To determine which statements are true, let's analyze each one step-by-step:
1. -1 is less than [tex]\(-\frac{4}{5}\)[/tex]:
[tex]\[
-\frac{4}{5} = -0.8
\][/tex]
Comparing [tex]\(-1\)[/tex] and [tex]\(-0.8\)[/tex]:
[tex]\(-1\)[/tex] is indeed less than [tex]\(-0.8\)[/tex]. So this statement is true.
2. -0.3 is less than [tex]\(\frac{1}{5}\)[/tex]:
[tex]\[
\frac{1}{5} = 0.2
\][/tex]
Comparing [tex]\(-0.3\)[/tex] and [tex]\(0.2\)[/tex]:
[tex]\(-0.3\)[/tex] is indeed less than [tex]\(0.2\)[/tex]. So this statement is true.
3. 0.6 is greater than 1:
Comparing [tex]\(0.6\)[/tex] and [tex]\(1\)[/tex]:
[tex]\(0.6\)[/tex] is not greater than [tex]\(1\)[/tex]. So this statement is false.
4. 0 is greater than -0.5:
Comparing [tex]\(0\)[/tex] and [tex]\(-0.5\)[/tex]:
[tex]\(0\)[/tex] is indeed greater than [tex]\(-0.5\)[/tex]. So this statement is true.
5. [tex]\(-\frac{3}{5}\)[/tex] is equal to -0.6:
[tex]\[
-\frac{3}{5} = -0.6
\][/tex]
[tex]\(-\frac{3}{5}\)[/tex] is indeed equal to [tex]\(-0.6\)[/tex]. So this statement is true.
By summarizing the true statements, we find that:
- The first statement is true.
- The second statement is true.
- The fourth statement is true.
- The fifth statement is true.
Thus, the true statements are:
Statement 1, Statement 2, Statement 4, and Statement 5.
So the indices of all true statements are [tex]\([1, 2, 4, 5]\)[/tex].
