Six hundred paving stones were examined for cracks, and 15 were found to be cracked. The same 600 stones were then examined for discoloration, and 27 were found to be discolored. A total of 564 stones were neither cracked nor discolored. One of these 600 stones is chosen at random. What is the probability that it is both cracked and distorted?

0.01

Step-by-step explanation:

Let the events are :

C = paving stones found to be cracked.

D = paving stones found to be discolored.

Given : Total stones : T = 600  (i)

C = 15

D=  27

C'∩D'=  564   (ii)

Since C'∩D' = (C∪D)' = T- C∪D         (iii)

From (i) , (ii)and (ii) , we have

564 = 600- C∪D

⇒ C∪D=600- 564= 36

Formula : C∩D= C+D- C∪D

Put values , we get

C∩D= 15+27-36=6

Now ,

The probability that it is both cracked and distorted is 0.01.

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

the factor is 2

step-by-step explanation:

let f(x)=8(3^(x−2)+2)

to stretch a graph by 3, it would be 3f(x)

g(x) =3f(x)

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

x     −2     0     2     4     6

f(x) 1/64 1/16   1/4     1     4

1/64 * z * z = 1/16

i multiplies by z twice because it its 2 steps from -2 to 0

1/64 z^2 = 1/16

multiply by 64 to clear the fraction on the left side

1/4 * 64 z^2 =1/16 *64

z^2 = 4

take the square root of each side

sqrt(z^2) = ±sqrt(4)

z = ±2  

we are multiplying by 2 each time.

0.0076, if you meant 4.125 divided by 0.03125 it would be 132

step-by-step explanation:

first you have to move the decimal in 0.03125 over until its behind the 5 which is 5 places over. now the number is 3125

then you have to move the decimal in 4.125, 5 places over. now the number is 4,112,500.

now you divide like you would normally would and get 0.0076