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3 years ago

Find 2 numbers who product is 15 and sum is 16.

Mathematics

1 answer:

Marizza181 [45]3 years ago

6 0

Answer:

15 and 1

Step-by-step explanation:

x and y are two numbers.

Two equations:

x · y = 15

x + y = 16

Rearrange one of the equations (I'll rearrange the sum equation):

x + y = 16

x = 16 - y

Substitute that to the other equation and solve for y:

x · y = 15

(16 - y) · y = 15

16 - y · y = 15

16 - y² = 15

-y² = 15 - 16

-y² = -1

y² = 1

y = √1

y = 1

Now substitute that to any of the equation and solve for x (in here, I'll choose the multiplication one):

x · y = 15

x · 1 = 15

x = 15

Now verify:

15 · 1 = 15

15 + 1 = 16

This is correct

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The method of moment (MOM) estimator as: $\mathbf{\hat {\theta} =(\dfrac{\overline X}{1-\overline X})^2}$

$\overline X = \dfrac{4}{9}$

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Step-by-step explanation:

From the question, the correct format for the probability density function is:

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Then;

$\overline X = \dfrac{\sqrt{\theta} }{\sqrt{\theta} +1 }$

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$\dfrac{1}{\sqrt{\theta}} =\dfrac{1}{\overline X} - 1$

$\dfrac{1}{\sqrt{\theta}} =\dfrac{1-\overline X}{\overline X}$

$\sqrt{\theta} =\dfrac{\overline X}{1-\overline X}$

squaring both sides, we have:

The method of moment (MOM) estimator as: $\mathbf{\hat {\theta} =(\dfrac{\overline X}{1-\overline X})^2}$

b) If the observations are $\dfrac{1}{2}, \dfrac{1}{3}, \dfrac{1}{2}$

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$\overline X = \dfrac{\dfrac{1}{2}+ \dfrac{1}{3}+\dfrac{1}{2}}{3}$

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$\overline X = \dfrac{\dfrac{8}{6}}{3}$

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Find 2 numbers who product is 15 and sum is 16.​

Find 2 numbers who product is 15 and sum is 16.