A county commissioner must vote on a resolution that would commit substantial resources to the construction of a sewer in an outlying residential area. Her fiscal decisions have been criticized in the past, so she decides to take a survey of residents in her district to find out whether they favor spending money for a sewer system. She will vote to appropriate funds only if she can be reasonably sure that a majority of the people in her district favor the measure. What hypotheses should she test?

Step-by-step explanation:

This is a hypothesis testing involving population proportion. The null hypothesis would be that fewer than or 50% of the people would favor spending money for a sewer system. Since she will vote to appropriate funds only if she can be reasonably sure that a majority of the people in her district favor the measure, then the alternative hypothesis which she should test is that more than 50% of the people would favor spending money for a sewer system.

-12 > a

step-by-step explanation:

-11 > 1 + a

subtract 1 from each side

-11-1 > 1-1+a

-12 > a

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.