In an August 2012 Gallup survey of 1,012 randomly selected U. S. adults (age 18 and over), 536 said that they were dissatisfied with the quality of education students receive in kindergarten through grade 12. a. Test, at the 5% significance level, if this sample provides evidence that the proportion of Americans who are dissatisfied with education in kindergarten through grade 12 differs significantly from 50%.
b. Is the Test Significant? Why or Why not.

Yes, result is significant ; PVALUE < α

Step-by-step explanation:

Given :

x = 536

n = sample size = 1012

Phat = x / n = 536 / 1012 = 0.5296 = 0.53

H0 : P0 = 0.5

H1 : P0 > 0.5

Test statistic :

(Phat - P0) ÷ sqrt[(P0(1 - P0)) / n]

1-P0 = 1 - 0.5 = 0.5

(0.53 - 0.5) ÷ sqrt[(0.5*0.5)/1012]

0.03 ÷ 0.0157173

= 1.9087

Pvalue :

Using the Pvalue from test statistic :

Pvalue = 0.02815

To test if result is significant :

α = 0.05

0.02815 < 0.05

Pvalue < α ; Hence, result is significant at α=0.05; Hence, we reject H0.

choice b is correct

step-by-step explanation:

we have been given the following system of inequalities;

we are required to graph the solution to the system of inequalities. using a graphing tool, the graph of the system is as shown in the attachment. the continuous line represents the graph of while the dotted line represents .

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".