Sports of the 25 baseball players on the baltimore orioles 2005 roster, 17 threw right handed, 12 were over 30 years old, and 9 both threw right handed and were over 30 years old. How many players on the team neither threw right handed nor were over 30 years old?

5

Step-by-step explanation:

Let R be the event that players threw right-handed.

Let O be the event that players were over 30 years old.

Given: Total players = 25

n(R) = 17 ,   n(O) = 12  , n(R and O)=9

According to the probability formula,

n(R or O) = n(R)+n(O)-n(R and O)

⇒ n(R or O) =17+12-9

⇒ n(R or O) = 20

Now , n(neither R nor O) = Total - n(R or O)

= 25-20

=5

Hence, the number of players on the team neither threw right-handed nor were over 30 years old = 5

i'm sure goog can you get that answer

(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