Answer:
5th graders = 93 people 6th graders = 156 teachers = 51
Step-by-step explanation:
93 5th graders bought shirts, 156 6th graders bought shirts, 51 teachers bought shirts
The equation for point-slope form is
![y-y_{1}=m(x-x_{1})](https://tex.z-dn.net/?f=y-y_%7B1%7D%3Dm%28x-x_%7B1%7D%29)
m being the slope, y1 being the second point in the (2, -6) and the x1 being the first point in the (2, -6).
So the equation would look like this (for point-slope):
![y-(-6)=- \frac{3}{4}(x-2) \\ or \\ y+6=- \frac{3}{4}(x-2)](https://tex.z-dn.net/?f=y-%28-6%29%3D-%20%5Cfrac%7B3%7D%7B4%7D%28x-2%29%20%5C%5C%20or%20%5C%5C%20y%2B6%3D-%20%20%5Cfrac%7B3%7D%7B4%7D%28x-2%29%20)
If you're looking for slope-intercept form you can simplify the equation:
![y+6=- \frac{3}{4}(x-2) \\ \\ y+6=- \frac{3}{4}x+ \frac{6}{4} \\ \\ y+6-6=- \frac{3}{4}x+ \frac{6}{4}-6 \\ \\ y=- \frac{3}{4}x- \frac{18}{4}](https://tex.z-dn.net/?f=y%2B6%3D-%20%5Cfrac%7B3%7D%7B4%7D%28x-2%29%20%5C%5C%20%20%5C%5C%20y%2B6%3D-%20%5Cfrac%7B3%7D%7B4%7Dx%2B%20%5Cfrac%7B6%7D%7B4%7D%20%5C%5C%20%20%5C%5C%20y%2B6-6%3D-%20%5Cfrac%7B3%7D%7B4%7Dx%2B%20%5Cfrac%7B6%7D%7B4%7D-6%20%5C%5C%20%20%5C%5C%20y%3D-%20%5Cfrac%7B3%7D%7B4%7Dx-%20%5Cfrac%7B18%7D%7B4%7D)
If you're looking for the standard form of the equation, you can take the slope-intercept equation and turn it into standard form:
Answer:
-10/2 or -5 for the slope
Step-by-step explanation:
rise over run: it's going down 10 and over 2 or
for every 5 down it goes 1 over
Answer:
option A and B are correct.
Step-by-step explanation:
Given: ![p(t) = \frac{64}{1 + 11e^{-.08t} }](https://tex.z-dn.net/?f=p%28t%29%20%3D%20%5Cfrac%7B64%7D%7B1%20%2B%2011e%5E%7B-.08t%7D%20%7D)
Option A: ![\lim_{t \to \infty} \frac{64}{1 + 11e^{-.08(\infty)} } = \frac{64}{1 + 0} = 64](https://tex.z-dn.net/?f=%5Clim_%7Bt%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B64%7D%7B1%20%2B%2011e%5E%7B-.08%28%5Cinfty%29%7D%20%7D%20%20%3D%20%5Cfrac%7B64%7D%7B1%20%2B%200%7D%20%20%3D%2064)
Option A is true,
Option B: ![P(0) = \frac{64}{1 + 11} = 5.33](https://tex.z-dn.net/?f=P%280%29%20%3D%20%5Cfrac%7B64%7D%7B1%20%2B%2011%7D%20%20%3D%205.33)
Option B is also true.
Option C:
![P(t + 1) = \frac{64}{1 + 11e^{-.08(t + 1)} } = \frac{64}{1 + 10.15e^{-.08t} } \\1.08 · P(t) = \frac{64 · 1.08 }{1 + 11e^{-.08t} } = \frac{69.12}{1 + 11e^{-.08t} }](https://tex.z-dn.net/?f=P%28t%20%2B%201%29%20%3D%20%5Cfrac%7B64%7D%7B1%20%2B%2011e%5E%7B-.08%28t%20%2B%201%29%7D%20%7D%20%20%3D%20%5Cfrac%7B64%7D%7B1%20%2B%2010.15e%5E%7B-.08t%7D%20%7D%20%5C%5C1.08%20%C2%B7%20P%28t%29%20%3D%20%5Cfrac%7B64%20%C2%B7%201.08%20%7D%7B1%20%2B%2011e%5E%7B-.08t%7D%20%7D%20%20%20%3D%20%5Cfrac%7B69.12%7D%7B1%20%2B%2011e%5E%7B-.08t%7D%20%7D)
P(t + 1) ≠ 1.08 · P(t)
Option C is incorrect.
Option D: It is also incorrect, because according to option 2 earth's population will not grow exponentially without Bound.
I would guess that the answer would be A) likely but it not it would probably be C) certain