Answer: The required probability is 0.674.
Step-by-step explanation:
Since we have given that
Number of students in the Spanish class = 38
Number of students in the French class = 27
Number of students in the German class = 16
Number of students in both spanish and French = 14
Number of students in both Spanish and German = 6
Number of students in both French and German = 5
Number of students in all three class = 2
So, it becomes:
![n(S\cup F\cup G)=n(S)+n(F)+n(G)-n(S\cap F)-n(G\cap F)-n(S\cap G)+n(S\cap F\cap G)\\\\n(S\cup F\cup G)=38+27+16-14-5-6+2=58](https://tex.z-dn.net/?f=n%28S%5Ccup%20F%5Ccup%20G%29%3Dn%28S%29%2Bn%28F%29%2Bn%28G%29-n%28S%5Ccap%20F%29-n%28G%5Ccap%20F%29-n%28S%5Ccap%20G%29%2Bn%28S%5Ccap%20F%5Ccap%20G%29%5C%5C%5C%5Cn%28S%5Ccup%20F%5Ccup%20G%29%3D38%2B27%2B16-14-5-6%2B2%3D58)
So, Probability that he or she is taking at least one language class is given by
![\dfrac{58}{86}=0.674](https://tex.z-dn.net/?f=%5Cdfrac%7B58%7D%7B86%7D%3D0.674)
Hence, the required probability is 0.674.
Answer:
(-5, 0) ∪ (5, ∞)
Step-by-step explanation:
I find a graph convenient for this purpose. (See below)
__
When you want to find where a function is increasing or decreasing, you want to look at the sign of the derivative. Here, the derivative is ...
f'(x) = 4x^3 -100x = 4x(x^2 -25) = 4x(x +5)(x -5)
This has zeros at x=-5, x=0, and x=5. The sign of the derivative will be positive when 0 or 2 factors have negative signs. The signs change at the zeros. So, the intervals of f' having a positive sign are (-5, 0) and (5, ∞).
Try solving for the variable and get everything to one side
Answer:
not congruent
Step-by-step explanation:
angles are not equal