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3 years ago

Consider the graph of the quadratic function. Which interval on the x-axis has a negative rate of change?

Mathematics

2 answers:

asambeis [7]3 years ago

7 0

<span>1 to 2.5 is the correct answer</span>

crimeas [40]3 years ago

3 0

Answer:

D is correct

Step-by-step explanation:

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The US Census reported that it takes workers an average of 28 minutes to get home from work with standard deviation 5 minutes. A

xz_007 [3.2K]

Using the z-distribution, as we have the standard deviation for the population, to test the hypothesis, it is found that this is evidence that workers in the large city take longer than 28 minutes to get home from work.

<h3>What are the hypothesis tested?</h3>

At the null hypothesis, it is tested if the mean time is of 28 minutes, that is:

$H_0: \mu = 28$

At the alternative hypothesis, it is tested if the mean time is greater than 28 minutes, that is:

$H_1: \mu > 28$ .

<h3>What is the test statistic?</h3>

The test statistic is given by:

$z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

The parameters are:

$\overline{x}$ is the sample mean.

$\mu$ is the value tested at the null hypothesis.

$\sigma$ is the standard deviation of the sample.

n is the sample size.

In this problem, the values of the parameters are given by:

$\overline{x} = 32, \mu = 28, \sigma = 5, n = 10$

Hence:

$z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{32 - 28}{\frac{5}{\sqrt{10}}}$

$z = 2.53$

<h3>What is the decision?</h3>

Considering that we have a <em>right-tailed test</em>, as we are testing if the mean is greater than a value, with a standard <em>significance level of 0.05</em>, the critical value is of $z^\ast = 1.645$ .

Since the test statistic is greater than the critical value, it is found that this is evidence that workers in the large city take longer than 28 minutes to get home from work.

To learn more about the z-distribution, you can check brainly.com/question/26454209

4 0

2 years ago

sketch a unit circle with angle instandard positionquestions:a. For what values of 0 is the sine increasing? Decreasing?b. For w

liq [111]

We can draw a unit circle as:

The sine is the vertical leg (or vertical projection) of the triangle formed by the angle.

The cosine will be the horizontal leg (or horizontal projection) of this same triangle.

The hypotenuse of this triangle will be the radius if the unit circle (r = 1).

a) The sine will be increasing from θ = 0° until it reaches its maximum at 90°.

Then it will be decreasing for angles between 90° and 270°.

Between 270° and 0° it will be increasing again.

b) The cosine has a maximum value for an angle of 0°.

It will decrease until 180°.

Then it will be increasing from angles between 180° and 360°.

c) We can see in the unit circle that the sine is 0 when the angle is one the horizontal axis, like when θ = 0° or θ = 180°.

The cosine will be equal to 0 when the angle is vertical: θ = 90° and θ = 270°.

Answer:

a) Increasing: (0°, 90°) and (270°, 360°)

Decreasing: (90°, 270°)

b) Increasing: (180°, 360°)

Decreasing: (0°,180°).

c) Sin(θ) = 0 for θ = 0° and θ = 180°

Cos(θ) = 0 for θ = 90° and θ = 270°

4 0

2 years ago