A 12-sided solid has faces numbered 1 through 12
a. Find the probability of rolling a number greater than 5.
s. If the 12-sided solid is rolled 180 times, how many times
would you expect either a 3,9, or 11 to be rolled?

a) 7/12

b) 1/6

Step-by-step explanation:

(1)

Number greater than 5 include;

6, 7, 8, 9,10, 11, & 12

= 7

Prbabilyt of event = number of outcome / total number of possible events

= 7/ 12

(2)

Total number of possible events =  180 * 12

= 2160

Number of outcomes for;

Rolling a 3 = 1 * 120 / 2160 = 120/2160

Rolling a 9 = 1 * 120/2160 = 120/2160

Rolling a 11 = 1 * 120/2160 = 120/2160

Since we are using the OR rule, well add the possibilities

120/2160 * 3

360/2160

= 1/6

(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