An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. These classes are open to any of the 86 students in the school. There are 38 in the Spanish class, 27 in the French class, and 16 in the German class. There are 14 students that in both Spanish and French, 6 are in both Spanish and German, and 5 are in both French and German. In addition, there are 2 students taking all 3 classes. If one student is chosen randomly, what is the probability that he or she is taking at least one language class

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:

So, Probability that he or she is taking at least one language class is given by

Hence, the required probability is 0.674.

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204

angle efh= angle egh