Perpendicular lines are two or more lines that intersect at an angle of 90 degrees. Being y = m * x + b the equation of a line, two lines, with a slope other than zero, are orthogonal or perpenducillary if and only if the product of their slopes is -1. In other words, if two lines are perpendicular, they have their slopes reversed and sign changed.

In this case, with y = -4x-5 the slope will be -4. So the slope of the perpendicular line will be $\frac{1}{4}$ . Then the equation of the perpendicular line will be:

$y=\frac{1}{4}* x+b$

To find the value of b, you know the value of the point (-2,3). So x = -2 and y = 3. Replacing in the equation of the perpendicular line, you have:

$3=\frac{1}{4}* (-2)+b$

Solving, you get:

$3=-\frac{1}{2}+b$

$3+\frac{1}{2}=b$

$\frac{7}{2}=b$

The equation of the perpendicular line to y=-4*x-5 is $y=\frac{1}{4}*x+\frac{7}{2}$

8 0

3 years ago

A research center project involved a survey of 851 Internet users. It provided a variety of statistics on Internet users. (a) Th

kotykmax [81]

Answer:

The answer is "(0.9193924 , 0.9206076)".

Step-by-step explanation:

$\text{sample proportion}\ (SP) = 0.92\\\\\text{sample size}\ n = 851\\\\\text{Standard error} \ SE = \sqrt{\frac{(SP \times(1 - SP)}{n})}\\\\$

$= \sqrt{\frac{(0.92 \times (0.08)}{851})}\\\\= \sqrt{\frac{0.0736}{851}}\\\\= \sqrt{8.648\times 10^{-5}}\\\\=0.00031$

$\text{CI level is}\ 95\% \\\\\therefore\\\\ \alpha = 1 - 0.95 = 0.05\\\\\frac{\alpha}{2} = \frac{0.05}{2} = 0.025\\\\ Z_c = Z_{(\frac{\alpha}{2})} = 1.96$

Calculating the Margin of Error:

$ME = z_{c} \times SE\\\\$

$= 1.96 \times 0.00031\\\\ = 0.0006076$

$CI = (SP - z*SE, SP + z*SE)$

$= (0.92 - 1.96 * 0.00031 , 0.92 + 1.96 * 0.00031)\\\\ = (0.92 - 0.0006076 , 0.92 + 0.0006076)\\\\= (0.9193924 , 0.9206076)$

8 0

3 years ago