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2 years ago

N is less than 15 and greater than or equal to 3 On a number line

Mathematics

1 answer:

grin007 [14]2 years ago

3 0

The number line that represents the solution set of the inequality can be seen below.

<h3>How to graph the inequality?</h3>

Here we have the inequality:

15 > n ≥ 3

Then we need to have a open dot at the number 15 on the number line, and then a line that goes to the left until the value 3, where we must have a closed dot (because n = 3 is a solution of the inequality). The number line can be seen below.

If you want to learn more about inequalities:

brainly.com/question/18881247

#SPJ1

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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

2 years ago

Please help me? Show your work please! I give brainiest! (Or whatever it’s called :) )

azamat

You need to find the hypotenuse of the right triangle.

4² + 9² = c²
16 + 81 = c²
97 = c²
9.85 = c

There are 5,280 ft in a mile.
Multiply 9.85 by 5,280.

9.85 × 5,280 = 52,008
Multiply 52,008 by 110.

52,008 × 110 = <span>5,720,880

The estimated cost for constructing the street would be $</span>5,720,880.

8 0

3 years ago

The bill for lunch was 24.50 mr smith add a 20% tip how much did mr smith pay

miss Akunina [59]

Answer:

Mr.Smith paid $29.4.

Step-by-step explanation:

Mr.Smith paid $24.5 plus additional 20% of $24.5, and to figure out the total amount that he paid, we need to know what is 20% of $24.50.

20% of $24.50 is:

$\frac{20}{100}*24.5=0.2*24.6=4.9$ .

Mr.Smith paid additional $4.9; therefore, the total amount he paid was

$24.5 + $4.9 = $29.4.

Mr. smith paid $29.4.

4 0

3 years ago

2. Simplify ((–3)2)3

Nat2105 [25]

Answer:

-18

Step-by-step explanation:

((-3)2)3

First, you multiply -3 and 2 which equals -6

-3·2=-6

Then, you multiply -6 and 3 which equals -18

-6·3=-18

6 0

3 years ago

I speak without a mouth and hear without ears. I have no body, but I come alive with wind. What am I?

Genrish500 [490]

Answer:

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers