Given P(A) = 0.55, P(B) = 0.42 and P(AUB) = 0.639, find the value of
P(An B), rounding to the nearest thousandth, if necessary.

Answers

Answer 1

Answer:

The probability of A and B, denoted as P(A ∩ B) is equal to 0.331.

Step-by-step explanation:

Recall our formula for the probability of A or B:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

We are given are variables already, which we can once again define:

P(A) = 0.55P(B) = 0.42P(A ∪ B) = 0.639

To find P(A ∩ B), we start by plugging in the values into our formula:

0.639 = 0.55 + 0.42 - P(A ∩ B)

We can add the RHS of the equation:

0.639 = 0.97 - P(A ∩ B)

Subtracting 0.97 on both sides, we get closer to our answer:

-0.331 = -P(A ∩ B)

To obtain our final answer, we can simply just divide both sides by -1:

0.331 = P(A ∩ B)P(A ∩ B) = 0.331

Therefore, the probability of A and B is equal to 0.331.


Related Questions

Tom has 5 green cubes for every 3 yellow cubes. He has 16 cubes in total. Draw a diagram to represent please help me​

Answers

10 green cubes and 6 yellow cubes

hope it helps...!!!

What is the radius and diameter of the following circle?
14 cm

Answers

Answer:

Diameter : 14 cm

14÷2=7

Radius : 7

Step-by-step explanation:

Diameter is two time the Radius

Karly borrowed $6,200 from her parents for 4 years at an annual simple interest rate of 2.8%. How much interest will she pay if she pays the entire loan at the end of the fourth year?

Enter the answer in dollars and cents, and round to the nearest cent, if needed. Do not include the dollar sign. For example, if the answer is $0.61, only the number 0.61 should be entered.

Answers

Answer:

$724.11

Step-by-step explanation:

This requires the use of the growth formula.

Growth Formula:

[tex]y = a*(1+r)^x[/tex]

y = total/answer

a = starting value

r = rate (1.25 = 25%)

x = the amount of time (years/months)

Equation:

[tex]y = 6200 * (1+0.028)^4[/tex]

Solving:

y = $6924.11

$6924.11 - $6200 =  total interest

$724.11

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$6200\\ r=rate\to 2.8\%\to \frac{2.8}{100}\dotfill &0.028\\ t=years\dotfill &4 \end{cases} \\\\\\ I = (6200)(0.028)(4)\implies I=694.4[/tex]

What is 100 x 96 x 44?

Answers

Answer:

Step-by-step explanation:

100×96×44=100×(100-4)×44

=100×[100×44-4×44]

=100×[4400-176]

=100×4224

=422400

Answer:

422400

Step-by-step explanation:

100

x96

-------

9600

x44

----------

38400

+384000

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

422400

 Find the length of the third side. If necessary, write in simplest radical form.

IMAGE DOWN BELOW!

SOMEONE PLEASE HELP ME!! ILL GIVE YOU BRAINLIST ANSWER

Answers

Answer:

third side = 6

using pythagoras theorem:

a² + b² = c²

5² + (√11)² = c²25 + 11 = c²36 = c²c = √36c = 6

Answer:

The length of the third side is 6 units

Step-by-step explanation:

We know that this is an right angled triangle , so

by using Pythagoras theorem we can find out the third side of the triangle ..

=> P² + B² = H²

=> 5² + (√11)² = H²

=> 25 + 11 = H²

=> 36 = H²

=> √36 = H

=> 6 = H

help me ??????? please

Answers

Answer:

58%

Step-by-step explanation:

vertical angles are always the same

Jevator has a weight limit of
7. There are 3 people inside
An elevator has a weight limit of 1 ton there are 3 people inside the elevator Each person weighs 150
pounds. How many more
Pounds can the elevator safely hold?
450 pounds
850 pounds
1,550 pounds
1,850 pounds

Answers

Answer:

i think it would be 1550?

Step-by-step explanation:

im pretty sure you add teh weight of the three people and convert it to one ton

y = 3x + 1 -x + 2y = -3 solve system of equation by elimination

Answers


Question: y = 3x + 1 -x + 2y = -3
Answer:
x=1
y=-3


A, B and C are points on the line 2x+y=8

DCE is a straight line.
AB:BC=2:1
EC:DC=1:2

Work out the ratio Area of triangle AEC : Area of triangle BCD

Give your answer in its simplest form.

Answers

The ratio of the area of triangle AEC and area of triangle BCD is 21:14 if the A, B and C are points on the line 2x+y=8

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have line;

2x+y=8

x/4 + y/8 = 1

Coordinate for A(4, 0) and B(0, 8)

To find the coordinate C we will use external section formula:

Let (a, c) be a coordinate for C

AB : BC = 2:1

AC:BC = 3:1  

[tex]\rm C(a, b) =( \dfrac{-4}{3-1}, \ \dfrac{24}{3-1})[/tex]

C(a, b) = (-2, 12)

Let coordinate for E(0, e) and for D(f, 0)

EC:DC=1:2 and C(-2, 12)

So after applying section formula, we will get:

E(0, -3) and D(0, 36)

Area of triangle AEC = (1/2)(7)(12) = 42 square units

Area of triangle BCD = (1/2)(28)(2) = 28 square units

ratio of area of triangle AEC : area of triangle BCD = 42:28

= 21:14

Thus, the ratio of the area of triangle AEC and area of triangle BCD is 21:14 if the A, B and C are points on the line 2x+y=8

Learn more about the linear equation here:

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i dont understand this one

Answers

Answer:

C = 14[tex]\pi[/tex], A = 49[tex]\pi \\[/tex].

Step-by-step explanation:

C = Circumference, A = Area

So, the Circumference is 14[tex]\pi[/tex] and the area is 49[tex]\pi \\[/tex].

Hope this helps :)

X/3+7=12
Help :)
I need to write more to send it so…

Answers

Answer:

15

Step-by-step explanation:

To solve you have to get x by itself on one side.

x/3+7=12

First, you move the seven over.

x/3+7-7=12-7

Simplify.

x/3=5

Now to get x by itself you can multiply both sides by 3.

x/3*3=5*3

Simplify.

x=15

Answer:

x = 15

Step-by-step explanation:

x/3 + 3⋅7/3 = 12

x+3⋅7/3=12

x+21/3

X=15

There are a total of 165 dogs and cats waiting for homes at the Grand Strand Humane Society. The number of cats is 24 less than twice the number of dogs.
Part A: Identify both variables you are using, then write equations to represent both situations
Part B: How many dogs and cats are waiting to be adopted in the shelter? You must show work. Write your answer in the form of a sentence

Answers

Answer:

Part A

Let d = number of dogs

Let c = number of cats

Given:

total of 165 dogs and cats

⇒ d + c = 165

Given:

The number of cats is 24 less than twice the number of dogs

⇒ c = 2d - 24

Part B

Substitute  c = 2d - 24  into  d + c = 165  and solve for d:

⇒ d + 2d - 24 = 165

⇒ 3d - 24 = 165

⇒ 3d = 189

⇒ d = 63

Substitute found value of d into  d + c = 165  and solve for c:

⇒ 63 + c = 165

⇒ c = 102

Therefore, 63 dogs and 102 cats are adopted in the shelter.

Find the surface area of the figure.

Answers

Answer:

[tex] {108in}^{2} [/tex]

Step-by-step explanation:

to get the surface area of a pyramid you must take half of the product of the perimeter times the slant length and THEN add the area of the base to the total.

In this problem, the perimeter is 24. Slant height is 6, and area of the base is 36

1/2(24*6)+36= 108

If this answer helped you, I would appreciate it if you gave me the brainliest :D

Dora is making invitations for her party. Dora needs to make invitations for 54 of her friends. On Friday you helped her make 1/2 of the invitations. How many did you make?

Answers

Answer:

[tex] \frac{1}{2} of \: the \: invitations = \frac{1}{2} \times 54 \\ = 27invitations[/tex]

you made 27 of the invitations

Expand and simplify (4x−3y)(6x−5y).

Answers

Answer:

24x^2+15y^2-38xy

Step-by-step explanation:

(4x-3y)(6x-5y)

= 24x^2-20xy-18xy+15y^2

=24x^2+15y^2-38xy

The variable y is directly proportional to x. If y=3 when x=5, then what is y when x=20

Answers

Answer:

y=12

Step-by-step explanation:

y=k*x

3=5*k

k=3/5

y= (3/5)*x

y=(3/5)*20

y=12

What is the value of the exponential expression 24?
O A. 8
B. 32
O C. 64
O D. 16

Answers

Answer:

16

Step-by-step explanation:

2^4 is the same thing as 2*2*2*2*2. 2 times 2 is 4, times 2 is 8, times 2 again is 16.

Diego has budgeted $80 from his summer job earnings to buy gear for baseball. He needs a new mitt and new baseballs. The
mitt he wants cost $38. Each pack of baseballs cost $3.50.
A. Write an inequality that represents x, the number of packs of baseballs, that Diego can buy if there is no tax.

Answers

Answer:

X=^3.50
X=3/50
X=350<3.50>
Y= 2C/U-
es igual a Yx^2

Step-by-step explanation:

coronita plisss

What is the value of D?
5/6 = 1/3 + D

Answers

Answer:

1/3=2/6  d is 2/6

Step-by-step explanation:

Prove that AABE = ADCE, given that AE = DE, BE CE, with the same vertex measure ZE.​

Answers

Answer:

I don't understand the question

there were 150 people in a parade last year. This year there are 20 people in the parade. What is the percent change of people in the parade from last year to this year?

Answers

Answer:

7.5

Step-by-step explanation:

I need help I'm stuck ?

Answers

[tex]v = \frac{4}{3} \times \pi \times ({ \frac{8}{2} })^{3} \\ [/tex]

[tex]v = \frac{4}{3} \times 3 \times {4}^{3} \\ [/tex]

[tex]v = {4}^{4} [/tex]

[tex]v = {2}^{8} [/tex]

[tex]v = 256 \: \: {cm}^{3} [/tex]

Hello! How to sketch the graph?

Answers

Answer:

Draw your y and x axis , the y axis is going to be a vertical line while the x axis is going to be a horizontal line

15 days ago, the share of the Valmont family business was worth $156. Over the next 5 days, the stock value increased by $3 per day. Then its value went down by $5 a day for 10 days.

What is the value of the stock today?

Using Order of Operation
please answer i need it today :'(​

Answers

Answer:

compute the company's price-to-earnings (P/E) ratio.

Step-by-step explanation:

When companies issue additional shares, it increases the number of common stock being traded in the stock market. For existing investors,

8) What is the volume of the triangular prism?
A) 15 mm
B) 18 mm
C) 24 mm
D) 30 mm

Answers

D) 30 mm

should be it!! GL:)

The the volume of the triangular prism is 30mm so D

The answer is C, but I don't understand why- can anyone tell me?

Answers

Answer:

It's C because we are adding a number on the x but here we skip 5 so it's 6, and on y we add 4 up but since we skipped 5 we add 8 and we get 24. 6, 24. You may say "but SpiritBear, 17 plus eight is 25" and that is true, but if you notice the lowest dot actually starts on 5, not 4 making C right.

Hope this helped and wasn't too confusing

Equation 1
y = 5x + 32
Equation 2
4y = 28x + 184
First solve for X.

Answers

Equation 1: x= 1/5y + -32/5
Equation 2: x= 1/7y + -47/7

Which of the following expresses a potential difficulty with preference ballots?

Preference ballots only list one candidate per elected position.

Preference ballots are seldom used and difficult to produce.

The results of preference ballots can be time-consuming to compile.

It is easy to commit voter fraud by falsifying preference ballots.

Answers

The results of preference ballots can be time-consuming to compile

The potential difficulty with preference ballots expressed in the given options is: The results of preference ballots can be time-consuming to compile.

What is preference ballot?

A preference ballot is a type of ballot used in elections where voters indicate their order of preference for the candidates or options listed on the ballot.

Instead of simply selecting one option, voters rank the options in order of their preference, usually by indicating a first-choice, second-choice, and so on.

Preference ballots require more complex calculations to determine the winner, especially when there are more than two candidates. This can result in delays in announcing the results and can be time-consuming to compile.

Thus, this can result in delays in announcing the results and can be time-consuming to compile.

For more details regarding preference ballots, visit:

https://brainly.com/question/31264096

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I need this answered please

Answers

Answer:

domain: ( 3,6,6)

range : (b,a,d)

Write an equation for a quadratic function in vertex form with a vertex of (3,1) that has the point
(1,5).

Answers

Answer:

y = (x - 3)² + 1

Step-by-step explanation:

the equation of a quadratic function in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

here (h, k ) = (3, 1 ) , then

y = a(x - 3)² + 1

to find a substitute (1, 5 ) into the equatiuon

5 = a(1 - 3)² + 1 ( subtract 1 from both sides )

4 = a(- 2)² = 4a ( divide both sides by 4 )

1 = a

then equation of quadratic function is

y = (x - 3)² + 1

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