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ANTONII [103]
3 years ago
8

In a data distribution, the first quartile, the median and the means are 30.8, 48.5 and 42.0 respectively. If the coefficient sk

ewness is −0.38
a) What is the approximate value of the third quartile (Q3 ), correct to 2 decimal places.
b)What is the approximate value of the variance, correct to the nearest whole number
Mathematics
1 answer:
DerKrebs [107]3 years ago
7 0

Answer:

a) The third quartile Q₃ = 56.45

b) The variance = 2633.31

Step-by-step explanation:

a) The coefficient of skewness formula is given as follows;

SK = \dfrac{Q_{3}+Q_{1}-2Q_{_{2}}}{Q_{3}-Q_{1}}

Plugging in the values, we have;

-0.38 = \dfrac{Q_{3}+30.8-2 \times 48.5_{_{}}}{Q_{3}-30.8}

Solving gives Q₃ = 56.45

b) To determine the variance, we use the skewness formula as follows;

SK_{p} = \dfrac{Mean-\left (3\times Median - 2\times Mean  \right )}{\sigma } =   \dfrac{3\times\left ( Mean - Median \right )}{\sigma }

Plugging in the values, we get;

-0.38= \dfrac{42-\left (3\times 48.5- 2\times 42\right )}{\sigma } = \dfrac{-19.5}{\sigma}

\therefore \sigma =\dfrac{-19.5}{-0.38} = 51.32

The variance = σ² = 51.32² = 2633.31.

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Is the following function even, odd or neither? f(x)=x^3 +4x
erica [24]

Answer:

D, neither

Step-by-step explanation:

to determine whether a function is even, odd or neither, we need to know what it means

an even function is symmetric with respect to the y-axis

an odd function is symmetric with respect to the origin

to solve an equation to see if its even or odd, we would need to substitute <em>x</em> in the equation for <em>-x</em>.

in an even function when we substitute f(-x), it should be equal to to f(x)

in an odd function when we substitute f(-x), it should be equal to -f(x)

so lets test the function given to see if its even

f(x) = x³ + 4x

f(-x) = (-x)³ + 4(-x)

f(-x) = x³ - 4x

f(-x) = x³ - 4x ≠ f(x) = x³ + 4x

comparing this to the orignal function, we see that f(-x) = x³ - 4x is not even as we did not get the same output as the original function

now we should test to see if its odd. we have already seen what f(-x) is, now lets try -f(x) and compare it to f(-x) and f(x)

-f(x) = -(x³ + 4x) -->

-f(x) = -x³ - 4x ≠ f(-x) = x³ - 4x

f(-x) = x³ - 4x ≠ f(x) = x³ + 4x

comparing this to f(x) and f(-x), we see that it not odd as we did not get the same output

so the answer is D, neither even nor odd

6 0
3 years ago
Find the side length of a cube with a volume of 166 m
marin [14]
The answer is 5.5 m.


Cube
Volume = length x width x height

Since the length, width and the height are the same in cube, the formula can be:

Volume = length^3


Let x metres be the side length of the cube.

166 = x^3

x = ∛166

x = 5.495864.....

x = 5.5 (nearest tenth)
8 0
2 years ago
PLEASE HELP 20 POINTS!!!!!!!
svetoff [14.1K]

Answer:

18/25

Step-by-step explanation:

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3 0
2 years ago
WILL GIVE BRAINLEIST NEED TO TURN IN BY 9 P.M. PLS HURRY SUPER EASYIdentify the equation that does not belong with the other thr
BlackZzzverrR [31]

Answer:

C. x + 9 = 11

Step-by-step explanation:

We are trying to identify which of the equations does not match with the others. In this case, solve for x in each equation:

Option A):

6 + x = 9

Subtract 6 from both sides:

6 (-6) + x = 9 (-6)

x = 9 - 6

x = 3

Option B):

15 = x + 12

Subtract 12 from both sides:

15 (-12) = x + 12 (-12)

15 - 12 =  x

x = 3

Option C):

x + 9 = 11

Subtract 9 from both sides:

x + 9 (-9) = 11 (-9)

x = 11 - 9

x = 2

Option D):

7 + x = 10

Subtract 7 from both sides:

x + 7 (-7) = 10 (-7)

x = 10 - 7

x = 3

---------------------------------------------------------------------------------------------------------

As you can tell, all the equations end with x = 3 as there answers except C. x+9=11, making (C) your answer.

~

3 0
3 years ago
A piece of paper is cut and then folded into rectangular prism as shown below.
CaHeK987 [17]
A. C is on the bottom, Bis on the left
5 0
3 years ago
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