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MAVERICK [17]
3 years ago
9

Find 9P9 and 9C9. Why do the answers differ?​

Mathematics
1 answer:
sveta [45]3 years ago
3 0

We have been given two expressions 9P9\text{ and }9C9. We are asked to find the value of each.

To find 9P9, we will use permutations formula.

^nP_r=\frac{n!}{(n-r)!}, where

P = Number of permutations,

n = The total number of objects in the set,

r = Number of objects being chosen from the set.

9P9=\frac{9!}{(9-9)!}

9P9=\frac{9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}{(0)!}

9P9=\frac{362880}{1}                   Using 0!=1

9P9=362880

To find 9C9, we will use combinations formula.

^nC_r=\frac{n!}{r!(n-r)!}, where

C = Number of combinations,

n = The total number of objects in the set,

r = Number of objects being chosen from the set.

9C9=\frac{9!}{9!(9-9)!}

9C9=\frac{9!}{9!(0)!}

9C9=\frac{9!}{9!\cdot 1}     Using 0!=1

Cancelling out 9!, we will get:

9C9=\frac{1}{1}

9C9=1

The answers differ because order. With permutations we care about the order of the elements, while with combinations we don't.  

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Cost =$3

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Given

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Simplify to show the cost and amount of gas bought by each individual

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3(8 + 17)

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Answer:

m=\frac{27.75}{375}=0.074

Nowe we can find the means for x and y like this:

\bar x= \frac{\sum x_i}{n}=\frac{150}{12}=12.5

\bar y= \frac{\sum y_i}{n}=\frac{28.5}{12}=2.375

And we can find the intercept using this:

b=\bar y -m \bar x=2.375-(0.074*12.5)=1.45

So the line would be given by:

y=0.074 x +1.45

C. = 1.45 + 0.074x

Step-by-step explanation:

The data given is:

x: 5,5,510,10,10, 15,15,15, 20,20,20

y: 1.6,2.2,1.4, 1.9, 2.4,2.6, 2.3,2.7, 2.8,2.6, 2.9, 3.1

For this case we need to calculate the slope with the following formula:

m=\frac{S_{xy}}{S_{xx}}

Where:

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}

So we can find the sums like this:

\sum_{i=1}^n x_i = 150

\sum_{i=1}^n y_i =28.5

\sum_{i=1}^n x^2_i =2250

\sum_{i=1}^n y^2_i =70.69

\sum_{i=1}^n x_i y_i =384

With these we can find the sums:

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=2250-\frac{150^2}{12}=375

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=384-\frac{150*28.5}{12}=27.75

And the slope would be:

m=\frac{27.75}{375}=0.074

Nowe we can find the means for x and y like this:

\bar x= \frac{\sum x_i}{n}=\frac{150}{12}=12.5

\bar y= \frac{\sum y_i}{n}=\frac{28.5}{12}=2.375

And we can find the intercept using this:

b=\bar y -m \bar x=2.375-(0.074*12.5)=1.45

So the line would be given by:

y=0.074 x +1.45

C. = 1.45 + 0.074x

8 0
3 years ago
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