - 4t

y = √t + 1

Making t the subject of formula from equation 2,

t = (y - 1)^2

Inputting into equation 2,

x = (y - 1)^4 - 4 × (y - 1)^2

= (y - 1)^2 ((y - 1)^2 - 4)

= (y^2 - 2y + 1) × (y^2 - 2y + 1 - 4)

= (y^2 - 2y + 1) × (y^2 - 2y - 3)

= y^4 - 2y^3 - 3y^2 - 2y^3 + 4y^2 + 6y + y^2 - 2y - 3

x = y^4 - 4y^3 + 2y^2 + 4y - 3

x = (y - 1) × (y - 1) × (y - 3) × (y + 1)

The above equation of x and y is a function because the dependent variable, x is dependant on the values of the independent variable, y.

The upper bound of a 95% confidence interval for the proportion of individuals over the age of 25 in Oregon who do not have a high school diploma is of 0.2568.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the z-score that has a p-value of .

95% confidence level

So , z is the value of Z that has a p-value of , so .

In a sample of 234 individuals over the age of 25, chosen at random from the state of Oregon, 48 did not have a high school diploma.

This means that

The upper limit of this interval is:

The upper bound of a 95% confidence interval for the proportion of individuals over the age of 25 in Oregon who do not have a high school diploma is of 0.2568.