The approximate answer would be 18.144, but if you round it from the tenths place it would be 18.
Assuming all of the same coloured flags are in<span>distinguishable,</span>
![\text {Number of ways } = \dfrac{9!}{4!3!2!} = 1260](https://tex.z-dn.net/?f=%5Ctext%20%7BNumber%20of%20ways%20%7D%20%3D%20%20%5Cdfrac%7B9%21%7D%7B4%213%212%21%7D%20%3D%20%201260)
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Answer: 1260 ways
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Option D:
![\left(y^{2}+3 y+7\right)\left(8 y^{2}+y+1\right)=8 y^{4}+25 y^{3}+60 y^{2}+10y+7](https://tex.z-dn.net/?f=%5Cleft%28y%5E%7B2%7D%2B3%20y%2B7%5Cright%29%5Cleft%288%20y%5E%7B2%7D%2By%2B1%5Cright%29%3D8%20y%5E%7B4%7D%2B25%20y%5E%7B3%7D%2B60%20y%5E%7B2%7D%2B10y%2B7)
Solution:
Given expression is
.
<u>To find the product of the expression:</u>
![\left(y^{2}+3 y+7\right)\left(8 y^{2}+y+1\right)](https://tex.z-dn.net/?f=%5Cleft%28y%5E%7B2%7D%2B3%20y%2B7%5Cright%29%5Cleft%288%20y%5E%7B2%7D%2By%2B1%5Cright%29)
Multiply each term of the first term with each term of the 2nd term.
![=y^{2}\left(8 y^{2}+y+1\right) +3 y\left(8 y^{2}+y+1\right) +7\left(8 y^{2}+y+1\right)](https://tex.z-dn.net/?f=%3Dy%5E%7B2%7D%5Cleft%288%20y%5E%7B2%7D%2By%2B1%5Cright%29%20%2B3%20y%5Cleft%288%20y%5E%7B2%7D%2By%2B1%5Cright%29%20%2B7%5Cleft%288%20y%5E%7B2%7D%2By%2B1%5Cright%29)
Using the exponent rule: ![a^m \cdot a^n = a^{m+n}](https://tex.z-dn.net/?f=a%5Em%20%5Ccdot%20a%5En%20%3D%20a%5E%7Bm%2Bn%7D)
![=\left(8 y^{4}+y^3+y^2\right) +\left(24 y^{3}+3y^2+3y\right) +\left(56 y^{2}+7y+7\right)](https://tex.z-dn.net/?f=%3D%5Cleft%288%20y%5E%7B4%7D%2By%5E3%2By%5E2%5Cright%29%20%2B%5Cleft%2824%20y%5E%7B3%7D%2B3y%5E2%2B3y%5Cright%29%20%2B%5Cleft%2856%20y%5E%7B2%7D%2B7y%2B7%5Cright%29)
![=8 y^{4}+y^3+y^2+24 y^{3}+3y^2+3y+56 y^{2}+7y+7](https://tex.z-dn.net/?f=%3D8%20y%5E%7B4%7D%2By%5E3%2By%5E2%2B24%20y%5E%7B3%7D%2B3y%5E2%2B3y%2B56%20y%5E%7B2%7D%2B7y%2B7)
Arrange the terms with same power.
![=8 y^{4}+y^3+24 y^{3}+y^2+3y^2+56 y^{2}+7y+3y+7](https://tex.z-dn.net/?f=%3D8%20y%5E%7B4%7D%2By%5E3%2B24%20y%5E%7B3%7D%2By%5E2%2B3y%5E2%2B56%20y%5E%7B2%7D%2B7y%2B3y%2B7)
![=8 y^{4}+25 y^{3}+60 y^{2}+10y+7](https://tex.z-dn.net/?f=%3D8%20y%5E%7B4%7D%2B25%20y%5E%7B3%7D%2B60%20y%5E%7B2%7D%2B10y%2B7)
Hence option D is the correct answer.
![\left(y^{2}+3 y+7\right)\left(8 y^{2}+y+1\right)=8 y^{4}+25 y^{3}+60 y^{2}+10y+7](https://tex.z-dn.net/?f=%5Cleft%28y%5E%7B2%7D%2B3%20y%2B7%5Cright%29%5Cleft%288%20y%5E%7B2%7D%2By%2B1%5Cright%29%3D8%20y%5E%7B4%7D%2B25%20y%5E%7B3%7D%2B60%20y%5E%7B2%7D%2B10y%2B7)
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
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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
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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:
$7.28
Step-by-step explanation:
The average price, or the expected price, of any item in this specialty store is given by the weighted average of each item's price. That is, the sum of the products of each individual price by its corresponding sales mix:
![AP =(0.16*\$3)+(0.32*\$5)+(0.52*\$10)\\AP=\$7.28](https://tex.z-dn.net/?f=AP%20%3D%280.16%2A%5C%243%29%2B%280.32%2A%5C%245%29%2B%280.52%2A%5C%2410%29%5C%5CAP%3D%5C%247.28)
The average price of any item in the store is $7.28