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3 years ago

Which function below is the inverse of f(x)=7x-1/2

Mathematics

1 answer:

Margaret [11]3 years ago

5 0

We write f(x) in terms of y I.e y=7x-1/2.

Fractions are sometimes ambiguous, we eliminate the fraction by multiplaying the entire function by 2.so as to get 2y=14x-1.

Make x the subject, x=2y+1/14,

Thus the inverse f(x)=2x+1/14

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The results of a common standardized test used in psychology research is designed so that the population mean is 155 and the sta

galina1969 [7]

Answer:

The value <em>155</em> is zero standard deviations from the [population] mean, because $\\ x = \mu$ , and therefore $\\ z = 0$ .

Step-by-step explanation:

The key concept we need to manage here is the z-scores (or standardized values), and we can obtain a z-score using the next formula:

$\\ z = \frac{x - \mu}{\sigma}$ [1]

Where

z is the <em>z-score</em>.
x is the <em>raw score</em>: an observation from the normally distributed data that we want <em>standardize</em> using [1].
$\\ \mu$ is the <em>population mean</em>.
$\\ \sigma$ is the <em>population standard deviation</em>.

Carefully looking at [1], we can interpret it as <em>the distance from the mean of a raw value in standard deviations units. </em>When the z-score is <em>negative </em>indicates that the raw score, <em>x</em>, is <em>below</em> the population mean, $\\ \mu$ . Conversely, a <em>positive</em> z-score is telling us that <em>x</em> is <em>above</em> the population mean. A z-score is also fundamental when determining probabilities using the <em>standard normal distribution</em>.

For example, think about a z-score = 1. In this case, the raw score is, after being standardized using [1], <em>one standard deviation above</em> from the population mean. A z-score = -1 is also one standard deviation from the mean but <em>below</em> it.

These standardized values have always the same probability in the <em>standard normal distribution</em>, and this is the advantage of using it for calculating probabilities for normally distributed data.

A subject earns a score of 155. How many standard deviations from the mean is the value 155?

From the question, we know that:

x = 155.
$\\ \mu = 155$ .
$\\ \sigma = 50$ .

Having into account all the previous information, we can say that the raw score, <em>x = 155</em>, is <u><em>zero standard deviations units from the mean.</em></u> <u><em>The subject earned a score that equals the population mean.</em></u> Then, using [1]:

$\\ z = \frac{x - \mu}{\sigma}$

$\\ z = \frac{155 - 155}{50}$

$\\ z = \frac{0}{50}$

$\\ z = 0$

As we say before, the z-score "tells us" the distance from the population mean, and in this case this value equals zero:

$\\ x = \mu$

Therefore

$\\ z = 0$

So, the value 155 is zero standard deviations <em>from the [population] mean</em>.

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3 years ago