mineral=aluminite, cryptohalite, fluorannite, graphite, titanium, ziesite
density (g/cm^3)=1.68, 2 1/100, 3 7/40, 2.16, 4 2/5, 3.86
1. explain why the densities cannot be represented using set-builder notation.
2. use interval notation to describe a set of numbers that contains the densities of the minerals.
Actually, one could use set builder notation if you defined the set Y as {1.68,2 1/100, 3 7/40, 2.16, 4 2/5, 3.86 }
Then you could say density belongs to the set Y.
It is an odd way, but it is correct.
the set interval 0<D<10 contains the densities
1. Set-builder notation is a way to represent a set of numbers using a specific rule or condition. In this case, the densities provided for the minerals are not easily representable using set-builder notation because they are given as specific numerical values rather than a defined pattern or rule. Set-builder notation is typically used when the elements of a set can be described by a mathematical formula or a condition that can generate the elements of the set. Since the densities of the minerals are given as individual values, it does not allow for the use of set-builder notation.
2. To describe a set of numbers that contains the densities of the minerals using interval notation, we need to identify the minimum and maximum values observed among the given densities.
From the provided densities, we can see that the minimum density is 1.68 g/cm^3 and the maximum density is 4 2/5 or 8.4/5 g/cm^3, which is equivalent to 1.68 g/cm^3. So, the set of numbers containing the densities of the minerals can be described using interval notation as [1.68, 1.68].
In interval notation, the square brackets [ ] are used to indicate that the values are included in the set and the comma separates the minimum and maximum values. Therefore, [1.68, 1.68] represents a set that contains only the density value of 1.68 g/cm^3.