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S_A_V [24]
3 years ago
15

Find the mean median and mode of 5, 9, 7, 12, 6, 4, 10, 8, 14, 9, 4

Mathematics
1 answer:
Artemon [7]3 years ago
8 0

Answer:

Mean:8

Median:8.5

Mode:9,4

Step-by-step explanation:

Mean Steps:

mean(5,9,7,12,6,4,10,8,14,9,4)

To find the mean of the set 5,9,7,12,6,4,10,8,14,9,4 first add the members together.

5+9+7+12+6+4+10+8+14+9+4=88

The mean (average) of the set 5,9,7,12,6,4,10,8,14,9,4 is found by dividing the sum of its members by the number of the members, in this case 11.

88/11 = 8

Mode Steps:

Mode(5,9,7,12,4,10,8,14,9,4)

The mode of a set is the value that appears most often. The mode can have more than one value if two or more values appear the same number of times and more times than any other values in the set.

mode(5,9,7,12,4,10,8,14,9,4)

Putting the numbers in order can make it easier to find the mode because values that appear more than once will be next to each other.

4,4,5,7,8,9,9,10,12,14

In this case the mode has more than one value because 9 and 4 both appear 2 times, more often than any other values.

mode(4,4,5,7,8,9,9,10,12,14)=9,4

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What are the solutions to the equation 2(x-3)^2=54 ?
erastova [34]

Answer:

      x =(6-√108)/2=3-3√ 3 = -2.196

 x =(6+√108)/2=3+3√ 3 = 8.196

Step-by-step explanation:

Step  1  :

Equation at the end of step  1  :

2 • (x - 3)2 - 54 = 0

Step  2  :

 2.1    Evaluate :  (x-3)2   =  x2-6x+9 

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   2x2 - 12x - 36  =   2 • (x2 - 6x - 18) 

Adding  9  has completed the left hand side into a perfect square :

   x2-6x+9  =

   (x-3) • (x-3)  =

  (x-3)2  (x-3)1 =

   x-3

Now, applying the Square Root Principle to  Eq. #4.3.1  we get:

   x-3 = √ 27

Add  3  to both sides to obtain:

   x = 3 + √ 27

Since a square root has two values, one positive and the other negative

   x2 - 6x - 18 = 0

   has two solutions:

  x = 3 + √ 27

   or

  x = 3 - √ 27

Solve Quadratic Equation using the Quadratic Formula

 4.4     Solving    x2-6x-18 = 0 by the Quadratic Formula .

 According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

                                     

            - B  ±  √ B2-4AC

  x =   ————————

                      2A

  In our case,  A   =     1

                      B   =    -6

                      C   =  -18

Accordingly,  B2  -  4AC   =

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Applying the quadratic formula :

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   x  =    —————

                    2

Can  √ 108 be simplified ?

Yes!   The prime factorization of  108   is

   2•2•3•3•3 

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 108   =  √ 2•2•3•3•3   =2•3•√ 3   =

                ±  6 • √ 3

  √ 3   , rounded to 4 decimal digits, is   1.7321

 So now we are looking at:

           x  =  ( 6 ± 6 •  1.732 ) / 2

Two real solutions:

 x =(6+√108)/2=3+3√ 3 = 8.196

or:

 x =(6-√108)/2=3-3√ 3 = -2.196

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