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Serjik [45]
3 years ago
11

JA manufacturer determines that the cost of making a computer component is ​$3.161616. Write the repeating decimal cost as a fra

ction and as a mixed number.
Mathematics
1 answer:
Bad White [126]3 years ago
8 0

Answer:

The repeating decimal cost

a) As a fraction = $\frac{3161616}{1000000}

b) As a mixed number = $ 3\frac{161616}{1000000}

Step-by-step explanation:

The cost of making a computer component

= $3.161616

= $ 3 + 0.161616

Looking at the repeating decimal it is in 6 decimal places, hence to convert it to a fraction,

0.161616/ 1000000 × 1000000

= 161616/1000000

Therefore, the cost of making  the  computer component =

$3 + $161616/1000000

Step 1

We convert to a fraction

$3 + $161616/1000000

We find the LCM = 1000000

($3 × 1000000)+ ($161616× 1)/1000000

3000000 + 161616/1000000

= $ (3161616/1000000)

As a Mixed number = 3\frac{161616}{1000000}

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The relative variability is almost equal in both samples a slight greater variability can be noticed in the first sample.

Step-by-step explanation:

The coefficient of variation of a sample is defined as the ratio between the mean standard deviation and the sample mean. And it represents the percentage relation of the variation of the data with respect to the average.

CV=\frac{S}{\bar X}

In the case of the first sample you have:

CV=\frac{0.1252}{1.57}=0.07975

In the case of the second sample you have:

CV=\frac{0.1317}{1.72}=0.07657

The relative variability is almost equal in both samples a slight greater variability can be noticed in the first sample.

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2 tan 30°<br>II<br>1 + tan- 300​
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Question:

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}

Answer:

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}= sin(60^{\circ})

Step-by-step explanation:

Given

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}

Required

Simplify

In trigonometry:

tan(30^{\circ}) = \frac{1}{\sqrt{3}}

So, the expression becomes:

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{2 * \frac{1}{\sqrt{3}}}{1 + (\frac{1}{\sqrt{3}})^2}

Simplify the denominator

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{2 * \frac{1}{\sqrt{3}}}{1 + \frac{1}{3}}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{\frac{2}{\sqrt{3}}}{1 + \frac{1}{3}}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{\frac{2}{\sqrt{3}}}{ \frac{3+1}{3}}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{\frac{2}{\sqrt{3}}}{ \frac{4}{3}}

Express the fraction as:

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}= \frac{2}{\sqrt 3} / \frac{4}{3}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{2}{\sqrt 3} * \frac{3}{4}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{1}{\sqrt 3} * \frac{3}{2}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{3}{2\sqrt 3}

Rationalize

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{3}{2\sqrt 3} * \frac{\sqrt{3}}{\sqrt{3}}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{3\sqrt{3}}{2* 3}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{\sqrt{3}}{2}

In trigonometry:

sin(60^{\circ}) =  \frac{\sqrt{3}}{2}

Hence:

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}= sin(60^{\circ})

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