Is the following relation a function?

Mathematics

2 answers:

rjkz [21]3 years ago

3 0

Because for each x-value in the domain of this relationship, except for 0, there is more than one y-value, this is NOT a function.

garri49 [273]3 years ago

3 0

Hello!

This relation is not a function. Each input (domain or x value) must have only one output (range or y value). If you look at some of the x values, there are two points where the relation will intersect the x value.

For example, on this question (points aren't exact, this is just from perspective) there are points (1,1) and (1,-1). As you can see, this one has two outputs, so it is not a function.

A good way to test to see if a relation is a function is the "vertical line test". You draw (or imagine just to be a quick) a vertical line down towards the graphed relation. This vertical line can only intersect with the graphed relation ONCE. If it intersects with two parts of the relation, it is not a function.

In this scenario, if you drew a vertical line down at x=5, it would intersect with the relation at about 2 and negative 2. Since it intersected twice with the graphed relation, it is not a function.

I hope this helps!

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The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2885 and standard deviation

aliina [53]

Answer:

a. X~N(2,885, 651)

b. 0.086291

c. 0.00058

d. 3213.10 calories

Step-by-step explanation:

a. -A normal distribution is expressed in the form X~N(mean, standard deviation).

-Let X a random variable denoting the number of calories consumed.

-X is a is a normally distributed random variable with mean 2885 and standard deviation 651.

-This distribution is expressed as X~N(2,885, 651)

b. The probability that less than 2000 calories are consumed is calculated using the formula:

$P(X$

#substitute the given values in the formula to solve for P:

$P(X$

Hence, the probability of consuming less than 2000 calories is 0.08691

c. The proportion of customers consuming more than 5000 calories is calculated as:

$P(X>x)=P(z>\frac{\bar X-\mu}{\sigma})\\\\=P(Z>\frac{5000-2885}{651})\\\\=P(z>3.2488)\\\\=1-0.99942\\\\=0.00058$

Hence, the proportion of customers consuming over 5000 calories is 0.00058

d. The least amount of calories to get the award is calculated as:

1% is equivalent to a z value of 0.50399.

-We equate this to the formula to solve for the mean consumption:

$0.01=P(z>\frac{\bar X-\mu}{\sigma})\\\\=P(z>\frac{\bar X-2885}{651})\\\\\1\%=0.50399 \\\\\frac{\bar X-2885}{651}=0.50399 \\\\\bar X=0.50399\times 651+2885\\\\=3213.09$