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Irina-Kira [14]
3 years ago
8

4 What is the solution to the inequality -3x-42>3 ?

Mathematics
1 answer:
Vladimir [108]3 years ago
8 0

\huge \boxed{\mathbb{QUESTION} \downarrow}

  • What is the solution to the inequality -3x-42>3 ?

\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}

- 3 x - 42 \gt 3

Add 42 to both sides.

-3x>3+42

Add 3 and 42 to get 45.

-3x>45

Divide both sides by -3. As -3 is <0, the inequality direction has changed.

x

Divide 45 by -3 to get -15.

\huge \boxed{ \boxed{ \bf \: x

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Using the z-distribution, the 95% confidence interval for the percentage of red candies is of (7.84%, 33.18%). Since 33% is part of the interval, there is not enough evidence to conclude that the claim is wrong.

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions is given by:

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

In which:

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In this problem, we have a 95% confidence level, hence\alpha = 0.95, z is the value of Z that has a p-value of \frac{1+0.95}{2} = 0.975, so the critical value is z = 1.96.

Researching this problem on the internet, 8 out of 39 candies are red, hence the sample size and the estimate are given by:

n = 39, \pi = \frac{8}{39} = 0.2051

Hence the bounds of the interval are:

  • \pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2051 - 1.96\sqrt{\frac{0.2051(0.7949)}{39}} = 0.0784
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As a percentage, the 95% confidence interval for the percentage of red candies is of (7.84%, 33.18%). Since 33% is part of the interval, there is not enough evidence to conclude that the claim is wrong.

More can be learned about the z-distribution at brainly.com/question/25890103

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