44 boots were sold all together. To figure this out first you need to find how many of the other boots there were. 8 rugby boots and 12 hiking boots. 8 + 12 + 24 = 44.
Each petal of the region
![R](https://tex.z-dn.net/?f=R)
is the intersection of two circles, both of diameter 10. Each petal in turn is twice the area of a circular segment bounded by a chord of length
![5\sqrt2](https://tex.z-dn.net/?f=5%5Csqrt2)
, which implies the segment is subtended by an angle of
![\dfrac\pi2](https://tex.z-dn.net/?f=%5Cdfrac%5Cpi2)
. This means the area of the segment is
![\text{area}_{\text{segment}}=\text{area}_{\text{sector}}-\text{area}_{\text{triangle}}](https://tex.z-dn.net/?f=%5Ctext%7Barea%7D_%7B%5Ctext%7Bsegment%7D%7D%3D%5Ctext%7Barea%7D_%7B%5Ctext%7Bsector%7D%7D-%5Ctext%7Barea%7D_%7B%5Ctext%7Btriangle%7D%7D)
![\text{area}_{\text{segment}}=\dfrac{25\pi}4-\dfrac{25}2](https://tex.z-dn.net/?f=%5Ctext%7Barea%7D_%7B%5Ctext%7Bsegment%7D%7D%3D%5Cdfrac%7B25%5Cpi%7D4-%5Cdfrac%7B25%7D2)
This means the area of one petal is
![\dfrac{25\pi}2-25](https://tex.z-dn.net/?f=%5Cdfrac%7B25%5Cpi%7D2-25)
, and the area of
![R](https://tex.z-dn.net/?f=R)
is four times this, or
![50\pi-100](https://tex.z-dn.net/?f=50%5Cpi-100)
.
Meanwhile, the area of
![G](https://tex.z-dn.net/?f=G)
is simply the area of the square minus the area of
![R](https://tex.z-dn.net/?f=R)
, or
![10^2-(50\pi-100)=200-50\pi](https://tex.z-dn.net/?f=10%5E2-%2850%5Cpi-100%29%3D200-50%5Cpi)
.
So
![\mathbb P(X=R)=\dfrac{50\pi-100}{100}=\dfrac\pi2-1](https://tex.z-dn.net/?f=%5Cmathbb%20P%28X%3DR%29%3D%5Cdfrac%7B50%5Cpi-100%7D%7B100%7D%3D%5Cdfrac%5Cpi2-1)
![\mathbb P(X=G)=\dfrac{200-50\pi}{100}=2-\dfrac\pi2](https://tex.z-dn.net/?f=%5Cmathbb%20P%28X%3DG%29%3D%5Cdfrac%7B200-50%5Cpi%7D%7B100%7D%3D2-%5Cdfrac%5Cpi2)
![\mathbb P((X=R)\land(X=G))=0](https://tex.z-dn.net/?f=%5Cmathbb%20P%28%28X%3DR%29%5Cland%28X%3DG%29%29%3D0)
(provided these regions are indeed disjoint; it's hard to tell from the picture)
Not sure what 14 is asking?
15 would be 16.
The square root of width squared plus length squared equals the diagonal.
So if you just change the order of the equation you can find the length.
Double check it by doing it both ways to see if your answer is right.
Answer:
2 29/30
Step-by-step explanation: