Set A and the universal set U are defined as follows.
U={1,2,3,4,5,6)
A= {2,4,6}
Find the following sets.
Write your answer in roster form or as Ø.

Set A And The Universal Set U Are Defined As Follows.U={1,2,3,4,5,6)A= {2,4,6}Find The Following Sets.Write

Answers

Answer 1

Part (a)

Answer:   Ø

This is the empty set

------------------

Explanation:

It doesn't matter what set A is composed of. Intersecting any set with the empty set Ø will always result in the empty set.

This is because we're asking the question: "What does some set A and the empty set have in common?". The answer of course being "nothing" because there's nothing in Ø. Not even the value zero is in this set.

We can write Ø as { } which is a set of curly braces with nothing inside it.

=========================================================

Part (b)

Answer:  {1,2,3,4,5,6}

-----------------

Explanation:

When you union the universal set with any other set, you'll get the universal set.

The rule is [tex]A \cup B = B[/tex] where I've made B the universal set to avoid confusion of the letter U and the union symbol [tex]\cup[/tex] which looks nearly identical.

Why does this rule work? Well if an item is in set [tex]\overline{A}[/tex], then it's automatically in set U (everything is in set U; it's the universe). So we're not adding anything to the universe when applying a union involving this largest set.

It's like saying

A = set of stuff inside a persons house[tex]\overline{A}[/tex] = set of stuff outside a persons house (ie stuff that is not in set A)U = set of every item

we can see that [tex]\overline{A} \cup U[/tex] will basically form the set of every item, aka the universal set.


Related Questions

In a jail cell, there are 5 Democrats and 6 Republicans. Four of these people will be
chosen for early release. How many 4-person groups are possible?

Answers

two because there is 11 people in total and you have two 4 person groups so that would leave 3 people left and you cant make a 4 person group w 3 people

Combination is a way of arranging the required items from a collection of items where the order of selection is not relevant.

If in a jail cell, there are 5 Democrats and 6 Republicans, the possible ways to form a group of 4 is 330.

The number of possible groups is 330.

What is combination?

Combination is a way of arranging the required items from a collection of items where the order of selection is not relevant.

It is given as:

[tex]^nC_r = \frac{n!}{r!(n-r)!}[/tex]

We have,

The total number of people:

5 Democrats and 6 Republicans = 5 + 6 = 11.

The number of persons in a group = 4.

The number of groups possible are:

= [tex]^{11}C_4[/tex]

= 11! / 4! ( 11-4)!

= 11! / 4! 7!

= 11 x 10 x 9 x 8 / 4 x 3 x 2

= 330

Thus,

The number of possible groups is 330.

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This Venn diagram shows the pizza topping preferences for 9 students.
What elements are in A and B?
(Look at picture)

Answers

Answer:

I think the answer is C.

What is the simplified form of the complex fraction? 2x2+7x+6x2+x−64x2−9x2−5x+6

Answers

Answer:

3x - 124

Step-by-step explanation:

kindly find solutions in the picture above

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The simplified form of the complex expression 2x² + 7x + 6x² + x - 64x² - 9x² - 5x + 6 is

-65x² + 2x + 6

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

2x² + 7x + 6x² + x - 64x² - 9x² - 5x + 6

Combine all like terms.

(2x² + 6x² - 64x² - 9x²) + (7x - 5x) + 6

(8x² - 73x²) + 2x + 6

-65x² + 2x + 6

There are no common factors or like-terms to simplify.

So,

The simplified form is -65x² + 2x + 6

Thus,

The simplified form of the complex expression 2x² + 7x + 6x² + x - 64x² - 9x² - 5x + 6 is

-65x² + 2x + 6

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Check out this cube: 3 Find the surface area of the cube (above) using its net (below​

Answers

Answer:

54

Step-by-step explanation:

Surface area of a cube = 6a²

Where,

a = edge = 3

Surface area of a cube = 6a²

= 6 * (3)²

= 6 * (3 * 3)

= 6 * 9

= 54

Therefore,

The Surface area of the cube = 54

The product of two algebraic expression is 4x²-9.If one of the expression is (2x+3),find the other expression​

Answers

Answer:

Solution given:

we have formula

a²+b²=(a+b)(a-b)

now

4x²-9

(2x)²-3²

using formula

(2x+3)(2x-3)

other expression is 2x-3.

Answer:

( 2x - 3 )

Step-by-step explanation:

4x² - 9 is a perfect square meaning it can be factored into 2 expressions,

( 2x + 3 ) ( 2x - 3 )

There are 5 brown horses and 4 tan horses in a barn. Sonia will randomly select two horses to ride with her friend. What is the probability that
the first horse selected is tan and the second horse selected is brown?
20/81

5/18

2/9

1/20

Answers

Answer:

5/18

Step-by-step explanation:

The total number of horses present is 9

The probability that the first selected horse is tan is 4/9

So , now for the second choice , we are left with 8 total horses of which 5 is brown

The probability is 5/8

So the joint probability is the product of this two

That will be;

5/8 * 4/9 = 5/18

C=-(251x3+281)+3X251-(1-281)

Answers

Answer:

-1

Step-by-step explanation:

=-251x3+281 +251x3-1+281

=-1

Second time posting this. Please help!! :)

Answers

Answer:

Step-by-step explanation:

[tex]\frac{480+24(x-40)}{x}[/tex]

The numerator of the rational expression the money he earned for 'x' hours

The rate at which William is paid for each hour in excess of 40 hours 24.

x = 50 hours = (40 + 10 ) hours

The amount paid for excess 10 hours = 24 *10 = 240

Total amount earned for the week = 480 + 240 = 720

-2/3a+5/6a-1/5a-1/6

Answers

Answer:

[tex]\frac{-1}{30} a - \frac{1}{6}[/tex]

Step-by-step explanation:

Find the value of both variables.

Answers

[tex] \cos(45) = \frac{5 \sqrt{2} }{x} \\ \frac{1}{ \sqrt{2} } = \frac{5 \sqrt{2} }{x} \\ x = 10 \\ \\ \tan(45) = \frac{y}{5 \sqrt{2} } \\ 1 = \frac{y}{5 \sqrt{2} } \\ y = 5 \sqrt{2} [/tex]

I hope I helped you ^_^

Express 3.023 in P form where p and q are integers and q= 0 D​

Answers

Given:

The number is 3.023.

To find:

The given number in the form of [tex]\dfrac{p}{q}[/tex], where [tex]q\neq 0[/tex].

Solution:

The given number is 3.023. It can be written as:

[tex]3.023=3.023\times \dfrac{1000}{1000}[/tex]

[tex]3.023=\dfrac{3023}{1000}[/tex]

It cannot be simplified further because 3023 and 1000  have no common factors.

Therefore, the given number 3.023 can be written as [tex]\dfrac{3023}{1000}[/tex].

Question 6 of 25
In APQR, m P= 60°, m_ Q = 30°, and m2 R = 90°. Which of the following
statements about APQR are true?
Check all that apply.

Answers

Answer:

A, E, F

Step-by-step explanation:

From the angles given, we can infer that ΔPQR is a 30-60-90 special triangle. In a 30-60-90 triangle, the leg opposite the 30 degree angle is 1/2 the hypotenuse and the leg opposite the 60 degree angle is √3 times the one opposite the 30. Using this, we can say:

PR = 1/2 PQ which is just 2 PR = PQ(E)

PR √3 = QR (A)

We can substitute in PR from the first equation to the second to get:

√3/2 PQ = QR(F)

The height of a baseball in feet can be found by the equation -4.982 – 20t + 1000. How far has the
baseball traveled at t = 6?

Answers

Answer:

875.018

Step-by-step explanation:

To solve this, we must plug in 6 for our t value. So, we have the equation:

-4.982 - 20(6) + 1000

Following the rules of PEMDAS, we have:

-4.982 - 120 + 1000 = 875.018

help me please to solve this 2 questions pleasee faster.. i will mark you as brainliest​

Answers

Answer:

1. x=72, y=, 108

2.x=30, y=72

Step-by-step explanation:

Brainliest please~

1. 80 = -10b
2. 6 = 2n
3. -16r = 32

1.
2.
3.

Answers

Answer:

1. - 8

2. 3

3. - 2

Step-by-step explanation:

1.

80 = - 10b

- 10b = 80

b = 80 / - 10

b = - 8

2.

6 = 2n

2n = 6

n = 6 / 2

n = 3

3.

- 16r = 32

r = 32 / - 16

r = - 2

Answer:

1. b = - 8
2. n = 3
3. r = -16

Step-by-step explanation:

we’re trying to solve for each variable

1. 80 = -10b

Divide both sides by -10

80/-10 = -10b/-10

-8 = b

2. 6 = 2n

Divide both sides by 2

6/2 = 2/2n

3 = n

3. -16r = 32

Divide -16 by both sides

-16r/-16 = 32/-16

r = -16

What is the solution to this equation?
log_8 16 + 2log_8x =2

Answers

The awnser is I think x=2

The value of x for the given equation [tex]log_{8}[/tex](16) + 2[tex]log_{8}[/tex](x) = 2 will be 2 so option (B) must be correct.

What is a logarithm?

The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.

In another word, a logarithm is a different way to denote any number.

Given the equation

[tex]log_{8}[/tex](16) + 2[tex]log_{8}[/tex](x) = 2

We know that,

xlogb = log[tex]b^{x}[/tex]

So,

2[tex]log_{8}[/tex](x) = logx²

For the same base

logA + logB = log(AB)

So,

[tex]log_{8}[/tex](16) + [tex]log_{8}[/tex](x)² = 2

[tex]log_{8}[/tex](16x²) = 2

We know that

[tex]log_{a}[/tex](b) = c ⇒ b = [tex]a^{c}[/tex]

so,

[tex]log_{8}[/tex](16x²) = 2 ⇒ 8² = 16x²

x = 2 hence x = 2 will be correct answer.

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Give the order of symmetry from the fig 3
a)2
b)3
c)6
d)4

Answers

the order of symmetry is three as there are three of each repeated shape

aint the answer for this 10 just let me if im wrong​

Answers

Answer:

Yup

Step-by-step explanation:

how many metres are there in ½ of ⅕ km​

Answers

Step-by-step explanation:

1/5=1/5×1000=200

1/2 of 200

1/2×200=100

A machine with velocity ratio of 5 is used to raise a load with an effort of 500N . If the machine is 80% efficient , determine the magnitude of the load.​

Answers

Answer:

Solutions given:

Velocity ratio V.R =5

effort =500N

efficiency =80%

magnitude of load=?

mechanical advantage [M.A ]

we have

efficiency =M.A/V.R*100%

80=M.A./5*100

80/100*5=M.A

M.A.=4

again

we have

M.A =load/effort

4=load/500

load=500*4

load=2000N

the magnitude of the load is 2000N.

b. Compare the similar triangle proof from question 3 with the inscribed square

proof. How are they different? Which method was easier for you to understand?

(1 point)

Answers

Answer:

i might be wrong but this is what i put

Step-by-step explanation:

In question 3 it was comparing three triangles where now it is using the triangles to find the area of a square instead of proving that they are the same.

(8) The average daily temperatures in July of some cities in Texas are shown in the table. Which
of the following fiets the cities from greatest temperature to least temperatura
City
Average Daily
Temperature
Austin
84.52F
Dallas
85.9°F
San Antonio
85 F
Fort Worth
85.31°F
a. Dallas, Fort Worth, San Antonio, Austin
b. Austin, Dallas, San Antonio, Fort Worth
c. Austin, San Antonio, Fort Worth, Dallas
d. Dallas, San Antonio, Fort Worth, Austin

Answers

Answer:

A.

Step-by-step explanation:

85.9 > 85.31 > 85 > 84.52

Dallas, Fort Worth, San Antonio, Austin

WILL MARK BRAINLIEST

picture included^^^^

need help asap please n thank you!


^^^^

Answers

Answer:

14

Step-by-step explanation:

The a value is from the center to the maximum

We want from minimum to max so we need 2 times the amplitude

a = 7

2 *7 = 14

Use the coordinates of the labeled point to find the point-slope equation of the line.
(12, -1)

Answers

Answer:

Choice C.

[tex]y + 1 = - 2(x - 2)[/tex]

Step-by-step explanation:

When converting to

[tex]y = mx + b[/tex]

We are left with:

[tex]y = - 2x + 3[/tex]

Which fits both the x-intercept and y-intercept.

A diver begins at 140 feet below sea level. She descends at a steady rate of 7 feet per minute for 4.5 minutes. Then, she ascends 112.2 feet. What is her current depth?
Negative 549.3 feet
Negative 59.3 feet
59.3 feet
549.3 feet

Answers

Answer:

Step-by-step explanation:

starting point: 140 feet below sea level.=-140

she then decends= 7(4.5)=31.5

-140-31.5=-171.5

finally she ascends 112.2 feet

-171.5+112.2=-59.3 feet or 59.3 feet below sea level

Answer:

It's B

Step-by-step explanation:

Triangle ABC has vertices A(0, 2), B(5, 4), and C(5,0). Triangle A'B'C'has
corresponding vertices A'(-5, -1), B'(0, 1), and C'(0, -3). Which of the following
describes a translation that would produce triangle A'B'C' from the pre-image of
triangle ABC?
A) To the left five units, up three units.
B) To the left five units, down three units.
C) To the right five units, up three units.
D) To the right five units, down three units.

Answers

Answer:

B) To the left five units, down three units

Answer:

( B ) To the left five units, down three units.

1 point (1) Three times a number minus two times a number* Your answer

Answers

Answer:

Three times a number minus two times a number

3x-2x

=x

Shelley drove from New Haven, Connecticut, to New York City in 90 minutes. Which equation relates the distance she traveled to her speed?

a.distance = speed + 90
b.distance = speed × 90
c.distance − speed = 90
d.distance × 90 = speed

Answers

Answer:

b

Step-by-step explanation:

d = r * t

None of them are really correct, but the closest one is B. Look at the equation. Rate is multiplied by time. The result is distance.

The 90 minutes should be changed to hours.  No speedometer on a car is rated in feet per second.

1/x^-2 x=7 yeet yeet

Answers

Answer:

49

Step-by-step explanation:

x = 7

1 / x^-2

= x^2

= 7^2

= 49

Answer: 49

Step-by-step explanation: yeet

Solve the equation sine Ф=0.6792 for 0°≤Ф≤360

Answers

Answer:

42.78⁹, 137.22⁹.

Step-by-step explanation:

sine Ф=0.6792

Angle Ф in the first quadrant = 42.78 degrees.

The sine is also positive in the second quadrant so the second solutio is

180 - 42.78

= 137.33 degres.

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