Answer:
Step-by-step explanation:
We have been given that 1/2 of Ila’s work-space is covered in paper. 1/3 of the paper is covered in yellow sticky notes.
Ila’s work-space is covered in yellow sticky notes would be 1/3 of 1/2.
Therefore, of Ila’s workspace is covered in yellow sticky notes.
We know the following:
Cylinder volume: V₁ = π r² h
Ball (sphere) volume:V₂ =
π r³
where:
V - volume
r - radius of base of cylinder and diameter of ball
h - height of cylinder.
R = 13 cm ⇒ r = 13 ÷ 2 = 6.5
π = 3.14
a) Since balls touch all sides of cylinder (as shown in image), it can be concluded that height of cylinder is equal to sum of diameters of 3 balls and that radius of base of cylinder is equal to radius of ball:
h = 3 × r = 3 × 13 cm = 39 cm
r = 6.5 cm
So,
V₁ = <span>π r² h
</span><span>V₁ = </span>3.14 × (6.5 cm)² × 39 cm
V₁ = 5,173.9 cm³
b. The total volume of three balls is the sum of volumes of each ball:
Vₐ = 3 × <span>V₂
</span>Vₐ = 3 × <span>
π r³
</span>Vₐ = 3 ×
3.14<span> (6.5 cm)³</span>
Vₐ = 3,449.3 cm³
c. Percentage of the volume of the container occupied by three balls ould be expressed as ratio of volume of three balls and volume of cylinder:
V =
×100
V =
×100
V = 0.6666 ×100
V = 66.66%
Answer:
Step-by-step explanation:
for dot plot A, the mean is 90 to the medium becuase it has the most dots out of them all.
Answer:
slope = 40
Step-by-step explanation:
Calculate the slope m using the slope formula
m = 
with (x₁, y₁ ) = (2, 80) and (x₂, y₂ ) = (4, 160) ← 2 points on the line
m = 
= 
= 
= 40
Answer:
the solution is (2, -6)
Step-by-step explanation:
Substitute the second equation into the first, replacing y in the first:
2x - (-4x+2) = 10
Simplifying, we get:
2x + 4x - 2 = 10, or:
6x = 12, which yields x = 2.
Substituting 2 for x in the second equation yields y = -4(2) + 2 = 0, or y = -6
Then the solution is (2, -6).
