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1 year ago

Which of the following rational functions is graphed below?

Mathematics

2 answers:

AlekseyPX1 year ago

6 0

Answer:

The rational function that is graphed is B

navik [9.2K]1 year ago

5 0

<h2>Answer:</h2>

The rational function which is graphed below is:

Option: B

B. $F(x)=\dfrac{x}{(x-1)(x+1)}$

<h2>Step-by-step explanation:</h2>

From the graph of the function we see that the graph has vertical asymptote at x=1 and x= -1

Also, we know that while finding the vertical asymptote of the rational function we substitute denominator equal to zero and the values of such x will be the vertical asymptote.

Also, if the line y=0 act as a horizontal asymptote if the degree of polynomial in numerator is smaller than in the denominator.

The function in which above two property hold true is:

B. $F(x)=\dfrac{x}{(x-1)(x+1)}$

( since in option: A

If denominator equal to 0 then x=0 and -1

This means that the vertical asymptotes are 0 and -1 .

In option: C

If denominator is equal to zero.

Then x=0 and 1

This means that the vertical asymptotes are 0 and 1

In option: D

When denominator=0

then x=0

This means that the vertical asymptote is at x=0

which is false )

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Graph the line y = kx +1 if it is known that the point M belongs to it: M(1,3)

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Answer:

$M(x,y) = (1,3)$ belongs to the line $y = 2\cdot x +1$ . Please see attachment below to know the graph of the line.

Step-by-step explanation:

From Analytical Geometry we know that a line is represented by this formula:

$y=k\cdot x + b$

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$k$ - Slope, dimensionless.

$b$ - y-Intercept, dimensionless.

If we know that $b = 1$ , $x = 1$ and $y = 3$ , then we clear slope and solve the resulting expression:

$k = \frac{y-b}{x}$

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One of the solutions to x2 − 2x − 15 = 0 is x = −3. What is the other solution?

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Last year, 46% of business owners gave a holiday gift to their employees. A survey of business owners indicated that 35% plan to

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Answer:

a) Number = 60 *0.35=21

b) Since is a left tailed test the p value would be:

$p_v =P(Z$

c) If we compare the p value obtained and using the significance level given $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% the proportion of business owners providing holiday gifts had decreased from the 2008 level.

We can use as smallest significance level 0.044 and we got the same conclusion.

Step-by-step explanation:

Data given and notation

n=60 represent the random sample taken

X represent the business owners plan to provide a holiday gift to their employees

$\hat p=0.35$ estimated proportion of business owners plan to provide a holiday gift to their employees

$p_o=0.46$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Part a

On this case w ejust need to multiply the value of th sample size by the proportion given like this:

Number = 60 *0.35=21

2) Part b

We need to conduct a hypothesis in order to test the claim that the proportion of business owners providing holiday gifts had decreased from the 2008 level:

Null hypothesis: $p\geq 0.46$

Alternative hypothesis: $p < 0.46$

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.35 -0.46}{\sqrt{\frac{0.46(1-0.46)}{60}}}=-1.710$

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a left tailed test the p value would be:

$p_v =P(Z$

Part c

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