Answer:
7
Step-by-step explanation:
im pretty sure at least. since x is on a midpoint, it'd half of 14.
Answer:
(a) 10x^2−x−21
Step-by-step explanation:
The area of a rectangle is given by the formula ...
A = LW . . . . . where L is the length, and W is the width
__
The area of the given rectangle will be ...
A = (2x -3)(5x +7)
This product is simplified using the distributive property to eliminate parentheses. Then like terms are combined.
A = 2x(5x +7) -3(5x +7)
= (2x)(5x) +(2x)(7) -3(5x) -3(7)
= 10x^2 +14x -15x -21
A = 10x^2 -x -21
The expression 10x^2 -x -21 represents the area of the rectangle in square inches.
(1) From the information given, if we want to choose 5 colors from 8 distinct colors and the order in which the selection is made is relevant, then what we have is a permutation.
The formula is given as;
![nP_r=\frac{n!}{(n-r)!}](https://tex.z-dn.net/?f=nP_r%3D%5Cfrac%7Bn%21%7D%7B%28n-r%29%21%7D)
This formula means we need to select/arrange r items out of a total of n items and the anwer derived would be the total number of arrangements possible.
Therefore, we would have;
![\begin{gathered} nP_r\Rightarrow_8P_5 \\ _8P_5=\frac{8!}{(8-5)!}\Rightarrow\frac{8!}{3!} \\ _8P_5=\frac{8\times7\times6\times\ldots1}{3\times2\times1}\Rightarrow\frac{40320}{6} \\ _8P_5=6720 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20nP_r%5CRightarrow_8P_5%20%5C%5C%20_8P_5%3D%5Cfrac%7B8%21%7D%7B%288-5%29%21%7D%5CRightarrow%5Cfrac%7B8%21%7D%7B3%21%7D%20%5C%5C%20_8P_5%3D%5Cfrac%7B8%5Ctimes7%5Ctimes6%5Ctimes%5Cldots1%7D%7B3%5Ctimes2%5Ctimes1%7D%5CRightarrow%5Cfrac%7B40320%7D%7B6%7D%20%5C%5C%20_8P_5%3D6720%20%5Cend%7Bgathered%7D)
Therefore, if the order is relevant, this selection can be done in 6,720 ways.
(2) If the order is NOT relevant, then what we need to calculate is a combination and the formula is;
![_nC_r=\frac{n!}{(n-r)!r!}](https://tex.z-dn.net/?f=_nC_r%3D%5Cfrac%7Bn%21%7D%7B%28n-r%29%21r%21%7D)
The formula can now be applied as follows;
![\begin{gathered} _nC_r\Rightarrow_8C_5 \\ _8C_5=\frac{8!}{(8-5)!\times5!} \\ _8C_5=\frac{8!}{3!\times5!}\Rightarrow\frac{8\times7\times6\times\ldots1}{(3\times2\times1)\times(5\times4\times\ldots1)} \\ _8C_5=\frac{40320}{6\times120} \\ _8C_5=56 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20_nC_r%5CRightarrow_8C_5%20%5C%5C%20_8C_5%3D%5Cfrac%7B8%21%7D%7B%288-5%29%21%5Ctimes5%21%7D%20%5C%5C%20_8C_5%3D%5Cfrac%7B8%21%7D%7B3%21%5Ctimes5%21%7D%5CRightarrow%5Cfrac%7B8%5Ctimes7%5Ctimes6%5Ctimes%5Cldots1%7D%7B%283%5Ctimes2%5Ctimes1%29%5Ctimes%285%5Ctimes4%5Ctimes%5Cldots1%29%7D%20%5C%5C%20_8C_5%3D%5Cfrac%7B40320%7D%7B6%5Ctimes120%7D%20%5C%5C%20_8C_5%3D56%20%5Cend%7Bgathered%7D)
If the order is not relevant, then the selection can be done in 56 ways.
Answer:
I believe it is 218 cubic centimeters
Step-by-step explanation:
I FOUND THEM THEY ARE HIDING IN THE CLOUDS.