Answer:
True.
Step-by-step explanation:
The <em>empirical rule </em>states that for a bell shaped distribution, nearly all of the data will fall within three standard deviations of the mean.
<em>Chebyshev’s inequality </em>says that at least 
of data from a sample will fall within 
standard deviations from the mean.
We have to remember that Chebyshev’s inequality has been proven mathematically for any distribution. But the empirical rule is a tool created for bell shaped distributions.
Answer:
94
Step-by-step explanation:
The triangle is split into two similar triangles. They have the same shape but not the same size. To solve, write a proportion to find KY.
Cross multiply to solve for KY.
95.2(KY) = 168(34)
95.2KY = 5,712
KY = 60
Add KY to 34 to find x.
60 + 34 = 94.
Answer:
17
Step-by-step explanation:
Part (a)
The picture alone, without the frame, is 16 by 20
When accounting for the frame, the larger rectangle is 16+2x by 20+2x
We add up all four sides to get the perimeter
(16+2x)+(20+2x)+(16+2x)+(20+2x)
8x+72
or you can use this perimeter of a rectangle formula
P = 2(L+W)
P = 2(20+2x+16+2x)
P = 2(4x+36)
P = 8x+72
Answer: 8x+72
=========================================
Part (b)
Multiply the length and width to find the area of the rectangle.
area = length*width
A = L*W
A = (20+2x)*(16+2x)
A = 20(16+2x) + 2x(16+2x)
A = 320+40x + 32x + 4x^2
A = 4x^2 + 72x + 320
Answer: 4x^2 + 72x + 320
=========================================
Part (c)
Plug x = 2 into the perimeter equation found in part (a)
P = 8x+72
P = 8*2+72
P = 16+72
P = 88
Now plug x = 2 into the area equation found in part (b)
A = 4x^2 + 72x + 320
A = 4(2)^2 + 72(2) + 320
A = 4(4) + 72(2) + 320
A = 16 + 144 + 320
A = 160+320
A = 480
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Answers:
Perimeter = 88 inches
Area = 480 square inches
Answer:
The constant of proportionality k is given by k=y/x where y and x are two quantities that are directly proportional to each other. Once you know the constant of proportionality you can find an equation representing the directly proportional relationship between x and y, namely y=kx, with your specific k.
