Answer:
x = 56.25
Step-by-step explanation:
The sides of the rectangle are in the ratio 3:4, so those together with the diagonal of the rectangle make a 3-4-5 right triangle. The sum of these adjacent-side ratio units is 3+4 = 7, so the perimeter in ratio units is 2×7 = 14. The actual perimeter is 42 inches, so each ratio unit must stand for ...
(42 in)/(14 units) = 3 in/unit
The diagonal of the rectangle is the diameter of the circle. Its length is 5 units, or ...
(5 units)×(3 in/unit) = 15 inches.
Then the radius is half the diameter, or 7.5 inches.
The area of a circle is given by ...
A = πr² = π(7.5 in)² = 56.25π in²
The value of x is 56.25.
Answer: 1,733,760
Step-by-step explanation:
The number of combinations of selecting m things from n things is given by :-
Given : There are 21 mathematics majors and 129 computer science majors at a college.
Then, the number of ways to pick 4 representatives, so that 2 are mathematics majors and the other 2 are computer science majors :-
Hence, the number of ways to pick 4 representatives, so that 2 are mathematics majors and the other 2 are computer science majors =1,733,760