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3 years ago

What is the value of n In the following100 : 500 = n : 5

Mathematics

1 answer:

mrs_skeptik [129]3 years ago

6 0

Step-by-step explanation:

ratio means over so,

100 = n

500 5

500n = 500

500

n=1

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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.

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11 months ago

Find q if p = -12 and the quotient p/q = -3.

Klio2033 [76]

Answer:

The answer is B) 4

Explanation:

A negative times a negative equals a positive so options A and C are wrong.

-12 divided by 1/4 equals -48

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On a blueprint of a house, 48 millimeters represents 7 meters. The length of the living room is 60 millimeters on the blueprint.

Pani-rosa [81]

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Sam decided to lose weight and went on a diet. The figure below depicts a graph, showing how his weight changed during the year.

elena-14-01-66 [18.8K]

Answer:

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On the graph 100kg is where the line starts so that his weight when he started. Hope this made sense!

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What is the value of n In the following100 : 500 = n : 5​

What is the value of n In the following100 : 500 = n : 5