Of the 465 sophomores at eastside high school, exactly 13 are taking french ii or chemistry i or both. there are 40 sophomores taking french ii but not chemistry i, and 60 sophomores taking chemistry i but not french ii. how many sophomores are taking both french ii and chemistry i ?

Answer with explanation:

Number of Sophomores who are eating Outside the high school = 465

Number of sophomores ,out of 465 , who has taken, french ii(F) or chemistry i (C)or both(F∩C)=13

Number of sophomores ,out of 465 , who has taken, french ii but not chemistry i= 40

Number of sophomores ,out of 465 , who has taken, chemistry i but not french ii  = 60

To find, Number of sophomores who has taken both french ii and chemistry i, that is n(F ∪ C).

→→ n(F ∪ C)=n(F)+n(C)-n(F∩C)

⇒n(F ∪ C)= 40 + 60 -13

          =100 -13

          =87

So, 87 sophomores are taking both french ii and chemistry i.

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm