Of the 3737 people at a basketball team party, 2525 of them play basketball, 1515 are under six feet tall, and 5 do not play basketball and are six feet or taller. Determine the number of people at the party who play basketball and are under six feet tall, |B∩||B∩U| , where BB represents the set of people at the party who play basketball and U represents the set of people at the party who are under six feet tall.

8

Step-by-step explanation:

Universal Set, U=37

Number who play basketball, n(B)=25

Number who are under six feet, n(U)=15

Number of those who do not play basketball and are six feet or taller, n(B∪U)'=5

From set theory.

U=n(B)+n(U)-n(B∩U)+n(B∪U)'

37=25+15-n(B∩U)+5

37=45-n(B∩U)

Therefore:

n(B∩U)=45-37=8

Therefore, the number of people at the party who play basketball and are under six feet tall is 8.

351.23

step-by-step explanation:

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3