Answer: 0.025
Step-by-step explanation:
Given : A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between the interval [48.0 minutes, 58.0 minutes].
The probability density function :-
Now, the probability that a given class period runs between 50.25 and 50.5 minutes is given by :-
![\int^{50.5}_{50.25}\ f(x)\ dx\\\\=\int^{50.5}_{50.25}\ \dfrac{1}{10}\ dx\\\\=\dfrac{1}{10}|x|^{50.5}_{50.25}\\\\=\dfrac{1}{10}\ [50.5-50.25]=\dfrac{1}{10}\times(0.25)=0.025](https://tex.z-dn.net/?f=%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%5Cdfrac%7B1%7D%7B10%7D%7Cx%7C%5E%7B50.5%7D_%7B50.25%7D%5C%5C%5C%5C%3D%5Cdfrac%7B1%7D%7B10%7D%5C%20%5B50.5-50.25%5D%3D%5Cdfrac%7B1%7D%7B10%7D%5Ctimes%280.25%29%3D0.025)
Hence, the probability that a given class period runs between 50.25 and 50.5 minutes =0.025
Similarly , the probability of selecting a class that runs between 50.25 and 50.5 minutes = 0.025
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The value 7 in 26,475 is 10 times larger than 503,497
Answer:
5.7 meters
Step-by-step explanation:
The Pythagorean theorem can be used to find the second leg (b) of a triangle with diagonal (c) 6 meters and first leg (a) 2 meters.
c^2 = a^2 + b^2
6^2 = 2^2 +b^2
b^2 = 36 -4 = 32
b = √32 ≈ 5.7 . . . . meters
The kitchen is about 5.7 meters long.
Answer:
x = 9
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
- Equality Properties
Step-by-step explanation:
<u>Step 1: Define equation</u>
0.8x = 7.2
<u>Step 2: Solve for </u><em><u>x</u></em>
- Divide both sides by 0.8: x = 9
<u>Step 3: Check</u>
<em>Plug in x to verify it's a solution.</em>
- Substitute: 0.8(9) = 7.2
- Multiply: 7.2 = 7.2
7.2 does indeed equal 7.2. ∴ x = 9 is a solution.
And we have our final answer!
