Answer: The probability that a given class period runs between 51.5 and 51.75 minutes = 0.025
The probability of selecting a class that runs between 51.5 and 51.75 minutes = 0.025
Step-by-step explanation:
The probability density function for random variable x uniformly distributed in [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 46.0 and 56.0 minutes. Find the probability that a given class
Let x be the lengths of her classes.
![f(x)=\dfrac{1}{56-46}=\dfrac{1}{10}=0.1](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7B1%7D%7B56-46%7D%3D%5Cdfrac%7B1%7D%7B10%7D%3D0.1)
Then, the probability that a given class period runs between 51.5 and 51.75 minutes will be :-
![P(51.5](https://tex.z-dn.net/?f=P%2851.5%3CX%3C51.75%29%3D%5Cint%5E%7B51.75%7D_%7B51.5%20%7Df%28x%29%5C%20dx%5C%5C%5C%5C%3D%20%5Cint%5E%7B51.75%7D_%7B51.5%20%7D%280.1%29%5C%20dx%5C%5C%5C%5C%3D%280.1%29%5Bx%5D%5E%7B51.75%7D_%7B51.5%20%7D%5C%5C%5C%5C%3D%280.1%29%2851.75-51.5%29%3D0.025)
Hence, the probability that a given class period runs between 51.5 and 51.75 minutes = 0.025
The probability of selecting a class that runs between 51.5 and 51.75 minutes = 0.025
70 %
30/45 = 2/3 = about 0.67 and 70% (0.70) is the closest
Answer:
hardd sorry
Step-by-step explanation:>..
Answer:
2,602,255
Step-by-step explanation:
(a) This is the same as computing 4⁵⁵ (mod 11). We have
4² ≡ 16 ≡ 5 (mod 11)
4³ ≡ 4 • 5 ≡ 20 ≡ 9 (mod 11)
4⁴ ≡ 4 • 9 ≡ 36 ≡ 3 (mod 11)
4⁵ ≡ 4 • 3 ≡ 12 ≡ 1 (mod 11)
Then from here,
4⁵⁵ ≡ (4⁵)¹⁰ • 4⁵ ≡ 1¹⁰ • 1⁵ ≡ 1 (mod 11)
(b) Each term in the sum
4ⁿ + 4ⁿ⁺¹ + 4ⁿ⁺² + 4ⁿ⁺³ + 4ⁿ⁺⁴
has a common factor of 4ⁿ, so this sum is the same as
4ⁿ (1 + 4 + 16 + 64 + 256) = 4ⁿ • 341 = 4ⁿ • 11 • 31
So the sum is indeed divisible by 11 for all integers <em>n</em>.
(c) Since 4ⁿ = (2ⁿ)², we know the sum is also divisible by 11 when <em>a</em> = 2.