9,090,900.0099 is the answer.
To answer this question, we need to find the winning probability in either case.
Probability = no. of outcomes / total no. of possible outcomes
<u>When Hope pulled her defender :</u>
Total no. of games = 9
No. of games won = 3
Winning probability = 3/9 =1/3
<u>When Hope left her defender :</u>
Total no. of games = 10
No. of games won = 6
Winning probability = 6/10 = 3/5
We know that , 1/3 < 3/5.
So, Hope should not pull her defender, as the winning probability is better when Hope left her defender.
Answer : A. Hope should not pull her defender.
Answer:
46
Step-by-step explanation:
Let
represent a number with
in the ten's position and
is the one's position.
This means
actually has value of
.
We are given the sum of those digits of
is 10; this means
.
It says if 18 is added to the number
, then the result is
.
So
has value
and
has value
.
We are given then:
![(ab)+18=(ba)](https://tex.z-dn.net/?f=%28ab%29%2B18%3D%28ba%29)
![10a+b+18=10b+a](https://tex.z-dn.net/?f=10a%2Bb%2B18%3D10b%2Ba)
Subtract
on both sides:
![b+18=10b+a-10a](https://tex.z-dn.net/?f=b%2B18%3D10b%2Ba-10a)
Simplify:
![b+18=10b-9a](https://tex.z-dn.net/?f=b%2B18%3D10b-9a)
Subtract
on both sides:
![18=10b-b-9a](https://tex.z-dn.net/?f=18%3D10b-b-9a)
![18=9b-9a](https://tex.z-dn.net/?f=18%3D9b-9a)
Divide both sides by 9:
![2=b-a](https://tex.z-dn.net/?f=2%3Db-a)
Rearrange by commutative property:
![2=-a+b](https://tex.z-dn.net/?f=2%3D-a%2Bb)
So the system of equations we want to solve is:
![a+b=10](https://tex.z-dn.net/?f=a%2Bb%3D10)
![-a+b=2](https://tex.z-dn.net/?f=-a%2Bb%3D2)
-------------------------Add equations together (this will eliminate the variable
and allow you to go ahead and solve for
:
![0+2b=12](https://tex.z-dn.net/?f=0%2B2b%3D12)
![2b=12](https://tex.z-dn.net/?f=2b%3D12)
Divide both sides by 2:
![b=\frac{12}{2}](https://tex.z-dn.net/?f=b%3D%5Cfrac%7B12%7D%7B2%7D)
Simplify:
![b=6](https://tex.z-dn.net/?f=b%3D6)
If
and
, then
.
since 4+6=10.
So the original number is (46).
18 more than 46 is 18+46=(64) which is what we wanted.
We also have the sum of 4 and 6 is 10 as well.
Answer: 1 1/18
Step-by-step explanation: 5/6 + 2/9 I know this might seem like common, but <em>the </em><em>Numerator is the top number of a fraction</em><em> and the </em><em>Denominator is the bottom a fraction.</em> When the numerator and the denominator are the same such as 5/5 the fraction equals one (I know its real fancy). When you're multiplying a fraction that equals on by another fraction its really just multiplying by a fancy looking 1 that's disguised as a fraction such as 5/5. If you simplify it it goes to the fraction it was as long it was simplified to the max (5/5 x 1/2 = 5/10= 1/2)
- First, you need to find a like denominator, which is 18
- Then, you got to multiply each fraction to make them have common denominators ...multiply 5/6 by 3/3 ( 3/3 is just a fancy way of saying one) 5/6 x 3/3 = 15/18....multiply 2/9 by 2/2 (which is just another fancy way of saying one ) 2/9 x 2/2=4/18
- Next you add them but only the numerator 15/18 + 4/18 = 19/18
- Finally, you change the the fraction into a mixed number 1 and 1/18
<u><em>0.00266666667</em></u> m / min.