Using properties of sets show that : a) A ∩ (A’ U B) = A ∩ B b) A ∩ (A U B )’ = Ф

Answers

Answer 1

Answer:

a) From A ∩ A' = ∅, we have;

A ∩ (A' ∪ B) = A ∩ B

b) From A ∩ (A' ∩ B') = (A ∩ A') ∩ B' and A ∩ A' = ∅, we have;

A ∩ (A ∪ B)' = ∅

Step-by-step explanation:

a) By distributive law of sets, we have;

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

From the complementary law of sets, we have;

A ∩ A' = ∅

Therefore, for A ∩ (A' ∪ B) = A ∩ B, we have

A ∩ (A' ∪ B) = (A ∩ A') ∪ (A ∩ B) (distributive law of sets)

A ∩ A' = ∅ (complementary law of sets)

Therefore;

(A ∩ A') ∪ (A ∩ B) = ∅ ∪ (A ∩ B)  = (A ∩ B) (Addition to zero identity property)

∴  A ∩ (A' ∪ B) = A ∩ B

b) By De Morgan's law

(A ∪ B)' = A' ∩ B'

Therefore, A ∩ (A ∪ B)' = A ∩ (A' ∩ B')

By associative law of sets, we have;

A ∩ (A' ∩ B') = (A ∩ A') ∩ B'

A ∩ A' = ∅ (complementary law of sets)

Therefore, (A ∩ A') ∩ B' = ∅  ∩ B' = ∅

Which gives;

A ∩ (A ∪ B)' = ∅.


Related Questions

A study table of length 2 m and breath 1.25 m in decorted with square design of size 10x 10 find the number of such designs??? ​

Answers

Answer:

250

Step-by-step explanation:

Assuming that the shape of the table be rectangular in nature.

Area of the study table = Length * Breadth

Area of the study table = 2m * 1.25m

Area of the study table = 200cm * 125cm (since 100cm = 1m)

Area of the study table = 25000cm²

If the study table is decorated with square design of size 10cm x 10cm, the area of one square design is 100 cm².

The number of such square designs = Area of the study table/area of one square design

The number of such square designs = 25000cm²/100cm²

The number of such square designs = 250

Hence the number of such design is 250

Please answer quickly! A radio telescope has a parabolic surface, as shown below. A parabola opening up with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 1 meter and its width from left to right is 20 meters. If the telescope is 1 m deep and 20 m wide, how far is the focus from the vertex?

Answers

Answer:

Basing on the description, a parabola checking with vertex at origin, the formula with vertex at origin can be used, x^2 = 4py. p is the focus therefore with the dimensions given, we get yourself a 0.25 and this is the distance of the focus to the vertex.

The speed of a car going 50 miles per hour is equivalent to a speed of 80 kilometers per hour. At this rate, what is the speed, in kilometers per hour, of a car that is going 30 miles per hour?

Answers

Answer:

48 km/h

Step-by-step explanation:

80/50*30=48 km/h

I need help and fast!!!!

Answers

Answer:

H. b/a

Step-by-step explanation:

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Step 1: Label our variables

y₂ = 2b

y₁ = b

x₂ = 2a

x₁ = a

Step 2: Plug into formula

m = (2b - b)/(2a - a)

Step 3: Evaluate

m = b/a

Answer:

b/a

Step-by-step explanation:

We have two points so we can use the slope formula

m = (y2-y1)/(x2-x1)

    = ( 2b - b)/ ( 2a -a)

   = b/a

solving polynomial(-2y-6)(-3y-8)​

Answers

Answer:

(-2y-6)(-3y-8)

= 6y²+16y+18y+48

= 6y²+ 34 y +48

Hope this helps

if u have question let me know in comments ^_^

Answer:

Here is your answer!!!

Step-by-step explanation:

-2y(-3y-8)-6(-3y-8)

6y^2+16y+18y+48

6y^2+34y+48

Kyle rides his bicycle 15 mph for 2 hours how far does he travel

Answers

━━━━━━━☆☆━━━━━━━

▹ Answer

30 miles

▹ Step-by-Step Explanation

Multiply mph by hours:

15 mph * 2 hrs = 30 miles

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

What is the measure of angle X?

Answers

Answer: 71 degrees

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

Explanation:

Focus on triangle BDH

Interior angles B and D are given to be 40 and 31 respectively. Interior angle H is unknown

For any triangle, the interior angles always add to 180

B+D+H = 180

40+31+H = 180

H+71 = 180

H = 180-71

H = 109

Interior angle H is 109 degrees for triangle BDH

The exterior angle is 180 minus this measure

exterior angle = 180 - (interior angle)

exterior angle = 180 - 109

exterior angle = 71

Note how this is the sum of interior angles B and D, so you could use the remote interior angle theorem here.

Thirteen people on a sports team show up for a game. a. How many ways are there to choose 10 players to play the game? b. How many ways are there to assign the 10 different positions by selecting players from the 13 who show up?

Answers

Answer:

a)286 ways

b)1,037,836,800 ways

Step-by-step explanation:

a. How many ways are there to choose 10 players to play the game?

We have to take note of a key word here which is CHOOSE. For question a, order does not matter.

Hence, we use the combination formula. This is given as:

C(n, r) = nCr = n!/r! (n - r)!

n = 13, r = 10

13C10 = 13!/10! (13 - 10)!

= 13!/ 10! × (3!)

= 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 / (10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) × (3 × 2 × 1)

= 1716/6

= 286 ways.

b. How many ways are there to assign the 10 different positions by selecting players from the 13 who show up?

For question b as well, we take note of a key word which is ASSIGN. For question b, order is very important.

Therefore, the formula we use is the permutation formula.

P(n, r) = nPr = n!/(n - r)!

n = 13, r = 10

13P10 = 13!/ (13 - 10)!

= 13!/ 3!

= 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 / (3 × 2 × 1)

= 1,037,836,800 ways

Factor completely 3x^2 - x - 4

A.(3x - 4)(x + 1)

B.(3x + 4)(x - 1)

C.(3x - 2)(x + 2)

D.(3x - 1)(x + 4)

Answers

Answer:

B. [tex](3x-4)(x+1)[/tex]

Step-by-step explanation:

Y=-5x+30 x=10 what is the solution to the system of equations 1)(-20,10) 2)(10,-20) 3)(10,4) 4)(4,10)

Answers

Answer:

            2) (10, -20)

Step-by-step explanation:

y = - 5x + 30  and  x = 10  ⇒  y = -5•10 + 30 = -50 + 30 = -20

x = 10  and y = -20   ⇒  (10, -20)

Answer:

Its B. (10, –20)

Step-by-step explanation:

I just took the quiz on edge

If 4th term of an AP is 0. Prove that 25th term is triple the 11th term

Answers

Answer:

The 4th term = a+3d = 0,

or a = -3d.

The 25th term = a+24d = -3d+24d = 21d. ...

the 25th term is 3 times the 11th term. Proved.

Answer:

a^25 = 3 x a^11 .

Step-by-step explanation:

Given a^4 = 0

That is (a + 3d) = 0

⇒ a = - 3d ........... (1)

nth term of AP is given by an = a + (n – 1)d

a^11 = a + 10d = – 3d + 10d = 7d  [From (1)]

a^25 = a+ 24d = – 3d + 24d = 21d  [From (1)]

Hence

The answer is a^25=3 x a^11

The quotient of x^2+x-6/x^2-6x+5*x^2+2x-3/x^2-7x+10 has ___ in the numerator and ______ in the denominator.

Answers

Answer:

So the quotient of [tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex] has (x + 3)² in the numerator and (x + 5)² in the denominator.

Step-by-step explanation:

[tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex]

Factorizing the expressions we have

[tex]\frac{x^{2} + 3x -2x - 6}{x^{2} -x - 5x + 5} X \frac{x^{2} + 3x - x - 3}{x^{2} -2x -5x + 10}[/tex]

[tex]\frac{x(x + 3)- 2(x + 3)}{x(x -1) - 5(x - 1)} X \frac{x(x + 3) - 1(x + 3)}{x(x - 2) - 5(x - 2)}[/tex]

[tex]\frac{(x + 3)(x - 2)}{(x - 5)(x - 1)}X\frac{(x + 3)(x - 1)}{(x - 2)(x - 5)}[/tex]

Cancelling out the like factors, (x -1) and (x - 2), we have

[tex]\frac{(x + 3)(x + 3)}{(x - 5)(x - 5)}[/tex]

= [tex]\frac{(x + 3)^{2} }{(x + 5)^{2} }[/tex]

So the quotient of [tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex] has (x + 3)² in the numerator and (x + 5)² in the denominator.

How to do this question plz answer my question step by step plzz plz plz plz plz ​

Answers

I hope this helps you!

Identify whether each phrase is an expression, equation, or inequality.
Term
Phrase
Expression
3 - 53 =y
Inequality
7-5 <2.9
2 + 0
Equation
24"
t

Answers

Answer:

The identities of the terms are;

3 - 53 = y is an equation

7.5 < 2.9 is an inequality

2 + 0 is an expression

t is a term

24" is a term

Step-by-step explanation:

An equation is an expression with the equal to sign

3 - 53 = y is an equation

An inequality is a mathematical expression that contains an inequality sign

7.5 < 2.9 is an inequality

A term is a sole number or variable or the product of variables and numbers that come before and after mathematical operators such as +, ×, -, or ÷

t and 24" are terms.

3-2(x-1)=2+4x
How do you solve

Answers

Answer:

x = 1/2

Step-by-step explanation:

3 - 2(x - 1) = 2 + 4x

3 - 2x + 2 = 2 + 4x

-2x + 5 = 2 + 4x

-2x - 4x = 2 - 5

-6x = -3

x = -3/-6

x = 1/2

You would multiply the negative two by x then the negative to by negative one then you would get 3-2x+2=2+4x then you would ad 2 x to 4x and get 6x the. Subtract 3-2 and you would get 1 the. You would subtract the 2 from the 1 and get -1 and you would get -1=6x so you would divide 6x and 1 and you would get x=-1/6 ( hope this helps)

Shea made 11 of her first 17 free-throw attempts. What is the minimum number of her next 20 free-throw attempts that she must make for her overall success rate to be at least $80\%$? Express your answer to the nearest whole number.

Answers

Answer:

19 throws.

Step-by-step explanation:

For her success rate to be 80% in 37 throws she must make  0.8 * 37

= 29.6 throw - that is 30 to nearest throw.

So for the next 20 throws she must make  30 - 11 = 19 throws.

Simplify to create an equivalent expression.
5(10k + 1) + 2(2+8k)

Answers

Answer:

66k+9

Step-by-step explanation:

Let's simplify step-by-step.

5(10k+1)+2(2+8k)

Distribute:

=(5)(10k)+(5)(1)+(2)(2)+(2)(8k)

=50k+5+4+16k

Combine Like Terms:

=50k+5+4+16k

=(50k+16k)+(5+4)

=66k+9

Answer:

=66k+9

HOPE THIS HELPS!!!!!! :)

<3333333333

Help? It hard I try my best on a Separate picese

Answers

Answer: 508.81

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

Work Shown:

3 & 1/2 = 3 + 1/2 = 3 + 0.5 = 3.5

3.5% = 3.5/100 = 0.035

r = 0.035 is the decimal form of [tex]3\frac{1}{2}\%[/tex] which is used along with

P = 500 (principal deposit)n = 12 (compounding 12 times a year)t = 0.5 (6 months is half a year)

to get the following

A = P*(1+r/n)^(nt)

A = 500*(1+0.035/12)^(12*0.5)

A = 508.81405074594

A = 508.81

Extra info: Gabe earned A-P = 508.81 - 500 = 8.81 dollars in interest.

can someone plzz answer dis ma braincells dont seem to work ​

Answers

Answer:

Good luck undersatnding.

Step-by-step explanation:

1.

A) 27 (over) 4

B)  97 (over) 117

2.

C) 8

D) -243 (over) 32

3.

Square root of 25 is 5

Square root of 16 is 4

Square root of 9 is 3

Square root of 1 is 1

4.

E)  553 (over) 72

F) 11 (over) 56

G) 65 (over) 18

H) 28 (over) 9

5.

E) 35941

F) 81130

G) 79567.75

H) 20525.857

I dont know 7-8

9.

E) Negative

F) Positive

G) Positive

H) Negative

10.

Square root of 25 is 5

Square root of 64 is 8

Square root of 121 is 11

Square root of 225 is 15

I couldn't post images for 6, it wont let me.

Here is a rule to make a list of numbers: Each number is 4 less than 3 times the previous number. Start with 10, build a sequence of 5 numbers.

Answers

Answer:

10,26,74,218,650

Explanation:

Each number is 4 less then 3 times than previous number.

The list of number is bounded by a set of rules that guide the creation of the set of numbers. The first 5 terms are: 10, 26, 74, 218, 650

Represent the number of terms with n.

So, the nth term is: [tex]T_n[/tex]

The start of the build is 10 means:

[tex]T_1 = 10[/tex]

The rule to generate the next terms is:

[tex]T_{n+1} = 3 \times T_n - 4[/tex] ---- i.e. 4 less than 3 times the previous term

So, the next terms till the 5th are:

[tex]T_{2} = 3 \times 10 - 4 = 26[/tex]

[tex]T_{3} = 3 \times 26- 4 = 74[/tex]

[tex]T_{4} = 3 \times 74- 4 = 218[/tex]

[tex]T_{5} = 3 \times 218- 4 = 650[/tex]

So, the first 5 terms are: 10, 26, 74, 218, 650

Read more about patterns at:

https://brainly.com/question/13382968

What is a discrete probability​ distribution? What are the two conditions that determine a probability​ distribution? What is a discrete probability​ distribution? Choose the correct answer below. A. A discrete probability distribution exclusively lists probabilities. B. A discrete probability distribution lists each possible value a random variable can​ assume, together with its probability. C. A discrete probability distribution lists each possible value a random variable can assume. D. None of the above

Answers

Answer:

The answers to the question above are given below:

Step-by-step explanation:

Question: What is a discrete probability​ distribution?

Answer

A discrete distribution is very important in data research as it shows in tabular form the probabilities that can be found in a list of distribution values and their individual probabilities in counted data. Usually, from the pool of distribution of numbers, the discrete distribution shows the probability of having countable numbers out of the pool.

Question: Choose the correct answer below. A. A discrete probability distribution exclusively lists probabilities. B. A discrete probability distribution lists each possible value a random variable can​ assume, together with its probability. C. A discrete probability distribution lists each possible value a random variable can assume. D. None of the above

The correct answer is: option B "discrete probability distribution lists each possible value a random variable can​ assume, together with its probability."

Question: What are the two conditions that determine a probability​ distribution?

The correct answer is:

1. Since each value may not be zero, each probability must include between 0 and 1.

2. When probabilities are totaled, it must give 1.

Gavin is selling water bottles at a baseball game to help raise money for new uniforms.
Before the game, he buys 48 water bottles for a total of $18.50. At the game, he sells all of
the bottles for $1.25 each. How much profit does Gavin make?

Answers

The profit made by Gavin at the end of the game is $0.87 per bottle.

How to calculate profit?

The profit can be calculated by taking the difference of selling price and the cost price.

Given that,

The number of bottles bought for $18.50 is 48 and sold for $1.25 each.

Then, the cost for one bottle is 18.50/48 = $0.38.

As per the question the profit made can be calculated as the difference of selling price and cost price as,

Profit = Selling price - Cost Price

         =  1.25 - 0.38

         = $0.87

Hence, the profit earned by Gavin is given as $0.87 for each bottle.

To know more about profit click on,

https://brainly.com/question/7544724

#SPJ6

the cube root of 2 to the seventh power

Answers

Answer:

4 2^(1/3) or 5.0396841995794926590688424291129134022810058588060319203279004486... decimal

Step-by-step explanation:

Simplify the following:

(2^(1/3))^7

Hint: | For all a>=0, (a^(1/3))^m = a^(m/3). Apply this to (2^(1/3))^7.

Multiply exponents. (2^(1/3))^7 = 2^(7/3):

2^(7/3)

Hint: | Separate the exponent of 2^(7/3) into integer and fractional parts.

2^(7/3) = 2^(6/3 + 1/3) = 2^(6/3)×2^(1/3):

2^(6/3) 2^(1/3)

Hint: | Divide 6 by 3.

6/3 = (3×2)/3 = 2:

2^2 2^(1/3)

Hint: | Evaluate 2^2.

2^2 = 4:

Answer:  4 2^(1/3) or 5.0396841995794926590688424291129134022810058588060319203279004486... decimal

I need help and I will give five stars and a big thank you comrades

Answers

Answer:

A.

Step-by-step explanation:

A way to find the equation of the graph is to find the solutions.

On the graph, the solutions are where the function intersects the x-axis. That would be where x = -2, x = 1, and x = 3.

In the equations, you will need to find factors when the x is inputted, the factor equals 0. For example, one of the factors is (x + 2). This is because x + 2 = 0, so x = 0 - 2, so x = -2. So, the three factors are (x + 2), (x - 1), and (x - 3).

The correct equation is A.

Hope this helps!

Can you help me please.

Answers

Answer:

option 2.

Step-by-step explanation:

You use the y-intercept form: y=mx+b

mx=slope, and b=y-intercept.

Looking at this graph, you can see that the slope is -2/3 (rise over run), and the line is negative, so the slope becomes negative.

So now, we can see the only option having the slop -2/3x is option 2.

Please help!!! ***This is multiple choice!

Answers

Answer:

0.6

Step-by-step explanation:

A probability is the likelihood of an event occurring. A probability function is a function in which at any point, its probability value can be estimated. The integral of the probability function is always ≤ 1

To find the probability that x = 2 or 3, we simply add their respective individual probabilities, therefore:

P(X = 2 or 3) = P(X = 2) + P(X = 3) = P(2) + P(3) = 0.5 + 0.1 = 0.6.

P(X = 2 or 3) = 6

Ikyume is 62m away from Amadi, on a bearing of 012°. Becky is 42m away from Ikyume and on bearing of 082°. How far is Amadi from Becky, and on what bearing?

Answers

Answer:

Amadi is 86m far from Becky

Amadi is on the bearing of 78° .

Step-by-step explanation:

From the information given ,

let I represent Ikyume

A represent Amadi  and B represent Becky

From the information in the diagrammatic expression shown below:

Using cosine rule;

i² = a² + b² - 2ab cos (I)

i² = 42² + 62² - 2(42×62) cos (110°)

i² =  1764 + 3844 - 5208 (- 0.342)

i² =  1764 + 3844 -  ( - 1781.136)

i² = 1764 + 3844 + 1781.136

i² = 7389.136

i = [tex]\mathtt{\sqrt{7389.136}}[/tex]

i = 85.96

i [tex]\simeq[/tex] 86 m

Amadi is 86m far from Becky

From  point I , 12° = 12° at point A (alternate  angles)

In that quadrant = 90 - 12° = 78°

Therefore, Amadi is on the bearing of 78° .

hello :) why is the first one wrong?

Answers

Answer:

The cube only belongs to the x and not 2x.

The statement will only be true if there is a bracket around the 2x.

log₃(2x)³= 3log₃2x

logarithm power rule:

logₐ(x)^y = y ∙ logₐ(x)

Answer:

see explanation

Step-by-step explanation:

Given

[tex]log_{5}[/tex] 2x³

= [tex]log_{5}[/tex] 2 + [tex]log_{5}[/tex] x³

= [tex]log_{5}[/tex] 2 + 3[tex]log_{5}[/tex] x

-4-(3+6²)÷13-1²•(-12)=

Answers

Answer:

5

Step-by-step explanation:

-4-(3+6²)÷13-1²•(-12)=

PEMDAS

parrenthesis:

-4-81÷13-1² x (-12)

exponent:

-4-81÷12 x (-12)

multiplication:

-4-81÷ (-144)

divison:

- 4 - (- 9)

subtraction (Actaully addition +):

= 5

-(- makes plus so -4 + 9 makes 5

Hope this helps, have a good day!! :)

I NEED HELP I GIVE 5 STARS PLEASE ;(

Answers

the answer is 2 3/7
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