C. Line of symmetry is the correct answer
Answer:
80% probability that it will take Victoria greater than 8 minutes (total) for a puzzle that she has already been working on for 7 minutes
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X greater than x is given by the following formula.
![P(X > x) = 1 - \frac{x - a}{b-a}](https://tex.z-dn.net/?f=P%28X%20%3E%20x%29%20%3D%201%20-%20%5Cfrac%7Bx%20-%20a%7D%7Bb-a%7D)
Uniformly distributed random time between 4 minutes and 12 minutes.
This means that ![a = 4, b = 12](https://tex.z-dn.net/?f=a%20%3D%204%2C%20b%20%3D%2012)
What is the probability that it will take Victoria greater than 8 minutes (total) for a puzzle that she has already been working on for 7 minutes?
Already working for 7 minutes, so a is updated to 7.
![P(X > 8) = 1 - \frac{8 - 7}{12 - 7} = 0.8](https://tex.z-dn.net/?f=P%28X%20%3E%208%29%20%3D%201%20-%20%5Cfrac%7B8%20-%207%7D%7B12%20-%207%7D%20%3D%200.8)
80% probability that it will take Victoria greater than 8 minutes (total) for a puzzle that she has already been working on for 7 minutes
Umm... true....? I think thats right...
![QS\cong TV=8](https://tex.z-dn.net/?f=QS%5Ccong%20TV%3D8)
1) Since these triangles are congruent, then we can write out the following for congruent triangles have congruent sides:
![\begin{gathered} QS=TV \\ 3v+2=7v-6 \\ 3v-7v=-6-2 \\ -4v=-8 \\ 4v=8 \\ \frac{4v}{4}=\frac{8}{4} \\ v=2 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20QS%3DTV%20%5C%5C%203v%2B2%3D7v-6%20%5C%5C%203v-7v%3D-6-2%20%5C%5C%20-4v%3D-8%20%5C%5C%204v%3D8%20%5C%5C%20%5Cfrac%7B4v%7D%7B4%7D%3D%5Cfrac%7B8%7D%7B4%7D%20%5C%5C%20v%3D2%20%5Cend%7Bgathered%7D)
2) Still based on that principle, we can plug v=2 into any of those formulas to get the measure of QS and TV. So let's pick the simpler one:
![\begin{gathered} QS=3v+2 \\ QS=3(2)+2 \\ QS=6+2 \\ QS=8 \\ --- \\ TV=7(2)-6 \\ TV=14-6 \\ TV=8 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20QS%3D3v%2B2%20%5C%5C%20QS%3D3%282%29%2B2%20%5C%5C%20QS%3D6%2B2%20%5C%5C%20QS%3D8%20%5C%5C%20---%20%5C%5C%20TV%3D7%282%29-6%20%5C%5C%20TV%3D14-6%20%5C%5C%20TV%3D8%20%5Cend%7Bgathered%7D)
As we can see these segments are congruent.