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katrin [286]
3 years ago
5

The newly elected president needs to decide the remaining 6 spots available in the cabinet he/she is appointing. If there are 10

eligible candidates for these positions (where rank matters), how many different ways can the members of the cabinet be appointed?
Mathematics
1 answer:
zepelin [54]3 years ago
8 0

Answer: There are 151,200 ways the members can be appointed.

Step-by-step explanation:

Since we have given that

Number of eligible candidates = 10

Number of remaining spots available = 6

Here, rank matters.

so, we will use "Fundamental theorem of counting or by Permutation":

So, Number of different ways the members can be selected is given by

^{10}P_6=10\times 9\times 8\times 7\times 6\times 5\\\\=151,200

Hence, there are 151,200 ways the members can be appointed.

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The length of a rectangular driveway is five feet more than three times the width. The area is 350ft2. Find the width and length
crimeas [40]

Answer:

  • width -- 10 ft
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Step-by-step explanation:

We can let x represent the width. Then the length will be represented by (3x+5), a value 5 more than 3 times the width.

The area is the product of length and width, so is ...

  A = (3x +5)(x) = 3x^2 +5x

To make the area 350, we can find the value of x from ...

  3x^2 +5x = 350

This can be solved a number of ways. One of them is "completing the square".

  3(x^2 +5/3x) = 350

We choose to divide by 3 and add the square of half the x-coefficient.

  x^2 +5/3x +(5/6)^2 = (350/3) + (5/6)^2

  (x +5/6)^2 = 4225/36 . . . . simplify

  x +5/6 = ±√(4225/36) = ±10 5/6 . . . . take the square root

  x = 10  or  -11 2/3 . . . . subtract 5/6

The positive solution is the one of interest: x = 10.

The driveway is 10 ft wide and 35 ft long.

4 0
3 years ago
What is the solution to this equation?<br> -1/5(x+1 1/4)=-2 1/2
lubasha [3.4K]

\large\displaystyle\text{$\begin{gathered}\sf -\frac{1}{5}\left(x+1\frac{3}{4}\right)=-2\frac{1}{2}    \end{gathered}$}

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\large\displaystyle\text{$\begin{gathered}\sf \bf{-4\left(x+\frac{4+3}{4}\right)=-10(2\times2+1)  } \end{gathered}$}

Add 4 and 3 to get 7.

\large\displaystyle\text{$\begin{gathered}\sf \bf{-4\left(x+\frac{7}{4}\right)=-10(2\times2+1)  } \end{gathered}$}

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\large\displaystyle\text{$\begin{gathered}\sf \bf{-4x-4\times\left(\frac{7}{4}\right)=-10(2\times2+1)  } \end{gathered}$}

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\large\displaystyle\text{$\begin{gathered}\sf \bf{-4x-7=10\times5 \ \ \to \ \ [Multiply] }  \end{gathered}$}

\large\displaystyle\text{$\begin{gathered}\sf \bf{-4x-7=-50 } \end{gathered}$}

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\large\displaystyle\text{$\begin{gathered}\sf \bf{-4x=-50+7 \ \ \to \ \ [Add] } \end{gathered}$}

\large\displaystyle\text{$\begin{gathered}\sf \bf{-4x=-43 } \end{gathered}$}

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\large\displaystyle\text{$\begin{gathered}\sf \bf{x=\frac{43}{4} } \end{gathered}$}

simplify

\large\displaystyle\text{$\begin{gathered}\sf \bf{x=10\frac{3}{4} \ \ \to \ \ \ Answer } \end{gathered}$}

<h2>{ Pisces04 }</h2>
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