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Damm [24]
3 years ago
8

1. Use the graph of the rational function

Mathematics
1 answer:
Mrrafil [7]3 years ago
4 0

Answer:

As x \to -3^{+}, f(x) \to -\infty

Step-by-step explanation:

Given:

From the graph, we can conclude that:

The function has vertical asymptotes at x=-3\ and\ x=2

The function has horizontal asymptote at f(x)=0

Vertical asymptotes are those values of 'x' for which the functions tends towards infinity. Horizontal asymptote is the value of the function as the 'x' value tends to infinity.

Now, as x \to -3^{+} means the right hand limit of the function at x=-3

From the graph, the right hand limit is the right side of the asymptote of the function at x = -3. The right side shows that the function is tending towards negative infinity.

Therefore, As x \to -3^{+}, f(x) \to -\infty

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James is x years old now and the sum of his age is and his brothers age is 10.
Vesnalui [34]

Answer:

1) James brother is 10-x years old

2) James was 3 years ago x-3 years old

3) James brother was 3 years ago 7-x years old

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5) James is 4 years old, his brother is 6 years old

Step-by-step explanation:

3) 10 - x - 3 = 7 - x

5) 3* James age 3 years ago = James brothers age 3 years ago

<=> 3*(x-3) = 7-x

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6 0
3 years ago
A manufacturer must test that his bolts are 4.00 cm long when they come off the assembly line. He must recalibrate his machines
storchak [24]

Answer:

The null hypothesis is H_o: \mu = 4.

The alternate hypothesis is H_a: \mu \neq 4

The pvalue of the test is 0.0182 < 0.05, which means that there is sufficient evidence to show that the manufacturer needs to recalibrate the machines.

Step-by-step explanation:

A manufacturer must test that his bolts are 4.00 cm long when they come off the assembly line.

This means that the null hypothesis is that they are 4.00 cm long, that is:

H_o: \mu = 4

At the alternate hypothesis we test if it is different. So

H_a: \mu \neq 4

The test statistic is:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

In which X is the sample mean, \mu is the value tested at the null hypothesis, \sigma is the standard deviation and n is the size of the sample.

4 is tested at the null hypothesis:

This means that \mu = 4

After sampling 196 randomly selected bolts off the assembly line, he calculates the sample mean to be 4.14 cm.

This means that n = 196, X = 4.14

He knows that the population standard deviation is 0.83 cm.

This means that \sigma = 0.83

Value of the test statistic:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

z = \frac{4.14 - 4}{\frac{0.83}{\sqrt{196}}}

z = 2.36

Pvalue of the test and decision:

The pvalue of the test is the probability that the sample mean is different by at least 4.14 - 4 = 0.14 from the target value, which is P(|z| > 2.36), which is 2 multiplied by the pvalue of z = -2.36.

Looking at the z-table, z = -2.36 has a pvalue of 0.0091

2*0.0091 = 0.0182

The pvalue of the test is 0.0182 < 0.05, which means that there is sufficient evidence to show that the manufacturer needs to recalibrate the machines.

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2 years ago
the home teams score exceeded 2 times the visiting teams score by 5 if the visiting teams score is x which expression represents
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Answer:

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Step-by-step explanation:

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