5 yards + 3 yards = 8 yards of fabric. The answer is A. Hope this helps.
The slope-intercept form:
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
m - slope
b - y-intercept
Convert the equation of the line 4x - 7y = 7x + 4y to the slope-intercept form:
<em>subtract 4x from both sides</em>
<em>subtract 4y from both sides</em>
<em>divide both sides by (-11)</em>
![y=-\dfrac{3}{11}x](https://tex.z-dn.net/?f=y%3D-%5Cdfrac%7B3%7D%7B11%7Dx)
Let
and
then
![l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}](https://tex.z-dn.net/?f=l%5C%20%5Cperp%5C%20k%5Ciff%20m_1m_2%3D-1%5Cto%20m_2%3D-%5Cdfrac%7B1%7D%7Bm_1%7D)
We have
therefore the slope of the line perpendicular is
![m_2=-\dfrac{1}{-\frac{3}{11}}=\dfrac{11}{3}](https://tex.z-dn.net/?f=m_2%3D-%5Cdfrac%7B1%7D%7B-%5Cfrac%7B3%7D%7B11%7D%7D%3D%5Cdfrac%7B11%7D%7B3%7D)
Therefore we have:
![y=\dfrac{11}{3}x+b](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B11%7D%7B3%7Dx%2Bb)
Put the coordinates of the point (4, -4) to the equation of a line:
![-4=\dfrac{11}{3}(4)+b](https://tex.z-dn.net/?f=-4%3D%5Cdfrac%7B11%7D%7B3%7D%284%29%2Bb)
![-4=\dfrac{44}{3}+b](https://tex.z-dn.net/?f=-4%3D%5Cdfrac%7B44%7D%7B3%7D%2Bb)
<em>subtract
from both sides</em>
![-\dfrac{56}{3}=b](https://tex.z-dn.net/?f=-%5Cdfrac%7B56%7D%7B3%7D%3Db)
Answer: ![\boxed{y=\dfrac{11}{3}x-\dfrac{56}{3}}](https://tex.z-dn.net/?f=%5Cboxed%7By%3D%5Cdfrac%7B11%7D%7B3%7Dx-%5Cdfrac%7B56%7D%7B3%7D%7D)
Answer:
90 - 54w
Distribute 18 to both numbers.
<h3>
Answer: 1068</h3>
========================================================
Work Shown:
![n = \hat{p}*(1-\hat{p})\left(\frac{z}{E}\right)^2\\\\n \approx 0.5*(1-0.5)\left(\frac{1.96}{0.03}\right)^2\\\\n \approx 1067.111\\\\n \approx \boldsymbol{1068}\\\\](https://tex.z-dn.net/?f=n%20%3D%20%5Chat%7Bp%7D%2A%281-%5Chat%7Bp%7D%29%5Cleft%28%5Cfrac%7Bz%7D%7BE%7D%5Cright%29%5E2%5C%5C%5C%5Cn%20%5Capprox%200.5%2A%281-0.5%29%5Cleft%28%5Cfrac%7B1.96%7D%7B0.03%7D%5Cright%29%5E2%5C%5C%5C%5Cn%20%5Capprox%201067.111%5C%5C%5C%5Cn%20%5Capprox%20%5Cboldsymbol%7B1068%7D%5C%5C%5C%5C)
Notes:
- At 95% confidence, the z critical value is roughly z = 1.96 which is determined using a Z table.
- E = 0.03 to represent the 3% error.
- We're not told the value of
, so we assume the most conservative estimate of 0.5 - <u>Always</u> round up to the nearest integer. The value 1067.111 is closer to 1067, but we round up to 1068 to clear the hurdle needed.