Consider a school with two classes, A and B. In class A there are 15 girls and 17 boys. In class B, there are 19 girls and 10 boys. Both classes plan extracurricular activities for which each class forms a committee consisting of three students. How many possible committees are there such that the total of committee members of both classes combined consists of 4 girls

7700 committee

Step-by-step explanation:

Given that  In class A there are 15 girls and 17 boys.  And In class B, there are 19 girls and 10 boys

To find  possible committees of 3 such that the total of committee members of both classes combined consists of 4 girls, we will use combination technique

(15C2 × 17C1) + (19C2 × 10C1)

Or

(15C1× 17C2) + (19C3 ×10C0)

Or

(15C3 × 17C0) + (19C1 × 10C2)

Note that "or" means addition

(1785 + 1710) + (2040 + 855) + (455 + 855)

= 3495 + 2895 + 1310

= 7700 committee

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240