Write this number in two ways in expanded form 204.032

Show all work to identify the asymptotes and state the end behavior of the function f(x)=3x/x-9

lorasvet [3.4K]

Using the asymptote concept, we have that:

The vertical asymptote is x = 9.

The horizontal asymptote is y = 3.

The end behavior is that as $x \rightarrow \infty, y \rightarrow 3$ .

<h3>What are the asymptotes of a function f(x)?</h3>

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.

The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.

In this problem, the function is:

$f(x) = \frac{3x}{x - 9}$

For the vertical asymptote, we have that:

x - 9 = 0 -> x = 9.

For the horizontal asymptote:

$y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{3x}{x - 9} = \lim_{x \rightarrow \infty} \frac{3x}{x} = \lim_{x \rightarrow \infty} 3 = 3$

Hence, the end behavior is that as $x \rightarrow \infty, y \rightarrow 3$ .

More can be learned about asymptotes at brainly.com/question/16948935

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8 0

2 years ago

A type of bacterium triples in population every hour. Assuming you start with

VashaNatasha [74]

Answer:

7290

Step-by-step explanation:

Put 5 in the formula and evaluate.

a(5) = 90·3^(5-1) = 90·81 = 7290

There will be 7290 bacteria at the beginning of hour 5.

4 0

4 years ago

How long would it take to drive 300 miles with a constant speed of 176.1

Oxana [17]

Answer:

It would take about 1.7 hours

Step-by-step explanation:

divide 300 by 176.1

7 0

3 years ago

Last year, a comprehensive report stated that 28% of businesses in the northeast of Ohio were considered highly profitable. This

Alik [6]

Answer:

$z=\frac{0.38 -0.28}{\sqrt{\frac{0.28(1-0.28)}{50}}}=1.575$

$p_v =2*P(z>1.575)=0.115$

So the p value obtained was a very high value and using the significance level given $\alpha=0.01$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of businesses were highly profitable is not significantly different from 0.28 or 28%.

Step-by-step explanation:

Data given and notation

n=50 represent the random sample taken

X=19 represent the businesses were highly profitable

$\hat p=\frac{19}{50}=0.38$ estimated proportion of businesses were highly profitable

$p_o=0.28$ 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)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion of businesses were highly profitable is different from 0.28 or no, the system of hypothesis is.:

Null hypothesis: $p=0.28$

Alternative hypothesis: $p \neq 0.28$

When we conduct a proportion test we need to use the z statistic, 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 required we can replace in formula (1) like this:

$z=\frac{0.38 -0.28}{\sqrt{\frac{0.28(1-0.28)}{50}}}=1.575$

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 $\alpha=0.01$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(z>1.575)=0.115$

So the p value obtained was a very high value and using the significance level given $\alpha=0.01$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of businesses were highly profitable is not significantly different from 0.28 or 28%.

4 0

4 years ago

Gustavo is in a contest where he will win one of four possible

bulgar [2K]

Answer:

Step-by-step explanation:

One of four in number form is 1/4 this is the only thing I can tell you without knowing what the answer choices are or what the question is

3 0

3 years ago