\(\displaystyle -50< -3< 0< \frac{1}{2}\)

\(\displaystyle Negative\;numbers\;are\;smaller\;than\;0.\)

\(\displaystyle Positive\;number\;are\;greater\;than\;0.\)

isosceles: triangle with two equal sides and two equal angles

scalene: triangle with no equal sides and no equal angles

equilateral: triangle with three equal sides and three equal angles

A subset of a set \(\displaystyle C\), by definition, is any set that contains no elements not in \(\displaystyle C\).  Each of the following subsets can be seen to have at least one such element, which is underlined here:

\(\displaystyle \left \{ \underline{1}, 4, 8, 12, 20\right \}\)

\(\displaystyle \left \{ 8, \underline{9}, 10, 12, 16, 18\right \}\)

\(\displaystyle \left \{ 4, 6, 8, 10,\underline{ 11}, 14\right \}\)

\(\displaystyle \left \{ 2, 4, 6, \underline{9}, 12, 14\right \}\)

The remaining set can be seen to have only elements from \(\displaystyle C\):

\(\displaystyle \left \{ 4, 8, 12, 16, 20\right \}\subseteq \left \{ 2, \underline{4}, 6, \underline{8}, 10, \underline{12}, 14, \underline{16}, 18, \underline{20}\right \}\)

This is the correct choice.

\(\displaystyle A \cup B\) is the union of sets \(\displaystyle A\) and \(\displaystyle B\) - the set of all elements that appear in either \(\displaystyle A\) or \(\displaystyle B\). These elements are:

\(\displaystyle \left \{ a, b,c, d,e, f, h, i, j,k,m,p \right \}\)

which is a set with twelve elements.

\(\displaystyle When\: multiplying \: numbers \: by \: 11, \: the \: sum \: goes \: in\: between \: the \: two \: digits.\)

\(\displaystyle 43\times11=4\underline{7}3\Rightarrow 4\;\underline{4+3} \;3\)

\(\displaystyle 15\times11=1\underline{6}5\Rightarrow 1\;\underline{1+5} \;5\)

For negative numbers, the bigger the value next to the negative sign, the smaller the number. For example, \(\displaystyle -100\) is smaller than \(\displaystyle -1\). 

Use the tenths digit (the one to the right of the decimal point) to order the numbers:

The negative numbers with a \(\displaystyle 7\) in the tenths place are smaller than the numbers with a \(\displaystyle 6\) in the tenths place.

Then, use the hundredths place to order the numbers:

\(\displaystyle -0.69\) is smaller than \(\displaystyle -0.66\) since \(\displaystyle 9\) is larger than \(\displaystyle 6\). 

\(\displaystyle -0.71\) is smaller than \(\displaystyle -0.70\) since \(\displaystyle 1\) is larger than \(\displaystyle 0\). 

A prime number has exactly two factors: 1 and itself. 85 is immediately disqualified: any number that ends in 5 has 5 as a factor.

First, use the tenths digit (the one to the right of the decimal point) to order the numbers.

The numbers with a 6 in the tenths place are smaller than the numbers with a 7 in the tenths place.

Then, use the hundredths place to order the numbers.

0.66 is smaller than 0.69 since 6 is smaller than 9.

0.70 is smaller than 0.71 since 0 is smaller than 1. 

When ordering objects from largest to smallest, you need to compare the numbers. The largest number will always be the largest object. In this case, the number \(\displaystyle 12\) is bigger than \(\displaystyle 7\) and \(\displaystyle 8\) so the table comes first. The number \(\displaystyle 8\) is bigger than \(\displaystyle 7\) so the flower comes next. The number \(\displaystyle 7\) is the smallest number, so the vase is the smallest object. 

When ordering objects from largest to smallest, you need to compare the numbers. The largest number will always be the largest object. In this case, the number \(\displaystyle 19\) is bigger than \(\displaystyle 7\) and \(\displaystyle 12\) so the sun comes first. The number \(\displaystyle 12\) is bigger than \(\displaystyle 7\), so the moon comes next. The number \(\displaystyle 7\) is the smallest number, so the star is the smallest object.