Answer:
the second one(20)
Step-by-step explanation:
If you pretend 20 is x, you solve the equation by pluging in x (20) into the equation and it gives you 70, 70 is what the big part is and 70+20 is 90, which is the size of a 90degree side.
4(20)-10
80-10
70
70+20=90
A=1/3h(b1-b2). So h=3/(b1-b2)
1. Answer:
C. 1050
Step-by-step explanation:
To find the area of a rectangle, it is length * width * height
25 * 7 = 175
175 * 6 = 1050
2. Answer:
C. 8
Step-by-step explanation:
To find the missing dimension of a rectangle, you can easily just divide the total by each dimension
540 divided by 7.5 = 72
72 divided by 9 = 8
3. Answer:
D. 31,400
(31,415.9)
Step-by-step explanation:
The radius of the cylinder is 20
The height of the cylinder 25
πr2h is the formula used to find the volume of a cylinder
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)