Answer:
3/4 1/4
Step-by-step explanation:
Step-by-step explanation:
for question one the answer is the intial area of fire
2. is the decay factor
3. 38400
4. the initial population
Answer:
See the step by step solution
Step-by-step explanation:
Consider a more general case of the form
. We want to express it as a sine term only by using the following formula ![\sin(\alpha+\beta) = \sin(\alpha)\cos(\beta)+\sin(\beta)\cos(\alpha)](https://tex.z-dn.net/?f=%5Csin%28%5Calpha%2B%5Cbeta%29%20%3D%20%5Csin%28%5Calpha%29%5Ccos%28%5Cbeta%29%2B%5Csin%28%5Cbeta%29%5Ccos%28%5Calpha%29)
The trick consists on find a number
such that
. But, note that since
it is most likely that
. Then, we will use the following equations:
![\cos(\beta) =\frac{a}{\sqrt[]{a^2+b^2}=A,\sin(\beta) =\frac{b}{\sqrt[]{a^2+b^2}=B](https://tex.z-dn.net/?f=%5Ccos%28%5Cbeta%29%20%3D%5Cfrac%7Ba%7D%7B%5Csqrt%5B%5D%7Ba%5E2%2Bb%5E2%7D%3DA%2C%5Csin%28%5Cbeta%29%20%3D%5Cfrac%7Bb%7D%7B%5Csqrt%5B%5D%7Ba%5E2%2Bb%5E2%7D%3DB)
Then, problem turns out to be
,
where ![\beta = \tan^{-1}(\frac{B}{A})= \tan^{-1}(\frac{b}{a}). So, note that the frequency is the same. Then, a) Taking a=4 and b= 15 we have that 4 sin 2πt + 15 cos 2πt= [tex]\sqrt[]{15^2+4^2}\sin(2\pi t + \tan^{-1}\frac{15}{4})](https://tex.z-dn.net/?f=%5Cbeta%20%3D%20%5Ctan%5E%7B-1%7D%28%5Cfrac%7BB%7D%7BA%7D%29%3D%20%5Ctan%5E%7B-1%7D%28%5Cfrac%7Bb%7D%7Ba%7D%29.%20So%2C%20note%20that%20the%20frequency%20is%20the%20same.%20%3C%2Fp%3E%3Cp%3EThen%2C%20%3C%2Fp%3E%3Cp%3Ea%29%20Taking%20a%3D4%20and%20b%3D%2015%20we%20have%20that%204%20sin%202%CF%80t%20%2B%2015%20cos%202%CF%80t%3D%20%5Btex%5D%5Csqrt%5B%5D%7B15%5E2%2B4%5E2%7D%5Csin%282%5Cpi%20t%20%2B%20%5Ctan%5E%7B-1%7D%5Cfrac%7B15%7D%7B4%7D%29)
b) The amplitude is
. Since
the frequency is 1 Hz. The period is given by \frac{2\pi}{2\pi} = 1.
c) The function's graph is attached
Answer:
![\boxed {\boxed {\sf \frac{11}{25} \ or \ 0.44}}](https://tex.z-dn.net/?f=%5Cboxed%20%7B%5Cboxed%20%7B%5Csf%20%5Cfrac%7B11%7D%7B25%7D%20%5C%20or%20%5C%200.44%7D%7D)
Step-by-step explanation:
The probability of an event can be found by dividing the favorable outcomes by all outcomes.
![P=\frac{favorable \ outcomes}{all \ outcomes}](https://tex.z-dn.net/?f=P%3D%5Cfrac%7Bfavorable%20%5C%20outcomes%7D%7Ball%20%5C%20outcomes%7D)
We want to find the probability of a blue ball. In this situation, the favorable outcomes are the blue balls. The total number of balls is all the outcomes.
![P(blue)=\frac{blue \ balls }{all \ balls }](https://tex.z-dn.net/?f=P%28blue%29%3D%5Cfrac%7Bblue%20%5C%20balls%20%7D%7Ball%20%5C%20balls%20%7D)
There are 11blue balls.
- Find the total number of balls, which is the sum.
- 8 red+ 6 green + 11 blue=25 total
This fraction cannot be reduced further, so it is the answer. As a decimal it is:
![P(blue)=0.44](https://tex.z-dn.net/?f=P%28blue%29%3D0.44)
The probability of drawing a blue marble is <u>0.44 or 11/25</u>