(2,-1)(8,4)
slope = (4-(-1) / (8-2) = (4 + 1)/6 = 5/6
y - y1 = m(x - x1)
(8,4)...x1 = 8 and y1 = 4
slope(m) = 5/6
now we sub
y - 4 = 5/6(x - 8) <==point-slope form
y - 4 = 5/6x - 20/3
y = 5/6x - 20/3 + 4
y = 5/6x -20/3 + 12/3
y = 5/6x - 8/3
-5/6x + y = - 8/3...multiply by -6
5x - 6y = 16 <==standard form
Answer:
- 15
Step-by-step explanation:
Given f(x) divided by (x + h) then the remainder is the value of f(- h)
Here
f(x) = 3x³ - 5x² - 47x + k ← k is the constant term , then
f(- 3) = 3(- 3)³ - 5(- 3)² - 47(- 3) + k = 0 , that is
3(- 27) - 5(9) + 141 + k = 0
- 81 - 45 + 141 + k = 0
15 + k = 0 ( subtract 15 from both sides )
k = - 15
Answer:
Step-by-step explanation:
if the line is perperdicular to the first one:
![m_2=-\frac{1}{m_1}=-\frac{1}{\frac{1}{5}}=-5\](https://tex.z-dn.net/?f=m_2%3D-%5Cfrac%7B1%7D%7Bm_1%7D%3D-%5Cfrac%7B1%7D%7B%5Cfrac%7B1%7D%7B5%7D%7D%3D-5%5C)
if that line passes through the point (4, 0) the.
![y-y_o=m(x-x_o)\\\\y-(0)=-5(x-(4))~=>y=-5x+20](https://tex.z-dn.net/?f=y-y_o%3Dm%28x-x_o%29%5C%5C%5C%5Cy-%280%29%3D-5%28x-%284%29%29~%3D%3Ey%3D-5x%2B20)
Answer:
D) ± .0207
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.
![\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=%5Cpi%20%5Cpm%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
In which
z is the zscore that has a pvalue of
.
The width of the interval is given by the following formula:
![W = z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=W%20%3D%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
In a random sample of 810 women employees, it is found that 81 would prefer working for a female boss.
This means that ![n = 810, p = \frac{81}{810} = 0.1](https://tex.z-dn.net/?f=n%20%3D%20810%2C%20p%20%3D%20%5Cfrac%7B81%7D%7B810%7D%20%3D%200.1)
95% confidence level
So
, z is the value of Z that has a pvalue of
, so
.
The width of the 95% confidence interval for the proportion of women who prefer a female boss is
![W = z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=W%20%3D%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
![W = 1.94\sqrt{\frac{0.1*0.9}{810}} = 0.0207](https://tex.z-dn.net/?f=W%20%3D%201.94%5Csqrt%7B%5Cfrac%7B0.1%2A0.9%7D%7B810%7D%7D%20%3D%200.0207)
So the correct answer is:
D) ± .0207