The Venn diagram shows the number of students who passed their examination in French (F) and those who passed their examination in German (G). The number of students who did not pass either examination is b. a) Find the value of b if the total number of students is 55. b) One of the 55 students is selected at random. Written as a fraction, what is the probability that this student (i) passed both French and German, (ii) passed exactly one of these two subjects?

a) 8  b(i)) 19/55  b(ii)) 28/55

Step-by-step explanation:

To get the answer to B you add all of the numbers in the venn diagram which gives you 47 and then you subtract that from the overall number of students which gives you 8.

To find the number of students who passed french and german you take the number from the middle of the diagram (19) and put it out of the overall number of students which is 55 and so the answer is 19/55

To find the number of students that passed exactly one of these two subjects you put 17/55 (those who passed french) and 11/55 (those who passed german) and then you add them together which gives you 28/55.

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.