Given the following data for 120 Nile University students. 65 study French, 45 study German, 42 study Russian, 20 study French and German, 25 study French and Russian, 15 study German and Russian and 8 study all the three languages. a. Find the number of students studying at least one of the three languages.

b. Draw the Venn diagram for the data.

c. Find the number of students studying exactly one language.

d. Find the number of students studying exactly two languages.

△cde maps to △stu with the transformations (x, y) arrowright (x − 2, y − 2) arrowright (3x, 3y) arrowright (x, −y). if cd = a + 1, de = 2a − 1, st = 2b + 3 and tu = b + 6, find the values of a and b. the value of a is and the value of b is .

An office supply company conducted a survey before marketing a new paper shredder designed for home use. in the survey, 80 % of the people who tried the shredder were satisfied with it. because of this high satisfaction rate, the company decided to market the new shredder. assume that 80 % of all people are satisfied with this shredder. during a certain month, 100 customers bought this shredder. find the probability that of these 100 customers, the number who are satisfied is 69 or fewer.

An object in geometry with no width, length or height is a(n):