12 ÷ 75 = 0.16.
So she runs 0.16 miles per minute.
Hope it helps!
Answer:
![r(r-4\cos \theta)=0](https://tex.z-dn.net/?f=r%28r-4%5Ccos%20%5Ctheta%29%3D0)
Step-by-step explanation:
We are given the following equation:
![x^2 + y^2 -4x = 0](https://tex.z-dn.net/?f=x%5E2%20%2B%20y%5E2%20-4x%20%3D%200)
We have to convert it into polar form.
We put
![x = r \cos \theta\\y = r\sin \theta](https://tex.z-dn.net/?f=x%20%3D%20r%20%5Ccos%20%5Ctheta%5C%5Cy%20%3D%20r%5Csin%20%5Ctheta)
Putting values, we get:
![x^2 + y^2 -4x = 0\\(r\cos \theta)^2 + (r\sin \theta)^2 - 4(r\cos \theta) = 0\\r^2(\cos^2 \theta + \sin^2 \theta) - 4r\cos \theta = 0\\r^2 - 4r\cos \theta = 0\\r(r-4\cos \theta)=0](https://tex.z-dn.net/?f=x%5E2%20%2B%20y%5E2%20-4x%20%3D%200%5C%5C%28r%5Ccos%20%5Ctheta%29%5E2%20%2B%20%28r%5Csin%20%5Ctheta%29%5E2%20-%204%28r%5Ccos%20%5Ctheta%29%20%3D%200%5C%5Cr%5E2%28%5Ccos%5E2%20%5Ctheta%20%2B%20%5Csin%5E2%20%5Ctheta%29%20-%204r%5Ccos%20%5Ctheta%20%3D%200%5C%5Cr%5E2%20-%204r%5Ccos%20%5Ctheta%20%3D%200%5C%5Cr%28r-4%5Ccos%20%5Ctheta%29%3D0)
is the required polar form.
Answer:
r = sqrt(16/pi)
Step-by-step explanation:
Cylinder formula = r^2 x pi x height
176 pi/11pi = 16
16 = r^2 x pi
16/ pi = r^2
r = sqrt(16/pi)
Answer:
a) 9%
, not unusual
b) 42.4%
c) 48.4%
d) 11.1%
, 44.4%
, 44.4%
Step-by-step explanation:
We have the following information from the statement:
n = 12
r = 4
a)
P (likebothofthem) = P (likefirstsong) * P (likesecondsong)
P = 4/12 * 3/11
P = 0.09 = 9%
The probability is not unusual, unusual is considered less than 0.05 or 5%
b)
P (likeneither) = P (notlikefirstsong) * P (notlikesecondsong)
P = 8/12 * 7/11
P = 0.424 = 42.4%
c) P (likeexactlyoneofthem) = P (firstsongliked) * P (secondsongnotliked) + P (firstsongnotliked) * P (secondsongliked)
P = (4/12 * 8/11) + (8/12 * 4/11)
P = 0.484 = 48.4%
d)
a)
P (likebothofthem) = P (likefirstsong) * P (likesecondsong)
P = 4/12 * 4/12
P = 0.111 = 11.1%
The probability is not unusual, unusual is considered less than 0.05 or 5%
b)
P (likeneither) = P (notlikefirstsong) * P (notlikesecondsong)
P = 8/12 * 8/12
P = 0.444 = 44.4%
c) P (likeexactlyoneofthem) = P (firstsongliked) * P (secondsongnotliked) + P (firstsongnotliked) * P (secondsongliked)
P = (4/12 * 8/12) + (8/12 * 4/12)
P = 0.444 = 44.4%