Please show work entirely! I'm giving 15 points :-)
1 answer:
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Answer: 4,111.7 mm³
Step-by-step explanation:
You need to use this formula to calculate the volume of the square pyramid:
Where "s" is the lenght of any side of the square base and "h" is the height of the pyramid.
Find the height with the Pythagorean Theorem:
Where "a" is the hypotenuse and "b" and "c" are the legs of the right triangle. Let be "c" the height of the pyramid.
You can identify in the figure that:
Then, you can find the height:
Then, knowing that:
You can calculate the volume:
Hello!
For this uniform distribution, the shape of the density function is a line. We can begin by identifying key elements of the distribution:
Range: 6 to 14 pounds
Formula of density function:
y = 1/Range
1 - (14 - 6) = 1/8 = 0.125
f(x) = 0.125
1)
P(x = 7)
A uniform distribution is a continuous distribution, so the probability of x being an EXACT value is approximately 0.
<u>This is the same as if we took the following integral. (Finding the area under a curve with the same start and end point)</u>
Therefore, P(x = 7) = 0.
2)
We can think of this as finding the area of a rectangle.
The width would be the difference between 8.25 pounds and 12 pounds:
W = 12 - 8.25 = 3.75
The height would be the function (y = .125), or:
h = .125
Using the equation for the area of a rectangle: (A = h * w)
A = 3.75 * .125 = 0.469
Thus, P(8.25 < x < 12) = 0.469
3)
To find the probability GREATER than 10.50 pounds, we can subtract this value from the max value for the width:
W = 14 - 10.50 = 3.50
The height is the same as above:
h = .125
Solve for the area:
A = 3.50 * .125 = 0.4375
P(x > 10.5) = 0.4375