Translate to an algebraic expression. 44 more than why. The translation is

"write an equation of the perpendicular bisector or the segment with endpoints Q(-2,0) and R(6,12). what does y equal?

anygoal [31]

Answer:

The equation of perpendicular bisector of QR is:

y = -\frac{2}{3}x+\frac{22}{3}y=−32x+322

Step-by-step explanation:

Given points are:

Q(-2,0)\ and\ R(6,12)Q(−2,0) and R(6,12)

First of all, we have to find the slope of the given line

So,

m = \frac{y_2-y_1}{x_2-x_1}m=x2−x1y2−y1

Here

(x1,y1) = (-2,0)

(x2,y2) = (6,12)

Let m1 be the slope of QR:

Then

\begin{gathered}m_1 = \frac{12-0}{6+2}\\= \frac{12}{8}\\= \frac{3}{2}\end{gathered}m1=6+212−0=812=23

Let m2 be the slope of perpendicular bisector

We know that the product of slopes of two perpendicular lines is -1

\begin{gathered}m_1.m_2 = -1\\\frac{3}{2}.m_2 = -1\\m_2 = -1 * \frac{2}{3}\\m_2 = -\frac{2}{3}\end{gathered}m1.m2=−123.m2=−1m2=−1∗32m2=−32

The bisector will pass through the mid-point of QR

\begin{gathered}M = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})\\M = (\frac{-2+6}{2}, \frac{0+12}{2})\\M = (\frac{4}{2}, \frac{12}{2})\\M = (2,6)\end{gathered}M=(2x1+x2,2y1+y2)M=(2−2+6,20+12)M=(24,212)M=(2,6)

Slope-intercept form of equation is:

y = m_2x+by=m2x+b

Putting the value of slope

y = -\frac{2}{3}x+by=−32x+b

Putting (2,6) in the equation

\begin{gathered}6 = -\frac{2}{3}(2)+b\\6 = -\frac{4}{3}+b\\b = 6+\frac{4}{3}\\b = \frac{18+4}{3}\\b = \frac{22}{3}\end{gathered}6=−32(2)+b6=−34+bb=6+34b=318+4b=322

So,

y = -\frac{2}{3}x+\frac{22}{3}y=−32x+322

Hence,

The equation of perpendicular bisector of QR is:

y = -\frac{2}{3}x+\frac{22}{3}y=−32x+322

4 0

3 years ago

Express the confidence interval (0.036, 0.086) in the form of p-e< p

lina2011 [118]

Answer:

p-e< p < p+e

(0.061 - 0.025) < 0.061 < (0.061 + 0.025)

0.036 < 0.061 < 0.086

Step-by-step explanation:

Given;

Confidence interval CI = (a,b) = (0.036, 0.086)

Lower bound a = 0.036

Upper bound b = 0.086

To express in the form;

p-e< p < p+e

Where;

p = mean Proportion

and

e = margin of error

The mean p =( lower bound + higher bound)/2

p = (a+b)/2

Substituting the values;

p = (0.036+0.086)/2

Mean Proportion p = 0.061

The margin of error e = (b-a)/2

Substituting the given values;

e = (0.086-0.036)/2

e = 0.025

Re-writing in the stated form, with p = 0.061 and e = 0.025

p-e< p < p+e

(0.061 - 0.025) < 0.061 < (0.061 + 0.025)

0.036 < 0.061 < 0.086

6 0

4 years ago

According to the 2011 National Survey of Fishing, Hunting, and Wildlife-Associated Recreation, there were over 71 million wildif

suter [353]

Answer:

The probability that between 79% and 81%of the 500 sampled wildlife watchers actively observed mammals in 2011 is P=0.412.

Step-by-step explanation:

We know the population proportion π=0.8, according to the 2011 National Survey of Fishing, Hunting, and Wildlife-Associated Recreation.

If we take a sample from this population, and assuming the proportion is correct, it is expected that the sample's proportion to be equal to the population's proportion.

The standard deviation of the sample is equal to:

$\sigma_s=\sqrt{\frac{\pi(1-\pi)}{N}}=\sqrt{\frac{0.8*0.2}{500}}=0.018$

With the mean and the standard deviaion of the sample, we can calculate the z-value for 0.79 and 0.81:

$z=\frac{p-\pi}{\sigma}=\frac{0.79-0.80}{0.018} =\frac{-0.01}{0.018} = -0.55\\\\z=\frac{p-\pi}{\sigma}=\frac{0.81-0.80}{0.018} =\frac{0.01}{0.018} = 0.55$