Decide whether each of these sets of data is discrete or continuous

a: discrete

b: discrete

c: continuous

d: discrete

Step-by-step explanation:

A discrete set is a set with countable elements, while a continuous set is a dense set.

a) The number of buttons in a box.

Suppose that there are 30 buttons in a box.

We only can draw 1 button, 2 buttons, 3 buttons, etc.

So there are a lot of values that we can not get (like 1.5, 3.498, etc)

So this is a discrete set.

b) The weight of sweets in a bag.

Suppose that each sweet weights W.

Then the weight of the bag will be:

weight = B + n*W

Where B is the weight of the bag itself, and n is the number of sweets.

Now, suppose that we add another sweet, then we get:

weight = B + (n + 1)*W

Then we can see that this is not a dense set. The weight can increase (or decrease) only on multiples of W. Then this is a discrete set.

c) The volume of liquid in a bath.

Here we can add any volume of liquid that we want to the bath (it only would be discrete if we saw the system in a microscopical way) so the volume of liquid in the bath can be any value between zero and the maximum volume of liquid that the bath can have, then this is a continuous set.

d) The number of children at a swimming pool.

Similar to the case of the number of buttons in a box, here we only can have whole numbers, then this is a discrete set.

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

true

step-by-step explanation: