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3 years ago

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In the distribution, the first quartile,median and mean are 30.8,48.5 and 42.0 respectively. If the co efficient skewness is -0.

38, find the third quartile?

1 answer:

finlep [7]3 years ago

5 0

Answer:

The third quartile is 56.45

Step-by-step explanation:

The given parameters are;

The first quartile, Q₁ = 30.8

The median or second quartile, Q₂ = 48.5

The mean, $\bar x$ = 42.0

Coefficient of skewness = -0.38

The Bowley's coefficient of skewness (SK) is given as follows;

$SK = \dfrac{Q_3 + Q_1 - 2 \times Q_2}{Q_3 - Q_1}$

Plugging in the values, we have;

$-0.38 = \dfrac{Q_3 + 30.8 - 2 \times 48.5}{Q_3 - 30.8}$

Which gives;

-0.38×(Q₃ - 30.8) = Q₃ + 30.8 - 2 × 48.5

11.704 - 0.38·Q₃ = Q₃ - 66.2

1.38·Q₃ = 11.704 + 66.2 = 77.904

Q₃ = 56.45

The third quartile = 56.45.

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7. All of the following are perfect square trinomials EXCEPT one. Which is it?

wolverine [178]

Answer:

All answers EXCEPT answer C. are perfect square trinomials.

Step-by-step explanation:

A perfect square trinomial is polynomial that satisfies the following condition:

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Let prove if each option observe this:

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1) $4\cdot x^{2} + 12\cdot x\cdot y + 9\cdot y^{2}$ Given

2) $(2\cdot x)^{2}+ 2\cdot (2\cdot x)\cdot (3\cdot y)+(3\cdot y)^{2}$ Definition of power/Distributive, associative and commutative properties.

3) $a = 2\cdot x$ , $b = 3\cdot y$ Definition of perfect square trinomial/Result.

b) $9\cdot a^{2}-36\cdot a + 36$

1) $9\cdot a^{2}-36\cdot a + 36$ Given.

2) $(3\cdot a)^{2}-2\cdot (3\cdot a)\cdot 6 + 6^{2}$ Definition of power/Distributive, associative and commutative properties.

3) $a = 3\cdot a$ , $b = 6$ Definition of perfect square trinomial/Result.

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1) $x\cdot y^{2}-4\cdot x^{2}\cdot y^{2}+4\cdot x^{2}\cdot y^{2}$ Given

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d) $a^{2}\cdot b^{2}+4\cdot a^{3}\cdot b + 4\cdot a^{4}$

1) $a^{2}\cdot b^{2}+4\cdot a^{3}\cdot b + 4\cdot a^{4}$ Given

2) $(a\cdot b)^{2}+2\cdot (a\cdot b)\cdot (2\cdot a^{2})+(2\cdot a^{2})$ Definition of power/Distributive, associative and commutative properties.

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Martha wrote an example of a quadratic function for a homework assignment. The function she wrote is shown. f(x) = 5x3 + 2x2 + 7

larisa86 [58]

<u><em>Answer:</em></u>

<u>The two correct options are:</u>

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<u><em>Explanation:</em></u>

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<u>The given expression is:</u>

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Accordingly, Martha should get rid of the term with power 3 (5x³) in her equation

<u>This can be done by 2 methods:</u>

1- She simply eliminates the term with the third degree

2- She changes the degree of the term with degree 3 to a lower degree and combines it with any existent like term

<u>Comparing the above with the given options, we can conclude that the two correct options are:</u>

- The first term, 5x³, can be eliminated

- The exponent on the first term, 5x³, can be changed to 2 and then combined with the second term, 2x²

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