Letter c
-4-9=-13
What is saying u start at -4 See the arrow point go left on number line 9 spaces so your subtracting to give you-13
two equations which can model this situation is :
and
<u>Step-by-step explanation:</u>
Here we have , Bronson is an action and horror movie junkie. He started a movie review vlog and needs to keep up with his movie viewing at a high pace. It has been a total of 50 weeks since he has stated his vlog and he has watched 1250 movies. He has watched twice as many horror movies a action movies. We need to Write two equations that can model this situation. Let's find out:
Let Bronson watched x action movies and y horror movies , than according to question horror movies he watched is twice that of action movies i.e.
⇒
........(1)
Now , he has watched 1250 movies i.e.
⇒
.......(2)
⇒ ![x+2x=1250](https://tex.z-dn.net/?f=x%2B2x%3D1250)
⇒ ![3x=1250](https://tex.z-dn.net/?f=3x%3D1250)
Therefore , two equations which can model this situation is :
and
.
Answer:
2.7 PM
Step-by-step explanation:
Since, the rate of spread is proportional to the product of fraction y of people who have heard the rumour and the fraction who have not heard,
![\frac{dy}{dt}=ky(1-y)](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%3Dky%281-y%29)
![\frac{dy}{y(1-y)}=kdt](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7By%281-y%29%7D%3Dkdt)
![(\frac{1}{y}+\frac{1}{1-y})dy = kdt](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7By%7D%2B%5Cfrac%7B1%7D%7B1-y%7D%29dy%20%3D%20kdt)
Integrating both sides,
![\int (\frac{1}{y}+\frac{1}{1-y})dy = \int kdt](https://tex.z-dn.net/?f=%5Cint%20%28%5Cfrac%7B1%7D%7By%7D%2B%5Cfrac%7B1%7D%7B1-y%7D%29dy%20%3D%20%5Cint%20kdt)
![\ln y - \ln (1-y) = kt + C](https://tex.z-dn.net/?f=%5Cln%20y%20-%20%5Cln%20%281-y%29%20%3D%20kt%20%2B%20C)
![\ln (\frac{y}{1-y}) = kt + C](https://tex.z-dn.net/?f=%5Cln%20%28%5Cfrac%7By%7D%7B1-y%7D%29%20%3D%20kt%20%2B%20C)
![\frac{y}{1-y}=e^{kt + C}](https://tex.z-dn.net/?f=%5Cfrac%7By%7D%7B1-y%7D%3De%5E%7Bkt%20%2B%20C%7D)
![y = e^{kt+C} - y e^{kt+C}](https://tex.z-dn.net/?f=y%20%3D%20e%5E%7Bkt%2BC%7D%20-%20y%20e%5E%7Bkt%2BC%7D)
![y(1+e^{kt+C}) = e^{kt+C}](https://tex.z-dn.net/?f=y%281%2Be%5E%7Bkt%2BC%7D%29%20%3D%20e%5E%7Bkt%2BC%7D)
![y = \frac{e^{kt+C}}{1+e^{kt+C}}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7Be%5E%7Bkt%2BC%7D%7D%7B1%2Be%5E%7Bkt%2BC%7D%7D)
If t = 0, ( at 8 AM ), y = ![\frac{80}{2100}](https://tex.z-dn.net/?f=%5Cfrac%7B80%7D%7B2100%7D)
![\frac{80}{2100}= \frac{e^{0+C}}{1+e^{0+C}}](https://tex.z-dn.net/?f=%5Cfrac%7B80%7D%7B2100%7D%3D%20%5Cfrac%7Be%5E%7B0%2BC%7D%7D%7B1%2Be%5E%7B0%2BC%7D%7D)
![\frac{4}{105}=\frac{e^C}{1+e^C}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B105%7D%3D%5Cfrac%7Be%5EC%7D%7B1%2Be%5EC%7D)
![4 = 101e^C](https://tex.z-dn.net/?f=4%20%3D%20101e%5EC)
Now, at noon, i.e t = 4, y = ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
![\frac{1}{2}=\frac{e^{4k}.\frac{4}{101}}{1+e^{4k}.\frac{4}{101}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%3D%5Cfrac%7Be%5E%7B4k%7D.%5Cfrac%7B4%7D%7B101%7D%7D%7B1%2Be%5E%7B4k%7D.%5Cfrac%7B4%7D%7B101%7D%7D)
![\frac{1}{2}=\frac{4e^{4k}}{101+4e^{4k}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%3D%5Cfrac%7B4e%5E%7B4k%7D%7D%7B101%2B4e%5E%7B4k%7D%7D)
![101 + 4e^{4k}=8 e^{4k}](https://tex.z-dn.net/?f=101%20%2B%204e%5E%7B4k%7D%3D8%20e%5E%7B4k%7D)
![101 = 4e^{4k}](https://tex.z-dn.net/?f=101%20%3D%204e%5E%7B4k%7D)
![\frac{101}{4}=e^{4k}](https://tex.z-dn.net/?f=%5Cfrac%7B101%7D%7B4%7D%3De%5E%7B4k%7D)
![(\frac{101}{4})^\frac{1}{4} = e^k](https://tex.z-dn.net/?f=%28%5Cfrac%7B101%7D%7B4%7D%29%5E%5Cfrac%7B1%7D%7B4%7D%20%3D%20e%5Ek)
If ![y = \frac{90}{100}=\frac{9}{10}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B90%7D%7B100%7D%3D%5Cfrac%7B9%7D%7B10%7D)
![\frac{9}{10}= \frac{(\frac{101}{4})^\frac{t}{4}\times \frac{4}{101}}{1+(\frac{101}{4})^\frac{t}{4}\times \frac{4}{101}}](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B10%7D%3D%20%5Cfrac%7B%28%5Cfrac%7B101%7D%7B4%7D%29%5E%5Cfrac%7Bt%7D%7B4%7D%5Ctimes%20%5Cfrac%7B4%7D%7B101%7D%7D%7B1%2B%28%5Cfrac%7B101%7D%7B4%7D%29%5E%5Cfrac%7Bt%7D%7B4%7D%5Ctimes%20%5Cfrac%7B4%7D%7B101%7D%7D)
Using graphing calculator,
t ≈ 6.722,
Hence, after 6.722 hours since 8 AM, i.e. on 2.7 PM ( approx ) the 90% of the population have heard the rumour.
Concert 2/5 into a percent 5*20 = 100 (denominator) so 2* 20 =40
40/100 is 40%
I'm guessing you accidentally put the dor in front of 52 so it would be 40 at least and 52.57 at greatest