Ask question

Ask question

All categories

3 years ago

5

The figure below shows a shaded region and a non-shaded region. Angles in the figure that appear to be right angles are right an

gles.
What is the area, in square feet, of the shaded region?

What is the area, in square feet, of the non-shaded region?

2 answers:

Juli2301 [7.4K]3 years ago

8 0

Sorry I really need points

polet [3.4K]3 years ago

7 0

Answer:

Step-by-step explanatioihhin:

You might be interested in

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:

<h3>(a)</h3>

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.

<h3>(b)</h3>

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

olga55 [171]

Answer:

C

Explanation:

When a number is connected to a variable, (letter) you are multiplying them.

7 0

3 years ago

Find m angle dbc in the figur below

Gemiola [76]

Answer:

It like the once like Line with smaller angle (DBC) measure wouldn't 30* and by the exam the ratio of angle use by subjective by multiplying as large of angle.

oh, by the way I think I hope I'm right so good luck with that?

3 0

3 years ago

What is the simplified form of the following expression? <br><br> ^3sqrt(4x/5)

Vladimir [108]

Answer:

= (∛(100x))/5

Step-by-step explanation:

Given the expression; ∛(4x/5)

To simplify this we need to make denominator a perfect cube.

So multiply and divide 25 inside the cube root, so that the denominator will become a perfect cube of 5.

∛(4x/5) = ∛((4x/5)×(25/25))

= ∛(100x/125)

= ∛(100x/5³)

<u>= (∛100x)/5</u>

7 0

3 years ago

Find the midpoint of (0, 4) and (2, -2)

lidiya [134]

Answer:

$\text{Midpoint} = (1, \; 1)$

Step-by-step explanation:

$M = (x_M, \; y_M)$

$M = \left(\dfrac{x_1 + x_2}{2}, \; \dfrac{y_1 + y_2}{2}\right)$

$M = \left(\dfrac{0 + 2}{2}, \; \dfrac{4 + -2}{2}\right)$

$M = \left(\dfrac{2}{2}, \; \dfrac{2}{2}\right)$

$M = (1, \; 1)$

5 0

2 years ago

Read 2 more answers