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juin [17]
2 years ago
5

Calculate the number of subsets and the number of proper subsets for the set.

Mathematics
1 answer:
arlik [135]2 years ago
6 0

A set of n elements has 2ⁿ subsets. One of these subsets is the set itself, so this set would have 2ⁿ - 1 <em>proper</em> subsets.

The given set has 4 elements, so it has 2⁴ = 16 subsets and 2⁴ - 1 = 15 proper subsets.

Just to illustrate the claim, we have

• subsets of size 0 (1 of these):

{ } (empty set)

• subsets of size 1 (4 of these):

{1/6}, {1/7}, {1/8}, {1/9}

• subsets of size 2 (6 of these):

{1/6, 1/7}, {1/6, 1/8}, {1/6, 1/9}, {1/7, 1/8}, {1/7, 1/9}, {1/8, 1/9}

• subsets of size 3 (4 of these):

{1/6, 1/7, 1/8}, {1/6, 1/7, 1/9}, {1/6, 1/8, 1/9}, {1/7, 1/8, 1/9}

• subsets of size 4 (1 of these):

{1/6, 1/7, 1/8, 1/9}

and the last one is the only subset that is not a proper subset, because that subset = the set.

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Step-by-step explanation:

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3 years ago
Lisa's store collects 5% sales tax on every item sold if if she caused if she collected $22. In sales tax what was the cost of t
Advocard [28]
Im assuming the question is asking: if she collected $22 in sales tax what was the cost of the items her store sold.  you should make sure you type the question correctly otherwise it'll be hard to answer.

going with my assumption of what the question is, we want to find the total cost of all items her story sold.  let that cost be c. since there is 5% sales tax on everything and we know the sales tax is worth $22,m we have:

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3 years ago
What is the perimeter, in units, of polygon UVWXYZ? Enter your answer in the box.
nikitadnepr [17]

Given:

Consider the below figure attached with this question.

To find:

The perimeter of the polygon UVWXYZ.

Solution:

All sides and vertical and horizontal. So, we can easily find the side lengths of the given polygon by counting the boxes between two points.

From the figure it is clear that,

UV = 9 units

VW = 2 units

WX = 3 units

XY = 3 units

YZ = 6 units

ZU = 5 units

Now, perimeter is the sum of all the sides.

Perimeter=UV+VW+WX+XY+YZ+ZU

Perimeter=9+2+3+3+6+5

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Therefore, the perimeter of UVWXYZ is 28 units.

6 0
3 years ago
What’s the slope of the line?
Dmitry [639]
The slope of the line is 1. the equation would be y=x-3
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3 years ago
Is (0,0) (0,100) endpoints of a vertical line, a horizontal line, or neither?
kicyunya [14]

Answer:

it's a vertical line.

Step-by-step explanation:

only the Y coordinate changes making it vertical

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