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3 years ago

State the domain of the rational function. (2 points)

Mathematics

1 answer:

ELEN [110]3 years ago

8 0

Answer:

All real numbers except $4$ .

Step-by-step explanation:

The given function is

$f(x)=\frac{6}{4-x}$

This is a rational function.

The domain of a rational function is all real numbers except values that will make the denominator zero.

The denominator of the given function is $4-x$ .

So the domain is all real numbers except

$4-x=0$

We solve for $x$ to obtain,

$4=x$ or $x=4$ .

Therefore the domain is all real numbers except $x=4$ .

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3 years ago

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Step-by-step explanation:

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pashok25 [27]

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Step-by-step explanation:

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3 years ago

All 6 members of a family work. Their hourly wages (in dollars) are the following.37, 38, 39, 40, 39, 11Assuming that these wage

tiny-mole [99]

We have a sample that in fact represents the population.

We have to calculate the standard deviation of this population.

The difference between the standard deviation of a population comparing it to the calculation of the standard deviation of a sample is that we divide by the population side n instead of (n-1).

We have to start by calculating the mean of the population first:

$\begin{gathered} \mu=\dfrac{1}{n}\sum ^n_{i=1}\, x_i \\ \mu=\dfrac{1}{6}(37+38+39+40+39+11) \\ \mu=\dfrac{204}{6} \\ \mu=34 \end{gathered}$

Now, we can calculate the standard deviation as:

$\sigma=\sqrt[]{\dfrac{1}{n}\sum^n_{i=1}\, (x_i-\mu)^2}$ $\begin{gathered} \sigma=\sqrt[]{\dfrac{1}{6}((37-34)^2+(38-34)^2+(39-34)^2+(40-34)^2+(39-34)^2+(11-34)^2)} \\ \sigma=\sqrt[]{\frac{1}{6}(3^2+4^2+5^2+6^2+5^2+(-23)^2)} \\ \sigma=\sqrt[]{\frac{1}{6}(9+16+25+36+25+529)} \\ \sigma=\sqrt[]{\frac{1}{6}(640)} \\ \sigma\approx\sqrt[]{106.67} \\ \sigma\approx10.33 \end{gathered}$

Answer: the standard deviation of this population is approximately 10.33

3 0

2 years ago

A bag contains red marbles, white marbles, and blue marbles. Randomly choose two marbles, one at a time, and without replacement

dsp73

Answer:

$P(First\ White\ and\ Second\ Blue) = \frac{3}{28}$

$P(Same) = \frac{67}{210}$

Step-by-step explanation:

Given (Omitted from the question)

$Red = 7$

$White = 9$

$Blue = 5$

Solving (a): $P(First\ White\ and\ Second\ Blue)$

This is calculated using:

$P(First\ White\ and\ Second\ Blue) = P(White) * P(Blue)$

$P(First\ White\ and\ Second\ Blue) = \frac{n(White)}{Total} * \frac{n(Blue)}{Total - 1}$

<em>We used Total - 1 because it is a probability without replacement</em>

So, we have:

$P(First\ White\ and\ Second\ Blue) = \frac{9}{21} * \frac{5}{21 - 1}$

$P(First\ White\ and\ Second\ Blue) = \frac{9}{21} * \frac{5}{20}$

$P(First\ White\ and\ Second\ Blue) = \frac{9*5}{21*20}$

$P(First\ White\ and\ Second\ Blue) = \frac{45}{420}$

$P(First\ White\ and\ Second\ Blue) = \frac{3}{28}$

Solving (b) $P(Same)$

This is calculated as:

$P(Same) = P(First\ Blue\ and Second\ Blue)\$ $or\ P(First\ Red\ and Second\ Red)\ or\ P(First\ White\ and Second\ White)$

$P(Same) = (\frac{n(Blue)}{Total} * \frac{n(Blue)-1}{Total-1})+(\frac{n(Red)}{Total} * \frac{n(Red)-1}{Total-1})+(\frac{n(White)}{Total} * \frac{n(White)-1}{Total-1})$

$P(Same) = (\frac{5}{21} * \frac{4}{20})+(\frac{7}{21} * \frac{6}{20})+(\frac{9}{21} * \frac{8}{20})$

$P(Same) = \frac{20}{420}+\frac{42}{420} +\frac{72}{420}$

$P(Same) = \frac{20+42+72}{420}$

$P(Same) = \frac{134}{420}$

$P(Same) = \frac{67}{210}$

6 0

3 years ago