larry is flying at an altitude of 3,000 feet above ground level. Ground level is 188 feet above sea level. If he descends 567 fe
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Answer:
The origination fee on a mortgage of $400,000 is $7,000.
Step-by-step explanation:
Here, the mortgage value = $400,000
The origination fee = 1.75%
Now, the origination fee is calculated on the amount mortgaged.
⇒ 1.75 % of ($400,00) = Origination Fee
Now, 1.75 % of ($400,00) =
or, 1.75 % of ($400,00) = $ 7,000
Hence, the origination fee on a mortgage of $400,000 is $7,000.
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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