Answer:
x = 22
Step-by-step explanation:
Answer:
Sailboat A won the race, and it was going 8 feet per second.
Step-by-step explanation:
Sailboat A was traveling at 40 feet per every 5 seconds, so, to find how many feet it was going per second, we would do 40 feet/5 seconds, which is 8 feet.
Sailboat B was traveling at 56 feet per every 8 seconds, so we use the same method. 56 feet/8 seconds is 7 feet.
So, Sailboat A won because it was going faster! :)
Check the picture below.
since we know the radius of the larger semicircle is 8, thus its diameter is 16, which is the length of one side of the equilateral triangle. We also know the smaller semicircle has a radius of 1/3, and thus a diameter of 2/3, namely the lenght of one side of the small equilateral triangle.
now, if we just can get the area of the larger figure and the area of the smaller one and subtract the smaller from the larger, we'll be in effect making a hole/gap in the larger and what's leftover is the shaded figure.
![\bf \stackrel{\textit{area of a semi-circle}}{A=\cfrac{1}{2}\pi r^2\qquad r=radius}~\hspace{10em}\stackrel{\textit{area of an equilateral triangle}}{A=\cfrac{s^2\sqrt{3}}{4}\qquad s=\stackrel{side's}{length}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\Large Areas}}{\left[ \stackrel{\textit{larger figure}}{\cfrac{1}{2}\pi 8^2~~+~~\cfrac{16^2\sqrt{3}}{4}} \right]\qquad -\qquad \left[ \cfrac{1}{2}\pi \left( \cfrac{1}{3} \right)^2 +\cfrac{\left( \frac{2}{3} \right)^2\sqrt{3}}{4}\right]}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Barea%20of%20a%20semi-circle%7D%7D%7BA%3D%5Ccfrac%7B1%7D%7B2%7D%5Cpi%20r%5E2%5Cqquad%20r%3Dradius%7D~%5Chspace%7B10em%7D%5Cstackrel%7B%5Ctextit%7Barea%20of%20an%20equilateral%20triangle%7D%7D%7BA%3D%5Ccfrac%7Bs%5E2%5Csqrt%7B3%7D%7D%7B4%7D%5Cqquad%20s%3D%5Cstackrel%7Bside%27s%7D%7Blength%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7B%5CLarge%20Areas%7D%7D%7B%5Cleft%5B%20%5Cstackrel%7B%5Ctextit%7Blarger%20figure%7D%7D%7B%5Ccfrac%7B1%7D%7B2%7D%5Cpi%208%5E2~~%2B~~%5Ccfrac%7B16%5E2%5Csqrt%7B3%7D%7D%7B4%7D%7D%20%5Cright%5D%5Cqquad%20-%5Cqquad%20%5Cleft%5B%20%5Ccfrac%7B1%7D%7B2%7D%5Cpi%20%5Cleft%28%20%5Ccfrac%7B1%7D%7B3%7D%20%5Cright%29%5E2%20%2B%5Ccfrac%7B%5Cleft%28%20%5Cfrac%7B2%7D%7B3%7D%20%5Cright%29%5E2%5Csqrt%7B3%7D%7D%7B4%7D%5Cright%5D%7D)
![\bf \left[ 32\pi +64\sqrt{3} \right]\qquad -\qquad \left[ \cfrac{\pi }{18}+\cfrac{\frac{4}{9}\sqrt{3}}{4} \right] \\\\\\ \left[ 32\pi +64\sqrt{3} \right]\qquad -\qquad \left[ \cfrac{\pi }{18}+\cfrac{\sqrt{3}}{9} \right]~~\approx~~ 211.38 - 0.37~~\approx~~ 211.01](https://tex.z-dn.net/?f=%5Cbf%20%5Cleft%5B%2032%5Cpi%20%2B64%5Csqrt%7B3%7D%20%5Cright%5D%5Cqquad%20-%5Cqquad%20%5Cleft%5B%20%5Ccfrac%7B%5Cpi%20%7D%7B18%7D%2B%5Ccfrac%7B%5Cfrac%7B4%7D%7B9%7D%5Csqrt%7B3%7D%7D%7B4%7D%20%5Cright%5D%20%5C%5C%5C%5C%5C%5C%20%5Cleft%5B%2032%5Cpi%20%2B64%5Csqrt%7B3%7D%20%5Cright%5D%5Cqquad%20-%5Cqquad%20%5Cleft%5B%20%5Ccfrac%7B%5Cpi%20%7D%7B18%7D%2B%5Ccfrac%7B%5Csqrt%7B3%7D%7D%7B9%7D%20%5Cright%5D~~%5Capprox~~%20211.38%20-%200.37~~%5Capprox~~%20211.01)
Answer:
C
Step-by-step explanation:
substitute -1 into all of the formulas, if both sides are equal, then it is correct, for C:
2(x-2)+6 = 0, sub -1
2(-1-2)+6=0, simplify and work out
2(-3)+6=0
-6+6=0
0=0
According to the given, 1 in every 10 women has been a victim, therefore the probability of a victim of domestic abuse at some pint is

We need to use Binomial distribution to take a randomly sampled of 25 women and asked each whether she has been a victim.

Where x is the event that shows a victim of domestic abuse at some point.
We need to find the probability of these victim at least 2 has been victim of abuse, so
![P(x>=2) = 1- [P(x=0)+P(x=1)]](https://tex.z-dn.net/?f=P%28x%3E%3D2%29%20%3D%201-%20%5BP%28x%3D0%29%2BP%28x%3D1%29%5D)
![P(x>=2) = 1 - [^{25}C_0(0.10)^0(1-0.10)^{25-0}+^{25}C_1(0.10)^1(1-0.10)^{25-1}]](https://tex.z-dn.net/?f=P%28x%3E%3D2%29%20%3D%201%20-%20%5B%5E%7B25%7DC_0%280.10%29%5E0%281-0.10%29%5E%7B25-0%7D%2B%5E%7B25%7DC_1%280.10%29%5E1%281-0.10%29%5E%7B25-1%7D%5D)
![P(x>=2) = 1 - [0.07198+0.199]](https://tex.z-dn.net/?f=P%28x%3E%3D2%29%20%3D%201%20-%20%5B0.07198%2B0.199%5D)

So the probability is 0.729