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1 year ago

How many distinct pairs of disjoint non-empty subsets of A are there, the union of which is all of A?

1 answer:

5 0

A = {1, 2, 5, 6, 8}
{1} U {2, 5, 6, 8}
{2} U {1, 5, 6, 8}
{5} U {1, 2, 6, 8}
{6} U {1, 2, 5, 8}
{8} U {1, 2, 5, 6}
{1, 2} U {5, 6, 8}
{1, 5} U {2, 6, 8}
{1, 6} U {2, 5, 8}
{1, 8} U {2, 5, 6}
{1, 2, 5} U {6, 8}
{1, 2, 6} U {5, 8}
{1, 2, 8} U {5, 6}
{1, 5, 6} U {2, 8}
{1, 5, 8} U {2, 6}
{1, 6, 8} U {2, 5}
The answer is 15 distinct pairs of disjoint non-empty subsets.

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Which diagram represents a fraction equivalent to 75%?

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A freight carrier charges $0.57 for a package weighing up to one ounce plus and additional $0.32 for each additional ounce or fr

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1 year ago

A Sunday newspaper lists the 10 used car prices for a foreign compact, with age x measured in years and selling price y measured

Masteriza [31]

Question:

A Sunday newspaper lists the 10 used car prices for a foreign compact, with age x measured in years and selling price y measured in thousands of dollars. A Sunday newspaper lists the 10 used car prices for a foreign compact, with age x measured in years and selling price y measured in thousands of dollars.

Picture of data can be found in the picture attached.

Answer:

Slope = -1.71

Intercept = 22.05

Step-by-step explanation:

Equation of a line usually takes the general form :

ŷ = mx + c

Where :

m = slope or gradient

c = intercept

Inputting the data into a linear regression calculator ;

The output is : ŷ = -1.70872X + 22.04985

Comparing the output to the general formula;

The slope (m):

m = -1.70872 = -1.71(2 decimal places).

The intercept (c):

c = 22.04985 = 22.05(2 decimal places).

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2 years ago

During a field trip, 60 students are put into equal-sized groups. Describe two ways to interpret 60÷5 60 ÷ 5 in this context. Fi

Afina-wow [57]

The second question:

Consider the division expression $7\frac{1}{2} / 2$ . Select all multiplication equations that correspond to this division expression.

$2 * ? = 7\frac{1}{2}$ $7\frac{1}{2} * ?= 2$ $? * 2 = 7\frac{1}{2}$

$2* 7\frac{1}{2} = ?$ $? * 7\frac{1}{2} = 2$

Answer:

1. See Explanation

2. $2 * ? = 7\frac{1}{2}$ and $? * 2 = 7\frac{1}{2}$

Step-by-step explanation:

Solving (a):

Given

$Students = 60$

$Group = Equal\ Sized$

Required

Interpret $\frac{60}{5}$ in 2 ways

Interpretation 1: Number of groups if there are 5 students in each

Interpretation 2: Number of students in each group if there are 5 groups

Solving the quotient

$Quotient = \frac{60}{5}$

$Quotient = 12$

For Interpretation 1:

The quotient means: 12 groups

For Interpretation 2:

The quotient means: 12 students

Solving (b):

Given

$7\frac{1}{2} / 2$

Required

Select all equivalent multiplication equations

Let ? be the quotient of t $7\frac{1}{2} / 2$

So, we have:

$7\frac{1}{2}/2 = ?$

Multiply through by 2

$2 * 7\frac{1}{2}/2 = ? * 2$

$7\frac{1}{2} = ? * 2$

Rewrite as:

$? * 2 = 7\frac{1}{2}$ --- This is 1 equivalent expression

Apply commutative law of addition:

$2 * ? = 7\frac{1}{2}$ --- This is another equivalent expression

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1 year ago

You could win a giant jar of jelly beans if only you could guess how many are in the jar. You find a smaller jar such that the g

Gennadij [26K]

The giant jar of jelly beans is 5 times the size of the smaller jar. If there are 83 jelly beans in the smaller jar, the giant jar can be represented as 5(83).

5(83) = 415 jelly beans

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1 year ago

Read 2 more answers