A city hosted a music festival that included three concerts. According to the sales database, 28% of the audience attended the first concert, 42% attended the second one, 30% attended the third one, 80% attended at least one of the three concerts, 10% attended the first and second ones, 8% attended the first and third ones, and 7% attended the second and third ones. Find the probability that a randomly selected audient attended all the concerts

Answers

Answer 1

Answer:

[tex]P(X\cap Y\cap Z)=0.05[/tex]

Step-by-step explanation:

From the question we are told that:

Percentage of audience in first concert [tex]P(X)=0.28[/tex]

Percentage of audience in second concert [tex]P(Y)=0.42[/tex]

Percentage of audience in third concert [tex]P(Z)=0.30[/tex]

Audience Percentage at at-least one concert [tex]P(X \cup Y \cup Z)=0.80[/tex]

Percentage of audience at first & second concert [tex]P(X \cap Y)=0.10[/tex]

Percentage of audience in first & third concert [tex]P(X \cap Z)=0.08[/tex]

Percentage of audience in second & third concert [tex]P(Y\cap Z)=0.07[/tex]

 

Generally the equation for probability of attending all concerts [tex]P(X\cap Y\cap Z)[/tex]is mathematically given by

[tex]P(X \cup Y \cup Z)=P(X)+P(Y)+P(Z)-P(X \cap Y)-P(X \cap Z)-P(Y\cap Z)+P(X\cap Y\cap Z)[/tex]

[tex]P(X\cap Y\cap Z)=P(X \cup Y \cup Z)-P(X)-P(Y)-P(Z)+P(X \cap Y)+P(X \cap Z)+P(Y\cap Z)[/tex]

[tex]P(X\cap Y\cap Z)=0.80-0.28-0.42-0.30+0.10+0.80+0.70[/tex]

[tex]P(X\cap Y\cap Z)=0.05[/tex]

Therefore the probability that a randomly selected audient attended all the concerts

[tex]P(X\cap Y\cap Z)=0.05[/tex]


Related Questions

perimeter and area of a rectangular figure has a perimeter of 34cm its length is 9cm​

Answers

Answer:

Perimeter of rectangle = 32

Step-by-step explanation:

32 = 2(L+B)

L+B=16

B=16-L

B=16–9

B=7

AREA = L*B

AREA = 63sq.cm

1. Use ( − 4) 2 − 28 = 8 for the following: a. Explain why ( − 4) 2 − 28 = 8 has two solutions. (5 pts) b. Solve the equation to find the solutions. Show your work. (5 pts)

Answers

Well, ( − 4) 2 − 28 = 8 has two solutions because (-4) -w = 8 = ? once determined - 4 would equal 20 + the left over which is 8. This can be solved multiple ways and even backwards.

For the the equation (-4)² - 28 = 8 the solutions are x = 2 and x = -10.

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

The equation (-4)² - 28 = 8 has two solutions because when we square -4, we get 16.

When we subtract 28 from 16, we get -12.

But if we add 28 to -12, we get 16 again.

So we have two values of x that satisfy the equation: x = -4 and x = 4.

b. We can solve the equation by adding 28 to both sides:

(-4)² - 28 + 28 = 8 + 28

Simplifying, we get:

(-4)²= 36

Taking the square root of both sides, we get:

-4 = ±6

So the two solutions are:

x = -4 + 6 = 2

x = -4 - 6 = -10

Therefore, the solutions to the equation (-4)² - 28 = 8 are x = 2 and x = -10.

To learn more on Equation:

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What is the value of x in this octagon?
Enter your answer in the box.

Answers

Answer: 166 degrees

Step-by-step explanation:

An octagon has 1080 degrees in it. So just subtract all of the angles out of 1080.

1080-104-126-163-130-131-107-153= 166

ANSWER: 166 degrees

Answer:

166 degrees

Step-by-step explanation:

in an octagon, there are a total of 1080 degrees,

so we take all of the degrees we do know, and subtract them from 1,080 degrees! --- (1080-104-126-163-130-131-107-153= 166)

we end up with 166 degrees! :)

hope this helped!

Rewrite the function by completing the square. 2x^2 - 9x + 7 = 0.
Answer will look like this: (x + ____)^2 = ____
I need the blanks, any help? ​

Answers

Answer:

9=5

Step-by-step explanation:

Answer:

Step-by-step explanation:

2x²-9x+7=0

2x²-9x=-7

x²-9/2 x +(-9/4)²=-7+(-9/4)²

(x-9/4)²=-7+81/16=(-112+81)/16=-31/16

(x+(-9/4))²=-31/16

Please see attached pic

Answers

Answer:

D is the correct answer.

Step-by-step explanation:

-Subtract final value by start value

-Divide by start value

-Multiply by 100

Answer:

33%

Step-by-step explanation:


2. Bart and Jimmy's Ice Cream Shop are designing a new logo for their company. The logo is shown
below. What is the area of Bart and Jimmy's new logo?
A 88.26 cm?
B 74.13 cm
C 58.26 cm
D 44.13 cm
HURRY

Answers

Answer:

Marie Skłodowska-Curie

Polish chemist and pioneer in the field of radioactivity. First woman to become a professor at the University of Paris.

^ po polsku być powinno

Kto Polska?

What is the domain of the square root function graphed below? On a coordinate plane, a curve open up to the right in quadrant 4. It starts at (0, negative 1) and goes through (1, negative 2) and (4, negative 3). x less-than-or-equal-to negative 1 x greater-than-or-equal-to negative 1 x less-than-or-equal-to 0 x greater-than-or-equal-to 0

Answers

Answer:

Its D

Step-by-step explanation:

Ed2021

Answer

x greater-than-or-equal-to 0

Step-by-step explanation:

yes

Male and female teachers were asked whether they preferred to use a whiteboard or a projector while teaching. The responses are summarized in the table. Projector Whiteboard Total Male 22 10 32 Female 28 15 Total 25 75 What is the approximate probability that a teacher prefers projectors and is female?

Answers

Answer: c is the answer

C: 0.560

Step-by-step explanation:

Three methods for teaching mathematics to first graders are to be compared. Ten students are
randomly assigned to each of the methods, and the score on a quiz is recorded. What are the
response and treatment for this experiment?

Answers

Answer: The three methods are the treatments and the response is the score achieved on the quiz.

Step-by-step explanation:

The three techniques are the treatments, and the results are the final score.

what is response variable in the experiment?

The researcher predicts that a variable will change if the controlled variable changes; this variable is known as a responsive variable. A dependent variable is another name for a responsive variable.

Solution:

Three methods are assigned for teaching mathematics.

Randomly ten students are assigned to each of the method.

There scores are then recorded on a quiz.

It is clear that the response will be the score card of the students either scoring high marks or not being able to clear it.

And the treatments are three for if the student is not able to understand any of the method.

Hence the three methods serve as treatments, and the outcomes determine the final grade.  

Learn more about "Logical reasoning questions" here-

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PLZ HELP I NEED AWNSERS ASAP
a statistical question anticipates that answers will vary. which of these are examples of statistical questions?
A) how many computers are in the school's lab?
B) how many letters are in the wrong direction?
C) what are the favorite books of each member of the book club?
D) how many people volunteered to help at the community's Christmas
E) how many video games were purchased last year by each student in Mr.hills math class

Answers

E.

It gives a very precise question which will give much data.

1/2 x 288 = ???????
What is the answer?

Answers

Answer:144

Step-by-step explanation:

Use a calculator

or 1/2 x 288 =  288/2 = 144

Answer: 144

Step-by-step explanation:

I'm assuming that the "x" in this statement is a multiplication symbol.

Multiplying any number by 1/2 or 0.5 is the same thing as dividing it by 2.

Therfore the answer is 288/2 which is 144.

HELP! Does the pythagorean theorem work for every triangle or just for right triangles?

a. everytriangle

b. only right triangles

Answers

Answer:

This is so easy!

ONLY RIGHT TRIANGLES

Did you really ask this question?

Tip: You should learn the basics first.

What is the correct value for x , in the equation, 4x + 12 = 60?

Answers

Answer:

x = 12

Step-by-step explanation:

im 100% sure i hope this helps :)

Answer:

[tex]4x + 12 = 60 \\ 4x = 60 - 12 \\ 4x = 48 \\ x = \frac{48}{4} \\ x = 12[/tex]

=> 12 IՏ Tᕼᗴ ᑕOᖇᖇᗴᑕT ᗩᑎՏᗯᗴᖇ.

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ


Find the volume. Round to the nearest tenth if necessary.

Answers

Answer:

1,440

Step-by-step explanation:

When you find the volume, you have to multiply all the numbers.

So in this case:

10*12*12 = 1,440

What type of counting problem is this?

Johnny is a very picky eater, so he likes to use a lot of condiments. He has ketchup, salt, pepper, and shredded cheese at his disposal. His mother tells him he may only make two additions to his meal (i.e., he can add condiments only twice, regardless of whether or not he already used them). How many different ways can Johnny improve his meal?

Answers

The type of counting problem is combination with repetition.

What is combination ?

One of the several ways of choosing items from a large set of objects, without considering an order is termed as Combination.

As johnny  use a lot of condiments.

His mother tells him he may only make two additions to his meal.

He can add 2 condiments only twice, whether he already use them or not.

So, here we will use combination with repetition  because here same condiments can be added twice that is two times.

So, in how many different ways can johnny improve his meal can be determined by combination with repetition.

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Answer:

10

Step-by-step explanation:

In the figure TU is tangent to the circle at the U point. See below

Answers

Answer: 6

Explanation: 8 + 4 divided by 2 = 6

I know this is definitely the correct answer but I forgot which theorem it is. If you need any further explanation I will gladly try and find some more.

There are 165 deer in a state park. The population is increasing at the rate of 12% per year. Enter a prediction for how long it will take the population to reach 300. If necessary, round your answer to the nearest tenth.

The deer population will reach 300 in approximately _____
years.

Answers

The deer population will reach 309 in approximately 6 yrs


Year 1. 165•1.12=184.8
Year 2. 184.8•1.12=206.976
Year 3. 206.976•1.12=231.813
Year 4. 231.813•1.12=259.63
Year 5. 259.63•1.12=290.785
Year 6. 290.785•1.12=325.679

Therefore it will take 6 years for the deer’s population to reach 300

What is the solution to the to system equations in the graph?

Answers

Answer:

b

Step-by-step explanation:

The solution for system of two equations is simply the intersection of the two functions. Hence (b) is the answer

please help me.......​

Answers

Answer:

Step-by-step explanation:

Use SOH CAH TOA to recall how the trig functions fit on a triangle

SOH: Sin(Ф)= Opp / Hyp

CAH: Cos(Ф)= Adj / Hyp

TOA: Tan(Ф) = Opp / Adj

Let's use CAH  1st  , on the Lenovo building,  b/c we  have they Hypotenuse (Hyp)  and an angle and we want to know the other side of the Lenovo building

Cos(30) = x/294

294*Cos(30) = x

254.611 = x

Sin(30) = y / 294

294*Sin(30) = y

147 = y

perimeter = 147+254.611+294

perimeter Lenovo = 695.611 feet

For Asus building

hyp = sqrt [ ( 144.5*[tex]\sqrt{2}[/tex])^2 +  144.5*[tex]\sqrt{2}[/tex])^2 )]

hyp = 289

perimeter = 289+144.5*[tex]\sqrt{2}[/tex]+144.5*[tex]\sqrt{2}[/tex]

perimeter Asus = 697.7077

The difference of the two buildings is

697.7077 -  695.611 =2.09671 feet

the difference is 2.10 feet ( rounded to nearest 100th)

The period of a pendulum is the length
of time required to complete one swing
back and forth. If it takes 1.4 sec for a
0.49m pendulum to complete one period,
'What is the period of a 0.36 mpendulum?

Answers

Answer:

T₂ = 1.2 s

Step-by-step explanation:

The time period of a simple pendulum is given by :

[tex]T=2\pi \sqrt{\dfrac{L}{g}}[/tex]

Where

L is length of the pendulum

g is acceleration due to gravity

We have,

T₁ = 1.4 s, L₁ = 0.49 m, L₂ = 0.36 m, T₂= ?

[tex]\dfrac{T_1}{T_2}=\sqrt{\dfrac{L_1}{L_2}} \\\\T_2=\dfrac{T_1}{\sqrt{\dfrac{L_1}{L_2}}}\\\\T_2=\dfrac{1.4}{\sqrt{\dfrac{0.49}{0.36}}}\\\\T_2=1.2\ s[/tex]

So, the new time period is equal to 1.2 seconds.

She has 12 watermelons, 30 pears, and 42 apples

For each basket Kerra makes they must have the same number of fruit.

She must use all the fruit.



What is the greatest number of baskets that Kerra can make?

Answers

Six because all can be divided by six
12/6=2
30/6=5
42/6=7

Of 300 students in the cafeteria, 180 had lunch. Write the simplified ratio of the students in the cafeteria to the students that had lunch.

Answers

Answer:

300 : 180 = 5 : 3

Answer...
300 : 180 = 5 : 3

find the angle measure x in the following figures

Answers

The answer would be x=60

Cody is purchasing sports equiptment for $161.37. In Colorado, the sales tax is 2.9%. What is the total cost, including tax, on his purchase? ​

Answers

Answer:

$166.04

Step-by-step explanation:

take the price and add the percentage.

Answer:

166.05

Step-by-step explanation:

161.37x1.029

If a team of minors drill a hole 50.4 m into a rock formation and drill at a steady rate of 2.8 m/min. how long does it take to drill the hole

Answers

Answer:

t = 18 minutes.

Step-by-step explanation:

We can find the time by using the following kinematic equation:

[tex] y_{f} - y_{0} = v_{0}t + \frac{1}{2}at^{2} [/tex]  

[tex] \Delta y = v_{0}t + \frac{1}{2}at^{2} [/tex]  

Where:  

Δy: is the difference between the initial and the final height = 50.4 m

t: is the time  

a: is the acceleration

v₀: is the velocity of the drill = 2.8 m/min

Since the speed of perforation is constant, the acceleration is zero so:

[tex]\Delta y = v_{0}t[/tex]    

Then, by solving the above equation for "t" we have:

[tex] t = \frac{\Delta y}{v_{0}} = \frac{50.4 m}{2.8 m/min} = 18 min [/tex]

Therefore, it takes 18 minutes to drill the hole.  

I hope it helps you!    

It takes 24 hours to drive from town A to town B. At an average speed of 31 mph, how far is it?

Answers

Answer:

744 miles

Step-by-step explanation:

each hour is 31 miles

the drive is 24 hours

31*24=744

Answer:

744 miles

Step-by-step explanation:

Determine the equation of this circle. *

Answers

Answer:

b is correct center of circle is x=4 y=-2

radius = 3

Hey can you guys please help me understand. I need to find the answer to this question and my teacher explained how to do the assignment HORRIBLY. Please explain to me how you got the answer :)​

Answers

mmm  answer is 139.5 (C)

7x4.5=31.5

12x9=108

108+31.5=139.5

Answer:

A=139.5cm^2

Step-by-step explanation:

12x9=108---->Area of the rectangle A=l x w

9x7=63 divided by 2=31.5--->Area of the triangle  A=1/2 (b x h)

108+31.5=139.5cm^2

Hope this helps and can you give me brainliest pls?

Consider the following problem: The box fill weight of Frosted Flakes breakfast cereal follows a normal distribution with a mean of 9.75 ounces and a standard deviation of 0.27 ounces. A sample of 25 boxes filled this morning showed a mean of 9.85 ounces. At the 0.05 significance level, can we conclude that the mean weight is more than 9.75 ounces per box

Answers

Answer:

Yes, we can

Step-by-step explanation:

H0 : μ = 9.75

H1 : μ > 9.75

n = 25 ; xbar = 9.85 ; σ = 0.27

The test statistic:

T = (xbar - μ) ÷ (σ / √n)

T = (9.85 -9.75) ÷ (0.27 ÷ √25)

T = 0.1 ÷ 0.054

T = 1.85

We can obtain the Pvalue from the test statistic using the Pvalue calculator :

Pvalue at t score = 1.85 ; 24 = 0.038

If Pvalue < α ; Reject H0

α = 0.05

Since Pvalue < α ; We reject H0 and conclude that mean weight is more than 9.75 ounces per box

In the figure below, find the mZ6, in degrees, if m2 = 75°?
87
413
50° 2
1
56
PLEASE HELPP

Answers

Answer:

75 degrees

Step-by-step explanation:

2 and 4 are vertical angles so 4 is 75.

4 and 6 are alternate exterior angles so have same value.

6 is 75 degrees.

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