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3 years ago

Why is it helpful to rewrite inequalities

Mathematics

1 answer:

mr_godi [17]3 years ago

7 0

Answer:

that puts the solution in the form ...

variable is ...

Step-by-step explanation:

It isn't always.

Often, we like to have a solution be in the form ...

variable is ...

So, for an inequality, that puts the variable on the left:

x > 3

y < 27

Personally, I like to see the answer in a form that has the variable and its values in the same relation as on a number line. This means, my preferred inequality symbols are < or ≤, since those have the smaller numbers on the left. I would write the first example above as ...

3 < x

showing that the shaded portion of the number line (representing possible values of the variable) is to the right of the open circle at 3. For me, it is more mental effort to translate x > 3 to the same image.

The forms we choose to use are all about making communication as easy as possible.

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Answer:

Step-by-step explanation:

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2 years ago

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3 years ago

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Answer:

Step-by-step explanation:

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2 years ago

There are 2,000 eligible voters in a precinct. A total of 500 voters are randomly selected and asked whether they plan to vote f

Ann [662]

Answer:

$0.7 - 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.647$

$0.7 + 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.753$

And the 99% confidence interval would be given (0.647;0.753).

So the correct answer would be:

a. 0.647 and 0.753

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

The estimated population proportion for this case is:

$\hat p = \frac{350}{500}=0.7$

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=2.58$

And replacing into the confidence interval formula we got:

$0.7 - 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.647$

$0.7 + 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.753$

And the 99% confidence interval would be given (0.647;0.753).

So the correct answer would be:

a. 0.647 and 0.753

7 0

2 years ago