How can you tell if a relation is a function

Mathematics

2 answers:

AnnyKZ [126]2 years ago

7 0

Vertical line test. Also there is only one y for every x.

BaLLatris [955]2 years ago

5 0

One way to tell if a relation is a function is by using something called the vertical line test. In other words, if we can draw a vertical that passes through more than one point on a graph, then the relation does not represent a function. Another way to tell if a relation represents a function is by looking at the X coordinates of each ordered pair. If any of the ordered pairs have the same X coordinate, then the relation is not a function.

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A survey was conducted that asked 1003 1003 people how many books they had read in the past year. results indicated that x overb

kirill115 [55]

The confidence interval is

$10.5\pm1.35 = (9.15, 11.85)$ . This means that we can be 99% confident that the mean number of books people read lies between 9.15 and 11.85.

To find the confidence interval, we first find the z-score associated with it:

Convert 99% to a decimal: 0.99
Subtract from 1: 1-0.99=0.01
Divide by 2: 0.01/2 = 0.005
Subtract from 1: 1-0.005 = 0.995

Using a z-table (http://www.z-table.com) we see that this is associated with a z-score between 2.57 and 2.58. Since both are equally far from this value we will use 2.575.

We calculate the margin of error using

$ME=z*\frac{s}{\sqrt{n}}
\\
\\=2.575*\frac{16.6}{\sqrt{1003}}=1.35$

This means that the confidence interval is
$10.5\pm1.35$

The lower limit is given by 10.5-1.35 = 9.15.
The upper limit is given by 10.5+1.35 = 11.85

5 0

2 years ago

The dwarves of the Grey Mountains wish to conduct a survey of their pick-axes in order to construct a 99% confidence interval ab

Dmitry_Shevchenko [17]

Answer:

The minimum sample size needed is 125.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

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

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

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

For this problem, we have that:

$\pi = 0.25$

99% confidence level

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

What minimum sample size would be necessary in order ensure a margin of error of 10 percentage points (or less) if they use the prior estimate that 25 percent of the pick-axes are in need of repair?

This minimum sample size is n.

n is found when $M = 0.1$