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3 years ago

Can anyone help pls two more

Mathematics

1 answer:

Andreas93 [3]3 years ago

5 0

Answer:

I'll explain below, just follow the directions. I can't directly draw it.

Step-by-step explanation:

find the length and the width of a rectangle whose perimeter is 18 ft

2L + 2W = 18

simplify, divide by 2

L + W = 9

L = (9-W)

whose area is 20 square feet

L*W = 20

Replace L with (9-W)

W(9-W) = 20

-W^2 + 9W - 20 = 0

Multiply by -1, easier to factor

W^2 - 9W + 20

Factors to

(W-4)(W-5) = 0

Two solutions

W = 4 ft is width, then 5 ft is the Length

and

W = 5 ft is the width, then 4 ft

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Find out the number of combinations and the number of permutations for 8 objects taken 6 at a time. Express your answer in exact

umka2103 [35]

Solution:

The permutation formula is expressed as

$\begin{gathered} P^n_r=\frac{n!}{(n-r)!} \\ \end{gathered}$

The combination formula is expressed as

$\begin{gathered} C^n_r=\frac{n!}{(n-r)!r!} \\ \\ \end{gathered}$

where

$\begin{gathered} n\Rightarrow total\text{ number of objects} \\ r\Rightarrow number\text{ of object selected} \end{gathered}$

Given that 6 objects are taken at a time from 8, this implies that

$\begin{gathered} n=8 \\ r=6 \end{gathered}$

Thus,

Number of permuations:

$\begin{gathered} P^8_6=\frac{8!}{(8-6)!} \\ =\frac{8!}{2!}=\frac{8\times7\times6\times5\times4\times3\times2!}{2!} \\ 2!\text{ cancel out, thus we have} \\ \begin{equation*} 8\times7\times6\times5\times4\times3 \end{equation*} \\ \Rightarrow P_6^8=20160 \end{gathered}$

Number of combinations:

$\begin{gathered} C^8_6=\frac{8!}{(8-6)!6!} \\ =\frac{8!}{2!\times6!}=\frac{8\times7\times6!}{6!\times2\times1} \\ 6!\text{ cancel out, thus we have} \\ \frac{8\times7}{2} \\ \Rightarrow C_6^8=28 \end{gathered}$

Hence, there are 28 combinations and 20160 permutations.

7 0

1 year ago

Help now pls bby pls

lions [1.4K]

Answer:

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3 years ago

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2 years ago

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