Answer:
108 children can get candy
Step-by-step explanation:
324 divided by 3 equals 108
Answer:
the expected area of the resulting circular region is 616.38 m²
Step-by-step explanation:
Given that:
otherwise
The expected area of the resulting circular region is:
= ![E(\pi r^2)](https://tex.z-dn.net/?f=E%28%5Cpi%20r%5E2%29)
= ![\pi E (r^2)](https://tex.z-dn.net/?f=%5Cpi%20E%20%28r%5E2%29)
To calculate ![E(r^2)](https://tex.z-dn.net/?f=E%28r%5E2%29)
![E(r^2) = \int\limits^{15}_{13} {r^2} \ f(r) \ dr](https://tex.z-dn.net/?f=E%28r%5E2%29%20%3D%20%5Cint%5Climits%5E%7B15%7D_%7B13%7D%20%7Br%5E2%7D%20%20%5C%20f%28r%29%20%5C%20dr)
![E(r^2) = \int\limits^{15}_{13} \ \dfrac{3r^2}{4}(1-(14-r)^2)dr](https://tex.z-dn.net/?f=E%28r%5E2%29%20%3D%20%5Cint%5Climits%5E%7B15%7D_%7B13%7D%20%5C%20%5Cdfrac%7B3r%5E2%7D%7B4%7D%281-%2814-r%29%5E2%29dr)
![E(r^2) = \dfrac{3}{4} \int\limits^{15}_{13} \ r^2 (1-196-r^2+28r) dr](https://tex.z-dn.net/?f=E%28r%5E2%29%20%3D%20%5Cdfrac%7B3%7D%7B4%7D%20%5Cint%5Climits%5E%7B15%7D_%7B13%7D%20%5C%20r%5E2%20%281-196-r%5E2%2B28r%29%20dr)
![E(r^2) = \dfrac{3}{4} \int\limits^{15}_{13} \ r^2 (28r^3-r^4-195r^2)dr](https://tex.z-dn.net/?f=E%28r%5E2%29%20%3D%20%5Cdfrac%7B3%7D%7B4%7D%20%5Cint%5Climits%5E%7B15%7D_%7B13%7D%20%5C%20r%5E2%20%2828r%5E3-r%5E4-195r%5E2%29dr)
![E(r^2) = \dfrac{3}{4}[\dfrac{28 r^4}{4}-\dfrac{r^5}{5}-\dfrac{195r^3}{3}]^{^{15}}}__{13}](https://tex.z-dn.net/?f=E%28r%5E2%29%20%3D%20%5Cdfrac%7B3%7D%7B4%7D%5B%5Cdfrac%7B28%20r%5E4%7D%7B4%7D-%5Cdfrac%7Br%5E5%7D%7B5%7D-%5Cdfrac%7B195r%5E3%7D%7B3%7D%5D%5E%7B%5E%7B15%7D%7D%7D__%7B13%7D)
![E(r^2) = \dfrac{3}{4} [ \dfrac{28 \times 50625}{4} - \dfrac{759375}{5} - \dfrac{195 \times 3375}{3} ]-[ \dfrac{28 \times 28561}{4} - \dfrac{371293}{5} - \dfrac{195 \times 2197}{3} ]](https://tex.z-dn.net/?f=E%28r%5E2%29%20%3D%20%5Cdfrac%7B3%7D%7B4%7D%20%5B%20%5Cdfrac%7B28%20%5Ctimes%2050625%7D%7B4%7D%20-%20%20%5Cdfrac%7B759375%7D%7B5%7D%20-%20%5Cdfrac%7B195%20%5Ctimes%203375%7D%7B3%7D%20%5D-%5B%20%5Cdfrac%7B28%20%5Ctimes%2028561%7D%7B4%7D%20-%20%5Cdfrac%7B371293%7D%7B5%7D%20-%20%5Cdfrac%7B195%20%5Ctimes%202197%7D%7B3%7D%20%5D)
![E(r^2) = \dfrac{3}{4} [ 354375-151875-219375-199927+74258.6+142805]](https://tex.z-dn.net/?f=E%28r%5E2%29%20%3D%20%5Cdfrac%7B3%7D%7B4%7D%20%5B%20354375-151875-219375-199927%2B74258.6%2B142805%5D)
![E(r^2) = \dfrac{3}{4} [261.6]](https://tex.z-dn.net/?f=E%28r%5E2%29%20%3D%20%5Cdfrac%7B3%7D%7B4%7D%20%5B261.6%5D)
![E(r^2) = 196.2](https://tex.z-dn.net/?f=E%28r%5E2%29%20%3D%20196.2)
Recall:
The expected area of the resulting circular region is:
= ![E(\pi r^2)](https://tex.z-dn.net/?f=E%28%5Cpi%20r%5E2%29)
= ![\pi E (r^2)](https://tex.z-dn.net/?f=%5Cpi%20E%20%28r%5E2%29)
where;
![E(r^2) = 196.2](https://tex.z-dn.net/?f=E%28r%5E2%29%20%3D%20196.2)
Then
The expected area of the resulting circular region is:
= ![\pi \times 196.2](https://tex.z-dn.net/?f=%5Cpi%20%5Ctimes%20196.2)
= 616.38 m²
Answer:
answer in comment
Step-by-step explanation:
So, we have to find the slope of the line. We are given two points, so we can use those:
(x1,y1) = (-4,6)
(x2,y2) = (1,2)
m = (y2-y1)/(x2-x1) = (2-6)/(1--4) = (2-6)/(1+4) = -4/5
Also, we know that point-slope is of the form:
(y-y1) = m*(x-x1)
It doesn't matter which point you use, though, you can also use:
(y-y2) = m*(x-x2)
So we can plug the variables into the equation and get:
(y-2) = -4/5*(x-1)
OR
(y-6) = -4/5*(x+4)
The answer is B and I am happy to help you out