Suppose U is a set containing 75 elements and that A1, A2, A3 and A4 are subsets of U such that each subset Ai contains 28 elements, the intersection of any two of the four subsets contains 12 elements, the intersection of any three of the four subsets contains 5 elements, and the intersection of all four subsets contains 1 element.

a. What is |A1 ∪ A2 ∪ A3 ∪ A4|?
b. How many elements belong to exactly two of the four subsets?

tip $2.90

total $17.40

80° is the measure of gh

step-by-step explanation:

circle f is congruent to circle j

we have two circle with center f and j.

both circles are congruent. the radius of the circle would be equal.

see the attachment for the circle.

we are given ∠efd ≅ ∠gjh

therefore, arc (ed) = arc (gh)     (∴ circle f is congruent to circle j)

but ∠dfe=80°=arc (ed)

therefore, arc (gh) = 80°

thus, 80° is the measure of gh

the olimpics is not going to wokk out

step-by-step explanation:

answer: - (a)

(b) 88 seats

step-by-step explanation:

given: in an auditorium, there are 22 seats in the first row and 28 seats in the second row.

thus first term=

second term=

the number of seats in a row continues to increase by 6 with each additional row.

⇒d= 6

a) given formula :

b)   let the number of seats (n) = 12

substitute n=12 in the explicit rule formed in (a)

∴there are 88 seats in 12 rows.