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pychu [463]
2 years ago
9

A sine function has an amplitude of 3, a period of pi, and a phase shift of pi/2. What is the y-intercept of the function?

Mathematics
1 answer:
jarptica [38.1K]2 years ago
5 0

Based on the calculations, we can logically deduce that the y-intercept of this sine function is equal to: A. 3.

<u>Given the following data:</u>

  • Amplitude = 3
  • Period = π
  • Phase shift = π/2

<h3>How to determine the y-intercept of this function?</h3>

Mathematically, a sine function is modeled by this equation:

y = Asin(ωt + ø)

<u>Where:</u>

  • A represents the amplitude.
  • ω represents angular velocity.
  • t represents the period.
  • ø represents the phase shift.

Also, the period of a sine wave is given by:

t = 2π/ω

2 = 2π/ω

ω = 2

Substituting the given parameters into the equation, we have;

y = 3sin(2t + π/2)

At t = 0, we have:

y = 3sin(2(0) + π/2)

y = 3sin(π/2)

y = 3sin(90)

y = 3 × 1

y = 3.

In conclusion, we can logically deduce that the y-intercept of this sine function is equal to 3.

Read more on phase shift here: brainly.com/question/27692212

#SPJ1

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We would like to create a confidence interval.
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c.A 90% confidence level and a sample size of 300 subjects.

Step-by-step explanation:

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M = z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

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In this problem

The proportions are the same for all the options, so we are going to write our margins of error as functions of \sqrt{\pi(1-\pi)}

So

a.A 99% confidence level and a sample size of 50 subjects.

n = 50

99% confidence interval

So \alpha = 0.01, z is the value of Z that has a pvalue of 1 - \frac{0.01}{2} = 0.995, so Z = 2.575.

The margin of error is

M = z\sqrt{\frac{\pi(1-\pi)}{n}} = \frac{2.575}{\sqrt{50}}\sqrt{\pi(1-\pi)} = 0.3642\sqrt{\pi(1-\pi)}

b.A 90% confidence level and a sample size of 50 subjects.

n = 50

90% confidence interval

So \alpha = 0.1, z is the value of Z that has a pvalue of 1 - \frac{0.1}{2} = 0.95, so Z = 1.645.

The margin of error is

M = z\sqrt{\frac{\pi(1-\pi)}{n}} = \frac{1.645}{\sqrt{50}}\sqrt{\pi(1-\pi)} = 0.2623\sqrt{\pi(1-\pi)}

c.A 90% confidence level and a sample size of 300 subjects.

n = 300

90% confidence interval

So \alpha = 0.1, z is the value of Z that has a pvalue of 1 - \frac{0.1}{2} = 0.95, so Z = 1.645.

The margin of error is

M = z\sqrt{\frac{\pi(1-\pi)}{n}} = \frac{1.645}{\sqrt{300}}\sqrt{\pi(1-\pi)} = 0.0950\sqrt{\pi(1-\pi)}

This produces smallest margin of error.

d.A 99% confidence level and a sample size of 300 subjects.

n = 300

99% confidence interval

So \alpha = 0.01, z is the value of Z that has a pvalue of 1 - \frac{0.01}{2} = 0.995, so Z = 2.575.

The margin of error is

M = z\sqrt{\frac{\pi(1-\pi)}{n}} = \frac{2.575}{\sqrt{300}}\sqrt{\pi(1-\pi)} = 0.1487\sqrt{\pi(1-\pi)}

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3 years ago
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