Answer:
If 7 is deleted from the set, the median will stay the same.
About half of the values are greater than the mean.
If 2 is deleted from the set, the median will stay the same.
If one of the 5s is deleted from the set, the set will become bimodal.
Answer: 0.025
Step-by-step explanation:
The probability density function for a random variable that is uniformly distributed on interval [a,b] is given by :-
![f(x)=\dfrac{1}{b-a}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7B1%7D%7Bb-a%7D)
Given : A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 45.0 and 55.0 minutes.
Let x be the random variable that denotes the lengths of her classes.
Then, the probability density function = ![f(x)=\dfrac{1}{55-45}=\dfrac{1}{10}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7B1%7D%7B55-45%7D%3D%5Cdfrac%7B1%7D%7B10%7D)
Now, the probability that a given class period runs between 50.25 and 50.5 minutes will be :-
![P(50.25](https://tex.z-dn.net/?f=P%2850.25%3Cx%3C50.5%29%3D%5Cint%5E%7B50.5%7D_%7B50.25%7D%5C%20f%28x%29%5C%20dx%5C%5C%5C%5C%3D%5Cint%5E%7B50.5%7D_%7B50.25%7D%5C%20%5Cdfrac%7B1%7D%7B10%7D%5C%20dx%5C%5C%5C%5C%3D%20%5Cdfrac%7B1%7D%7B10%7D%5Bx%5D%5E%7B50.5%7D_%7B50.25%7D%5C%5C%5C%5C%3D%5Cdfrac%7B1%7D%7B10%7D%5B50.5-50.25%5D%5C%5C%5C%5C%3D%5Cdfrac%7B1%7D%7B10%7D%5B0.25%5D%3D0.025)
Hence, the required probability =0.025
8x+6 <54
subtract 6 from each side
8x < 48
divide by 8
x<6
Choice A
3rd tile first, then 1st tile, 4th tile, 2nd tile.
Step-by-step explanation:
![4\left(3\cdot \:8-x\right)=4](https://tex.z-dn.net/?f=4%5Cleft%283%5Ccdot%20%5C%3A8-x%5Cright%29%3D4)
![\mathrm{Divide\:both\:sides\:by\:}4](https://tex.z-dn.net/?f=%5Cmathrm%7BDivide%5C%3Aboth%5C%3Asides%5C%3Aby%5C%3A%7D4)
![\frac{4\left(3\cdot \:8-x\right)}{4}=\frac{4}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B4%5Cleft%283%5Ccdot%20%5C%3A8-x%5Cright%29%7D%7B4%7D%3D%5Cfrac%7B4%7D%7B4%7D)
![Simplify](https://tex.z-dn.net/?f=Simplify)
![24-x=1](https://tex.z-dn.net/?f=24-x%3D1)
![\mathrm{Subtract\:}24\mathrm{\:from\:both\:sides}](https://tex.z-dn.net/?f=%5Cmathrm%7BSubtract%5C%3A%7D24%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D)
![24-x-24=1-24](https://tex.z-dn.net/?f=24-x-24%3D1-24)
![Simplify](https://tex.z-dn.net/?f=Simplify)
![-x=-23](https://tex.z-dn.net/?f=-x%3D-23)
![\mathrm{Divide\:both\:sides\:by\:}-1](https://tex.z-dn.net/?f=%5Cmathrm%7BDivide%5C%3Aboth%5C%3Asides%5C%3Aby%5C%3A%7D-1)
![\frac{-x}{-1}=\frac{-23}{-1}](https://tex.z-dn.net/?f=%5Cfrac%7B-x%7D%7B-1%7D%3D%5Cfrac%7B-23%7D%7B-1%7D)
![Simplify](https://tex.z-dn.net/?f=Simplify)
![x=23](https://tex.z-dn.net/?f=x%3D23)