Assuming the equation is 3x-2y+4=0 then the equation of the line, solving for y in terms of x, gives y=3/2x+2 the slope of this line is 3/2 then the slope of a line that is perpendicular is -2/3 .An easy way to see this is to draw the line. By definition the slope, m=tan(α) where α is the angle the line makes with the x axis. Let L=slope of the perpendicular line then L=tan(β) but the two lines with the x axis form a right triangle hence α+π-β=π/2 so β=π/2+α and L=tan(β)=tan(π/2+α)=-cot(α) = -1/tan(α)=-1/m.In our problem m=3/2 so L=-2/3.The geometry becomes clear if you make a sketch of the two lines. Hope this helps
Answer:
1/6
Step-by-step explanation:
Answer:
Sample size of 586 or higher.
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 zscore that has a pvalue of 
.
The margin of error is:
95% confidence level
So 
, z is the value of Z that has a pvalue of 
, so 
.
What sample size could be 95% confident that the estimated (sample) proportion is within 4 percentage points of the true population proportion?
Sample size of at least n when 
42.1% of women-owned businesses provided retirement plans contributions, which means that 
. So
We need a sample size of 586 or higher.
These angles are supplementary.
Complementary angles add up to 90 degrees. Supplementary angles add up to 180 degrees. 82 degrees + 98 degrees = 180 degrees.
