Answer:
Median is 114.5 (or 115 if rounded to nearest ten)
Mode is 144.
Mean is 110.
Step-by-step explanation:
First, you have to put the numbers from least to greatest.
62, 81, 103, 126, 144, 144
The median is the middle number but, in this number set, there are 2 numbers in the middle. When you have two numbers in the middle you add them both up and then divide by 2.
The mode is the number you see the most. 144 is the number you see the most.
To find the mean, add all the numbers and divide by how many numbers there are.
If you add them all together you get 660
660 divided by 6 is 110. Therefore, your mean is 110.
The average rate of change over a given interval is the slope of the secant line through the endpoints of the interval.
![m = \dfrac{f(b)-f(a)}{b-a} = \dfrac{f(103)-f(100)}{103-100}\\\\ = \dfrac{(103)^2-2500-[(100)^2-2500]}{103-100} = \dfrac{609}{3}=203](https://tex.z-dn.net/?f=m%20%3D%20%5Cdfrac%7Bf%28b%29-f%28a%29%7D%7Bb-a%7D%20%3D%20%20%5Cdfrac%7Bf%28103%29-f%28100%29%7D%7B103-100%7D%5C%5C%5C%5C%20%3D%20%5Cdfrac%7B%28103%29%5E2-2500-%5B%28100%29%5E2-2500%5D%7D%7B103-100%7D%20%3D%20%20%5Cdfrac%7B609%7D%7B3%7D%3D203)
$203/unit.The instantaneous rate of change at a certain point is the slope of the tangent line.
We differentiate C to get 2x. We substitute 100 for x to get that the instantaneous rate of change at 100 is
$200/unit.
Answer:
5/11 or 0.4545
Step-by-step explanation:
10/22 = 5/11 or 0.4545
Wow. This is complicated. It's not hard ... it just has a lot of steps to it.
-- The top, round surface, where the cups and glasses sit:
A circle. The area of a circle is (pi) (radius)²
= (3.14) (24 inches)²
= (3.14) (576 square inches)
= 1,808.64 square inches
-- The 8-inch edge around the table-top.
This is actually a long skinny rectangle, wrapped around it.
The width of the rectangle is 8 inches.
The length of the rectangle is the circumference of the table-top.
Circumference of a circle = (pi) (diameter)
= (pi) (2 x radius)
= (3.14) (48 inches)
= 150.72 inches
Area of the long skinny rectangle = (8 inches) x (150.72 inches)
= 1,205.76 square inches .
-- Legs.
Each leg is a rectangular prism.
Area of the bottom of the leg, where it stands on the floor
= (2.5 inches) x (2.5 inches) = 6.25 square inches
Area of each of the 4 sides =
= (10 inches) x (2.5 inches) = 25 square inches
Area of the top of the leg: glued to the table-top; not stained.
Total surface area of each leg = (6.25 + 25) = 31.25 square inches)
Surface area of all 4 legs = (4) x (31.25) = 125 square inches.
So far, we have:
-- table-top . . . . . . . . . . . . 1,808.64 square inches
-- strip around table-top . . 1,205.76 square inches
-- 4 legs . . . . . . . . . . . . . . . 125 square inches
Total 3,139.4 square inches
This is not one of the choices.
Did I miss something ?
What about the underside of the tabletop ?
That's (the same area as the top of the table-top)
minus
(the 4 little squares where the legs are glued on) .
Let's try that.
Area of the full round surface of the table-top = 1,808.64 square inches
... Each little square
where a leg is glued on = (2.5 x 2.5) = 6.25 sq inches.
Four of them = (4 x 6.25) = 25 square inches
Area of the part of the underside that needs to be stained =
(1,808.64 - 25) = 1,783.64 square inches
So now we have:
-- top surface of the table-top. . . . . 1,808.64 square inches
-- strip around table-top . . . . . . . . . . 1,205.76 square inches
-- bottom surface of the table-top . . 1,783.64 square inches
-- 4 legs. . . . . . . . . . . . . . . . . . . . . . . 125 square inches
Total: 4,923.04 square inches
At this point, I'm going to pull a fast one on you, and talk to you
like the Engineer that I am. You might not like it.
This answer that I have is not exactly the same as any of the choices.
But it's only 12.5 square inches (0.25%) less than one of them.
So now I'm going to say:
-- the choice of 4,935.54 must be the correct one;
-- I must have made a small arithmetic error somewhere, but
I believe I worked the problem correctly; and
-- I've already spent enough time on this one to earn 5 points,
and I'm not going to spend any more of it.
Answer:
x - 5 at the top and 5x at the bottom
