All categories

4 years ago

Determine the domain of the following graph

Mathematics

1 answer:

Lunna [17]4 years ago

8 0

Answer:

-3 ≥ x ≥ 9

Step-by-step explanation:

The domain are the x-values of every point in your graph. Since it a continuous domain, it'll be represented with ≥. Your two extremities are -3 and 9. Therefore, your domain is -3 ≥ x ≥ 9.

You might be interested in

A distribution of values is normal with a mean of 60 and a standard deviation of 16. From this distribution, you are drawing sam

professor190 [17]

Answer:

The interval containing the middle-most 76% of sample means is between 56.24 and 63.76.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

A distribution of values is normal with a mean of 60 and a standard deviation of 16.

This means that $\mu = 60, \sigma = 16$

Samples of size 25:

This means that $n = 25, s = \frac{16}{\sqrt{25}} = 3.2$

Find the interval containing the middle-most 76% of sample means.

Between the 50 - (76/2) = 12th percentile and the 50 + (76/2) = 88th percentile.

12th percentile:

X when Z has a p-value of 0.12, so X when Z = -1.175.

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$-1.175 = \frac{X - 60}{3.2}$

$X - 60 = -1.175*3.2$

$X = 56.24$

88th percentile:

$Z = \frac{X - \mu}{s}$

$1.175 = \frac{X - 60}{3.2}$

$X - 60 = 1.175*3.2$

$X = 63.76$

The interval containing the middle-most 76% of sample means is between 56.24 and 63.76.

3 0

3 years ago

Find three consecutive even numbers whose sum is 1884.

Scilla [17]

Answer:

smallest number=626

middle number=628

larger number=630

Step-by-step explanation:

To find the numbers, let's use n as the variable. Since we know that the numbers are consecutive even numbers, we know that they increase by 2. For example, we could have 2+4+6=12.

Knowing that the consecutive numbers increase by two's, we can use this.

smallest number: n

middle number: n+2

larger number: n+4

All we have to do is add these together and set it equal to 1884.

n+(n+2)+(n+4)=1884 [combine like terms]

3n+6=1884 [subtract both sides by 6]

3n=1878 [divide both sides by 3]

n=626

Now that we know n=626, we also know that the other numbers are 626, 628, 630 respectively.

5 0

3 years ago