The volume of the space not filled by the sphere is the difference between the volume of a cube with edge length 6 inches and the volume of a sphere with radius 3 inches.
<h3><u>Cube</u></h3>
The volume of a cube of edge length s is
... V = s³
When the edge length is 6 in, the volume is
... V = (6 in)³ = 216 in³
<h3><u>Sphere</u></h3>
The volume of a sphere with radius r is
... V = (4/3)π·r³
When the radius is 3 in, the volume is
... V = (4/3)π·(3 in)³ = 36π in³
<h3><u>Space</u></h3>
Then the volume of the space between the cube and the sphere is
... Vcube - Vsphere = 216 in³ - 36π in³ ≈ 102.9 in³ . . . . corresponding to choice C
<span>These types of lines are called contour lines. Though the image is flat and on a two dimensional sheet of paper, they suggest the volume of the shape. Such drawings are often done very quickly or with a single hand motion.</span>
The probability of choosing a white pair of socks is
Answer: 5/11
The probability of choosing a white tee shirt is
answer: 1/2
The probability of both being white is
answer: 5/22
<u>Options</u>
![(A)\left(-\infty , \dfrac23\right]\\\\(B)\left(-\infty , \dfrac23\right) \\\\(C)(\frac23\right, \infty ) \\\\(D) [\frac23\right, \infty )](https://tex.z-dn.net/?f=%28A%29%5Cleft%28-%5Cinfty%20%2C%20%5Cdfrac23%5Cright%5D%5C%5C%5C%5C%28B%29%5Cleft%28-%5Cinfty%20%2C%20%5Cdfrac23%5Cright%29%20%5C%5C%5C%5C%28C%29%28%5Cfrac23%5Cright%2C%20%5Cinfty%20%29%20%5C%5C%5C%5C%28D%29%20%5B%5Cfrac23%5Cright%2C%20%5Cinfty%20%29)
Answer:
Step-by-step explanation:
Given the solution to an inequality
{x|x>2/3}
The solution set does not include 
, therefore, it must be open at the left. Recall that we use a curvy bracket ( to denote openness at the left.
Since x is greater than , the solution set contains all values of larger than up till infinity. Since infinity is an arbitrarily large value, we also use an open bracket at the right.
Therefore, another way to represent the solution {x|x>2/3} is:
The correct option is C.
