A ∩ B = ∅. P(B) = .9 P(A ∪ B) = .9. Find P(A).

Answers

Answer 1

Answer:

Given:  P(A ∩ B) = 0, P(B) = 0.9, P(A ∪ B) = 0.9.

We have: P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

=>  0.9 = P(A) + 0.9 - 0

=> P(A) = 0.9 - 0.9 = 0

 

Hope this helps!

:)


Related Questions

In an election of housing society,there are 30 voters.Each of them gives the vote.Three persons X,Y and Z are standing for post secretary.If Mr.X got 2/5 of the total votes and Me.Z got 1/4 of the total votes then how much did Mr.Y get?

Answers

Answer:

Mr Y got 10 votes

Step-by-step explanation:

The election of the housing society has 30 voters. Each of them gives the vote. The three person vying for the post of secretary are X, Y and Z.

Le us calculate the votes of each contestant

Mr X

He got 2/5 of the total votes

number of votes = 2/5 × 30

number of votes = 60/5

number of votes = 12

Mr Z

He got 1/4 of the total votes

number of votes = 1/4 × 30

number of votes = 30/4

number of votes = 1/4 × 30

number of votes = 7.5 ≈ 8 votes

Mr Y

The remaining votes will be 30 - 12 - 8 = 10 votes

Therefore,

Mr Y got 10 votes

Given that D is the midpoint of AB and B is the midpoint of AC, which statement must be true? A line has points A, D, B, K, C. AD = One-thirdAC AC = 4DB AB + DC = AC BK = KC

Answers

Answer:

AC = 4DB

Step-by-step explanation:

see attachment

Given that B is the midpoint of AC, this means that AB≅BC.

Also, D is the midpoint of AB, therefore AD≅DB.

This shows that AD is 1/4 of the length of AC, since it is 1/2 of the length (1/2 x 1/2 = 1/4).  DB is the same length, since it is congruent to AD.

Thus, AC = 4DB.

Answer:

B. AC = 4DB

May I have brainliest please? :)

Christine,milan, and Scott sent a total of 145 messages during the weekend . Christine sent 7 more messages than Scott . Milan sent 4 times as many messages as Scott . How many messages did they each send?

Answers

Answer:

number of message sent by Scott is 23

number of message sent by Christine is   30

number of message sent by Milan is 92

Step-by-step explanation:

Total message sent by Christine,Milan, and Scott : 145

Let number of message sent by Scott be x .

Given that Christine sent 7 more messages than Scott

number of message sent by Christine is   x+7

It is also given that  Milan sent 4 times as many messages as Scott

number of message sent by Milan is   4*x = 4x.

Thus, sum of message sent by Christine,milan, and Scott  in terms of x

= x + x + 7 + 4x = 6x + 7

we already know that Total message sent by Christine,milan, and Scott is 145

thus,  6x + 7 should be equal to 145

6x + 7 = 145

=>6x = 145 - 7 = 138

=> x = 138/6 = 23

Thus,  

number of message sent by Scott is x = 23

number of message sent by Christine is   x+7 = 23+7 = 30

number of message sent by Milan is   4x = 4*23 = 92

What is 15% of 80kg????

Answers

Answer:

12 kg

Step-by-step explanation:

15%×80 =

= 15×80/100

= 15×8/10

= 120/10

= 12 kg

find the value of x.
please help !!!

Answers

Answer:

62 degrees

Step-by-step explanation:

all triangles equal 180 degrees so you would add both angles together then subtract the sum of that by 180

Answer:

[tex]x=62^o[/tex]

Step-by-step explanation:

Since the addition of all internal angles of a triangle should add up to [tex]180^o[/tex], then, the missing angle can be found by subtracting the two known angles from [tex]180^o[/tex]:

[tex]x=180^o-68.5^o-49.5^o=62^o[/tex]

which law would you use to simplify the expression 3^10/3^4

Answers

Answer:

I would use the "quotient rule of exponents"

Step-by-step explanation:

I would use the "quotient rule of exponents" which states that to divide two exponents that have the same base, the result is the same base to an exponent which equals the subtraction of the exponent in the numerator of the original expression minus the exponent that base has in the denominator.

That is:

[tex]\frac{a^m}{a^n} =a^{m-n}[/tex]

Then in this case the simplified expression would be:

[tex]\frac{3^{10}}{3^4} =3^{10-4}=3^6[/tex]

Answer: quotient of powers

Step-by-step explanation:

Please answer correctly !!!!!! Will mark brainliest answer !!!!!!!!!!

Answers

the answer is a because it’s in the form that literally gives you the inverted x coordinates of the root

Caylee caylee build a rectangular prism using 18 cubes that are each measure 1 cm on each side. What could be the dimensions of her rectangular prism

Answers

Answer:

2cm by 3cm by 3cm.

Step-by-step explanation:

So, we are given the following data or parameters or information which is going to help us in solving this particular Question or problem;

=> We have a built rectangular prism.

=> The rectangular prism was built by using 18 cubes.

=> Each of the 18 cubes measure 1 cm on each side.

So, the dimensions of Carley's rectangular prism is given below as the multiples of 18 since each of the 18 cubes measure 1 cm on each side.

That's 2 cm × 3 cm × 3cm. Therefore, the length will be 2cm, breadth will be 3cm and height will be 3cm.

Karen is making a set of costumes for the school play using a piece of cloth. She reduces the length of the cloth she intends to use by 10%. If the initial length of the cloth that she wanted to use was 15 meters, what is the new length of the cloth she wants to use?

Answers

Answer:

The new length is 13.5 meters

Step-by-step explanation:

Here, we are interested in calculating the new length of the cloth she wants to use

What we know from the question is that she is making a reduction of 10% from an initial of 15 meters

Thus, the length she is to use can be calculated by first getting what 10% of 15 meters is

Mathematically, that would be ;

10/100 * 15 = 1.5 meters

We now subtract this from the total of 15 meters

= 15 meters - 1.5 meters = 13.5 meters

Find the value of x.
Please help

Answers

Answer:

x=5

Step-by-step explanation:

7/5=(2x-3)/x

5(2x-3)=7x

3x=15, x=5

The outside temperature at a place is - 20 degree Celsius and it drops 5 degrees every hour.How long it will take to reach the temperature zero degree Celsius?

Answers

Answer:

4 hours

Step-by-step explanation:

20-5x=0

5x= 20

x=4 hours

Add 7m/16+(-m/16) . Reduce, if possible.

Plzz answer quickly

Answers

Answer:

6m/16 = 3m/8

Step-by-step explanation:

since the fractions have the same denominator, just take out the operation on the numerators of the 2 fractions. So, 7m +(-m).

7m +(-M) is the same as 7m - m, so that is 6,

when you put it back together, you get 6m/16, simplify it to 3m/8

Three students use pens to write th enams of graduating seniors on thei rdiplomas. One writes 7 names in 6 minutes, another writes 17 names in 10 minuts, and the third writes 23 names in 15 minutes. How long, to the nearest minute, will the students take to the write the names on 440 diplomas if they work together?

Answers

Answer:

Total time  ≈ 100(nearest minutes)

Step-by-step explanation:

The rates at which each student writes names per minutes can be calculates as follows.

First student

6 minutes = 7 names

1 minute = 7/6 names

second student

10 minutes = 17 names

1 minute = 17/10 names

Third student

15 minutes = 23 names

1 minute = 23/15 names

Total time = 440/total rate

Total time = 440/1.17 + 1.7 + 1.53

Total time = 440/4.403

Total time = 99.931

Total time  ≈ 100(nearest minutes)

part 2. Find the value of the trig function indicated, use for that Pythagorean theorem to find the third side if you need it.​

Answers

Answer:  [tex]\bold{5)\ \cos \theta=\dfrac{\sqrt{11}}{6}\qquad 6)\ \tan \theta =\dfrac{8}{17}\qquad 7)\ \cos \theta = \dfrac{4}{3}\qquad 8)\ \cos \theta = \dfrac{\sqrt{10}}{10}}[/tex]

Step-by-Step Explanation:

Pythagorean Theorem is: a² + b² = c²  , where "c" is the hypotenuse

[tex]5)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{3\sqrt{11}}{18}\quad \rightarrow \large\boxed{\dfrac{\sqrt{11}}{6}}[/tex]

Note: (15)² + (3√11)² = hypotenuse²   →   hypotenuse = 18

[tex]6)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{8}{17}\quad =\large\boxed{\dfrac{8}{17}}[/tex]

Note: 8² + 15² = hypotenuse²   →   hypotenuse = 17

[tex]7)\ \tan \theta=\dfrac{\text{side opposite to}\ \theta}{\text{side adjacent to}\ \theta}=\dfrac{20}{15}\quad \rightarrow \large\boxed{\dfrac{4}{3}}[/tex]

Note: hypotenuse not needed for tan

[tex]8)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{2}{2\sqrt{10}}\quad =\large\boxed{\dfrac{\sqrt{10}}{10}}[/tex]

Note: 2² + 6² = hypotenuse²   →   hypotenuse = 2√10

5) cosθ = [tex]\frac{\sqrt{11} }{6}[/tex] , 6) cosθ = [tex]\frac{8}{17}[/tex] , 7) tanθ = [tex]\frac{4}{3}[/tex] , 8) cosθ = [tex]\frac{1}{\sqrt{10} }[/tex]

What is pythagorean theorem ?

If, a be the perpendicular, b be the base & c be the hypotenuse of a right angle triangle.

Then, [tex]c=\sqrt{a^{2}+ b^{2} }[/tex]

What are the trigonometric functions ?

cosθ = (Side adjacent to θ)/(Hypotenuse)

sinθ = (Side opposite to θ)/(Hypotenuse)

tanθ = (Side opposite to θ)/(Side adjacent to θ)

What are the values of required trigonometric functions ?

5) Hypotenuse = [tex]\sqrt{(3\sqrt{11}) ^{2} +15^{2} }[/tex]

                            = [tex]\sqrt{99+225}[/tex]

                            = [tex]\sqrt{324}[/tex] = 18

cosθ = (Side adjacent to θ)/(Hypotenuse)

           = [tex]\frac{3\sqrt{11} }{18}[/tex] =[tex]\frac{\sqrt{11} }{6}[/tex]

6) Hypotenuse = [tex]\sqrt{8^{2} +15^{2} }[/tex]

                             = [tex]\sqrt{64+225}[/tex]

                             = [tex]\sqrt{289}[/tex] = 17

cosθ = (Side adjacent to θ)/(Hypotenuse)

           = [tex]\frac{8}{17}[/tex]

7) tanθ = (Side opposite to θ)/(Side adjacent to θ)

               = [tex]\frac{20}{15}[/tex] = [tex]\frac{4}{3}[/tex]

8) Hypotenuse = [tex]\sqrt{2^{2} +6^{2} }[/tex]

                              = [tex]\sqrt{4+36}[/tex]

                              = [tex]\sqrt{40}[/tex] = [tex]2\sqrt{10}[/tex]

cosθ = (Side adjacent to θ)/(Hypotenuse)

            = [tex]\frac{2}{2\sqrt{10} }[/tex] = [tex]\frac{1}{\sqrt{10} }[/tex]

Learn more about trigonometric functions here :

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What is the quotient of 2,173 ÷ 53

Answers

Answer:

41

Step-by-step explanation:

Point A is at (6,-6) and point C is at (-6,-2). Find the coordinates of point B on line AC such that AB= 3/4 AC

Answers

Answer:

-3, -3

Step-by-step explanation:

The coordinates of point B on line AC is (6/7, -30/7).

Given that, A(6, -6), C(-6,-2) and AB= 3/4 AC.

What is the section formula?

The section formula is P(x, y)[tex]=(\frac{mx_{2} +nx_{1}}{m+n}, \frac{my_{2} +ny_{1}}{m+n} )[/tex].

Now, AB= 3/4 AC⇒AB:AC=3:4

P(x,y)[tex]=(\frac{3(-6)+4(6)}{3+4}, \frac{3(-2) +4(-6)}{3+4} )[/tex]

=(6/7, -30/7)

Therefore, the coordinates of point B on line AC is (6/7, -30/7).

To learn more about the coordinates visit:

https://brainly.com/question/7869125.

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Let the polynomials A = 7x² + 3xy and B = -3xy.
Determine A + B.
a) 7x²
b) 3xy
c) 7x² + 6xy
d) 14x² + 6xy
e) -3xy

Answers

Answer:

The answer is 7x²

Step-by-step explanation:

Since we have to add the two polynomials together, we write it as A+B=7x²+3xy-3xy. Now, we simplify, and we are left with A+B=7x²

20 PTS What is the sixth term of the sequence shown in the table? Term Value 1 –46,656 2 7,776 3 –1,296 4 216 5 6 {SEE IMAGE}

Answers

Answer:

a₆ = 6

Step-by-step explanation:

There is a common ratio r between consecutive terms in the sequence, that is

r = [tex]\frac{216}{-1296}[/tex] = [tex]\frac{-1296}{7776}[/tex] = [tex]\frac{7776}{-46656}[/tex] = - [tex]\frac{1}{6}[/tex]

This indicates the sequence is geometric.

To obtain any term in the sequence, multiply the previous term by r, thus

a₅ = 216 × - [tex]\frac{1}{6}[/tex] = - 36

a₆ = - 36 × - [tex]\frac{1}{6}[/tex] = 6

Answer:

It's 6

Step-by-step explanation:

Got it right!

1 –46,656

2 7,776

3 –1,296

4 216

5 36

6 6

divided by 6 every time

Plzzzzzz help me.......

Answers

Answer: 4 terms and 8 factors

Step-by-step explanation:

^

I really need to get this rain I will give you Brainlyest or whatever that thing is called if you get this right

Answers

Answer: A. SSS

Step-by-step explanation:

The two triangles are congruent through SSS which means Side-Side-Side. This is because each side of the triangle correlates between the two of them. They both have a 8, 6, and 3 side.

Answer:

SSS

Step-by-step explanation:

The given triangles have 3 equal sides: 3, 6 and 8

So the answer is SSS (side-side-side)

x:28=1:8
Whats the answer eh​

Answers

Answer:

Step-by-step explanation:

We can setup the equation as

x/28 = 1/8

Cross multiplying we get

8x = 28

Dividing by 8 we get

x = 28/8 = 7/2

-30 belongs to what family of real numbers ?

Answers

Answer: Irrational numbers

i believe it would be an integer

=
O RATIOS, PROPORTIONS, AND MEASUREMENT
Writing ratios for real-world situations
There are 8 new books and 9 used books on a shelf.
(a) What is the ratio of all books to new books?
(b) What is the ratio of all books to used books?
(a)
(b)
?
X​

Answers

Answer:

(a) ratio of all books to new books is   17 : 8  

or in quotient form: 17/8

(b) ratio of all books to used books is  17 : 9

or in quotient form: 17/9

Step-by-step explanation:

Number of new books = 8

Number of used books =  9

Total number of books = 17

Recall also that ratios are written with the symbol ":" in between the first quantity and then the second quantity, thus the symbol ":" replacing the word "to". For example "Ratio of a to b is written with the symbology:

a : b

which can also be translated to the quotient expression: a/b

Then the requested ratio of

(a) all books to new books is   17 : 8  

or in quotient form: 17/8

(b) all books to used books is  17 : 9

or in quotient form: 17/9

URGENT!!!!! LAST TWO QUESTIONS!!!!!!! WILL GIVE BRANLIEST!!!AT LEAST TAKE A LOOK!!!!!! PLS HELP!!!
6. What must be true in order for two triangles to be similar?

11. What is the measure of angle y?
A) 130°
B) 50°
C) 40°
D) 90°

Answers

Answer:

50

Step-by-step explanation:

The sum of angles in a triangle is 180 so the answer is 180 - 90 - 40 = 50.

Also, for your first question, 2 corresponding angles of the triangles must be congruent.

Answer:

B. 50°

Step-by-step explanation:

40°+90°+y = 180°

130°+y°=180°

y° =180°-130°

y = 50° (sum of the interior angles in a triangle=180°)

What is the length of the hypotenuse of the triangle when x=13

Answers

Answer:

90.80

Step-by-step explanation:

6x+4

= (6)(13)+4

= 78+4

=82

3x

=(3)(13)

= 39

So we know the sides are 39 and 82

Pythagoras theorem in triangles

= a2+b2= c2

Now, we know the value of a and B but not c (the hypotenuse)

Therefore,

c2 = (39)^2 + (82)^2

= 1521+ 6724

= 8245

so, c = √8245

= 90.80 unitd

A bookstore has 60 books about math this is 0.05% of the total number of books on the shelves how many books are there in the bookstore that are not about math

Answers

Answer:

119,940 books are not about math.

What I did:

60x2000=120,000

120,000-60=119,940

Answer:

119940

Step-by-step explanation:

.05 % are about math

b= books

b * .05% = 60

Change to decimal form

b * .0005 = 60

Divide each side by .0005

b = 60/.0005

b =120000 books in the store

we want the ones not about math

120000-60

119940

What is James average speed on his outward journey

Answers

Answer:

We wish to find his rate...

km per minute or km per hour:

 

His total time is:  15 + 5 + 20 = 40 minutes

His total distance is 2 km

 

Rate in km/minute:  2/40 = 1/20 = 0.05 km/minute

 

If you want km/hour then:

(0.05 km/minute)(60 minutes/hour) = 3 km/hour or kph

Step-by-step explanation:

James walks 1 km away from home in 15 minutes. He stops and rest for 5 minutes and then walks back home along the same path, but he spent 20 minutes to reach home.

find the size of angle yxz give your answer to 3 significant figures 20cm 8cm

Answers

tan X = |YZ| / |XZ| = 20/8 = 5/2

X = arctan(5/2) = 68.2°

Answer: 68.2°

The size of angle ∠YXZ is 68.3° given that sides YZ=20cm and XZ=8cm by using trigonometric ratios.

What are trigonometric ratios?

In a right angled triangle, if A is an angle other than right angle then trigonometric ratios are

sin A =[tex]\frac{opposite side}{hypotenuse}[/tex]

cos A=[tex]\frac{adjacent side}{hypotenuse}[/tex]

tan A =[tex]\frac{opposite side}{adjacent side}[/tex]

Calculate the angle ∠YXZ

Given YZ=20cm and XZ=8cm

Since the triangle is right angled, and opposite side and adjacent side are given we can find tan(∠YXZ )

tan (∠YXZ ) =20/8 =2.5

∠YXZ = arctan (2.5) =68.2°

Hence the size of angle ∠YXZ is 68.2° given that sides YZ=20cm and XZ=8cm.

Learn more about trigonometric ratios here :

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What is the decimal expansion of 30/6? And is it rational or irrational.

Answers

Answer:

5.0 rational

Step-by-step explanation:

30/6 = 5/1 =5.0

it's rational as it is a fraction

3. Shenker has 45 CDs.
He gives 10 CDs to his brother.
a) Write an equation you can solve to find how many CDs
Shenker has left.
b) Solve the equation.

Answers

Answer: The equation is 45-10=x the answer is 35

Step-by-step explanation: To make the equation you need to have and = sign so, we can do what he has (45) and subtract what he gives away (10) which would equal what he has left (x)

Answer:

45 (initial amount) - 10 (given to brother) = x (number of cd's left)

Equation:

    45 - 10 = x

Answer:

    35 CDs

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