Which of the following represents the proportion 6 is to 9 as 12 is to 18?
1 answer:
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Answer:
Step-by-step explanation:
Given
--- <em>not 296</em>
Required
Simplify the expression for total earning
The total amount is derived from:
Express percentage as decimal
Now, we can solve further:
<em>Hence, the simplified expression is 1.02n</em>
408.454 cubic inches of air is surrounding the ball in the box
Step-by-step explanation:
When a sphere is inscribed in a cube and touching all of its faces, then
- The diameter of the sphere = the side of the cube
- The empty volume of the cube is the difference between the volume of the cube and the volume of the sphere
∵ The basketball is shaped a sphere
∵ The box is shaped a cube
∵ The ball touching every wall of the box
∴ The diameter of the ball = the side of the box
∵ The length of one side of the cube = 9.5 inches
∴ The diameter of the ball = 9.5 inches
∵ The diameter of the ball = 2 r, where r is the radius of the ball
∴ 9.5 = 2 r
- Divide both sides by 2
∴ r = 4.75 inches
∵ The volume of the air that surrounded the ball in the box =
volume of the box - volume of the ball
∵ Volume box (cube) = s³
∵ s = 9.5 inches
∴ Volume of the box = (9.5)³
∴ Volume of the box = 857.375 inches³
∵ Volume the ball (sphere) = π r³
∵ r = 4.75
∴ Volume the ball = (π)(4.75)³
∴ Volume the ball = 448.921 inches³
Substitute the values of the volumes of the box and the ball in the rule above
∴ The volume of the air = 857.375 - 448.921
∴ The volume of the air = 408.454 inches³
408.454 cubic inches of air is surrounding the ball in the box
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Answer:
7. x = 5
8. x = 2, y = 6
9. x = 21, y = 39
Step-by-step explanation:
For a parallelogram, the lengths across intersection are equal.
7. For a parallelogram, the lengths across intersection are equal.
So that,
3x = 4x - 5
4x - 3x = 5
x = 5
8. For a parallelogram, the lengths across intersection are equal.
So that,
2x = 4
x =
x = 2
and
y - 1 = 2y -7
7 - 1 = 2y - y
y = 6
x = 2, y = 6
9. For a parallelogram, opposite angles have equal value.
Thus,
3x = (4x - 21)
3x = 4x - 21
x = 21
and
3y = (y + 78)
3y = y + 78
3y - y = 78
2y = 78
y =
= 39
y = 39
x = 21, y = 39