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3 years ago

LM is the mid segment of trapezoid ABCD. AB = 72 and DC= 104. What is LM?

Mathematics

2 answers:

Scorpion4ik [409]3 years ago

8 0

<span>88 mid segment formula is like finding the average [the top AB (72) + bottom (104)]/ by 2</span>

ankoles [38]3 years ago

3 0

72+104= 176
176/2=88
lm=88

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Let X be a set of size 20 and A CX be of size 10. (a) How many sets B are there that satisfy A Ç B Ç X? (b) How many sets B are

Svetlanka [38]

Answer:

(a) Number of sets B given that

A⊆B⊆C: 2¹⁰. (That is: A is a subset of B, B is a subset of C. B might be equal to C)
A⊂B⊂C: 2¹⁰ - 2. (That is: A is a proper subset of B, B is a proper subset of C. B≠C)

(b) Number of sets B given that set A and set B are disjoint, and that set B is a subset of set X: 2²⁰ - 2¹⁰.

Step-by-step explanation:

Let $x_1, x_2, \cdots, x_{20}$ denote the 20 elements of set X.

Let $x_1, x_2, \cdots, x_{10}$ denote elements of set X that are also part of set A.

For set A to be a subset of set B, each element in set A must also be present in set B. In other words, set B should also contain $x_1, x_2, \cdots, x_{10}$ .

For set B to be a subset of set C, all elements of set B also need to be in set C. In other words, all the elements of set B should come from $x_1, x_2, \cdots, x_{20}$ .

$\begin{array}{c|cccccccc}\text{Members of X} & x_1 & x_2 & \cdots & x_{10} & x_{11} & \cdots & x_{20}\\[0.5em]\displaystyle\text{Member of}\atop\displaystyle\text{Set A?} & \text{Yes}&\text{Yes}&\cdots &\text{Yes}& \text{No} & \cdots & \text{No}\\[0.5em]\displaystyle\text{Member of}\atop\displaystyle\text{Set B?}& \text{Yes}&\text{Yes}&\cdots &\text{Yes}& \text{Maybe} & \cdots & \text{Maybe}\end{array}$ .

For each element that might be in set B, there are two possibilities: either the element is in set B or it is not in set B. There are ten such elements. There are thus $2^{10} = 1024$ possibilities for set B.

In case the question connected set A and B, and set B and C using the symbol ⊂ (proper subset of) instead of ⊆, A ≠ B and B ≠ C. Two possibilities will need to be eliminated: B contains all ten "maybe" elements or B contains none of the ten "maybe" elements. That leaves $2^{10} -2 = 1024 - 2 = 1022$ possibilities.

Set A and set B are disjoint if none of the elements in set A are also in set B, and none of the elements in set B are in set A.

Start by considering the case when set A and set B are indeed disjoint.

$\begin{array}{c|cccccccc}\text{Members of X} & x_1 & x_2 & \cdots & x_{10} & x_{11} & \cdots & x_{20}\\[0.5em]\displaystyle\text{Member of}\atop\displaystyle\text{Set A?} & \text{Yes}&\text{Yes}&\cdots &\text{Yes}& \text{No} & \cdots & \text{No}\\[0.5em]\displaystyle\text{Member of}\atop\displaystyle\text{Set B?}& \text{No}&\text{No}&\cdots &\text{No}& \text{Maybe} & \cdots & \text{Maybe}\end{array}$ .

Set B might be an empty set. Once again, for each element that might be in set B, there are two possibilities: either the element is in set B or it is not in set B. There are ten such elements. There are thus $2^{10} = 1024$ possibilities for a set B that is disjoint with set A.

There are 20 elements in X so that's $2^{20} = 1048576$ possibilities for B ⊆ X if there's no restriction on B. However, since B cannot be disjoint with set A, there's only $2^{20} - 2^{10}$ possibilities left.

5 0

3 years ago

Find the real solution(s) by solving for x (round any decimals to the nearest 100th);<br> 5x = 320

baherus [9]

Answer:

x=64

Step-by-step explanation:

5x = 320

Divide each side by 5

5x/5 = 320/5

x=64

6 0

3 years ago

Read 2 more answers

The ratio of games won at to the games lost for a basketball team is 3:2. The team won 18 games. How many games did the team los

schepotkina [342]

A ratio of 3:2.

The easiest way to go about this is to divide the actual number of wins (18) by its corresponding element in the ratio.

So:

$\frac{18}{3}= 6$

This means every element on the ratio has a value of 6.

The amount of element in the ratio that correspond to losses is 2.

Multiply the actual amount of matches per element in the ratio by the number of elements that represents the losses in the ratio.

$6*2=12$

Your answer:

<em>"The team lost 12 games."</em>

7 0

3 years ago

Is this a function? Why or why not?

professor190 [17]

Answer:

Yes because there are no repeated dependent variables.

Step-by-step explanation:

7 0

2 years ago

Please help (puppy eyes)

-Dominant- [34]

First we have to find the decimal equivalent by dividing.
5 / 8 = 0.625

It can't be an Integer because decimals can't be intergers, so that's ruled out

It can't be repeating as it does end, so that's also ruled out

Since the decimal does end it can't be non-terminating, non-repeating

So the answer is Terminating Decimal by process of elimination

7 0

3 years ago