A state auto-inspection station has two inspection teams. team 1 is lenient and passes all automobiles of a recent vintage; team 2 rejects all autos on a ﬁrst inspection because their “headlights are not properly adjusted.” four unsuspecting drivers take their autos to the station for inspection on four different days and randomly select one of the two teams. a if all four cars are new and in excellent condition, what is the probability that three of the four will be rejected? b what is the probability that all four will pass?

Answers

Answer 1

The probability of passing and rejection is equally likely given that one of the teams are randomly selected for the inspection and that the drivers are unsuspecting.

Thus, P(passing) = 1/2
P(rejection) = 1/2

Part A:

The probability that three of the four will be rejected is given by

[tex]P(RRRP)=\ ^4C_3\times\left( \frac{1}{2} \right)^3\times\left( \frac{1}{2} \right) \\ \\ =4\times \frac{1}{8}\times \frac{1}{2} =\frac{1}{4}=25\%[/tex]

Part B:

The probability that all four will pass is given by

[tex]P(PPPP)=\ ^4C_4\times\left( \frac{1}{2} \right)^4\\ \\ =1\times \frac{1}{16} =\frac{1}{16}=6.25\%[/tex]

Related Questions

An art student wants to make a model of the classroom. The length of the classroom is 2.4 times its width. The length of the student's model is 42 in. What should the width of the model be?

Answers

Answer:

Width of the model is:

17.5 in

Step-by-step explanation:

The length of the classroom is 2.4 times its width.

Length=2.4×width

The length of the student's model is 42 in.

Let w be the width of student's model.

By using the equation Length=2.4×width , we get

42=2.4×w

⇒ [tex]w=\dfrac{42}{2.4}[/tex]

⇒ w=17.5

Hence, width of the model is:

17.5 in

Answer:answer is actually 17.5 in

Step-by-step explanation:

confused how do i create this?

Answers

Here's one way to construct the second triangle. See the attached image.

The lateral surface area of the wrapper for an ice cream cone is 47.1 cm squared.If the lateral height of the ice cream cone is 6cm,what would be the radius of the ice cream cone?

Answers

To determine the radius of the cone, we make use of the lateral surface area of the cone. The lateral surface of an object is the area of all the sides of a certain object. For a cone, it is the product of pi, the radius and the slant height (lateral height). We calculate as follows:
Lateral Surface Area = πrh
47.1 = πr(6)
r = 2.5 cm

juan drives to work. Due to traffic, he averages 22 miles per hour. He returns home averaging 32 per hour. The total time is 22.5 hours. Write and solve an equation to find the time juan spends driving to work.

Answers

32(22*22.5)

Hope I helped out

Kaitlin drove 260 miles using 12 gallons of gas. at this rate, how many gallons of gas would she need to drive 286 miles?

Answers

260 miles/12 gallons ≈21.7 miles per gallon
286 miles ÷ 21.7 ≈ 13.2 gallons needed

Mr. rancher wants to build a pen for his horse. he wants the pen to be 40 yards long and 50 yards wide. if the fencing comes in 5 foot pieces, how many pieces does mr. rancher need to buy?

Answers

(50 x 2) + (40 x 2) = 180 yards x 3 = 540 feet of fence needed. 540 / 5 = 108. He will need 108 pieces of fencing

There are 36 pieces need to buy by Mr. rancher.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The length of pen for his horse = 40 yards

The width of pen for his horse = 50 yards

And, The fencing comes in 5 foot pieces,

Now,

The perimeter of the pen for his horse = 2 (50 + 40)

= 2 x 90

= 180 yards

Since, The fencing comes in 5 foot pieces,

Hence, Number of pieces to buy by Mr. rancher = 180 / 5

= 36

Thus, There are 36 pieces need to buy by Mr. rancher.

Learn more about the division method visit:

https://brainly.com/question/917110

#SPJ5

Write the domain of the function given in the graph in set builder notation.

a. {x|x<=10}
b. {x|x<=0}
c. {x|x>10}
d. {x|x>0}

I can't get a picture of the graph so I'll try to explain. Y axis 0-5, going up by 1's, x axis 0-50, going up by 5's. Line starts at 10 on the x axis, goes up at an angle and stops at 40.

Answers

Based on what I understood, the graph would look something like this (attached as a picture). I don't know what angle it would be but I just assumed simple conditions where in the function is linear. From the given graph, the domain (x-values) would start from 10 to 40. Thus x would be equal to or greater than 10. The answer would be C.

You are going to order some of your favorite cookies. If you order two boxes it will cost you $14. If you place an order for eight boxes it will cost you $26. Write an equation that represents the cost of ordering your favorite cookies.

Step 1: Decide what information represents your two points.
Hint: The points are in the format (number of boxes of cookies, cost) as these are your two variables.

Point 1: Point 2:

Step 2: Use your two points to write an equation.

Answers

this is alittle confusing but im guessing youre suppose to put 14 and 26 oin a numberline? so that would be why theres a point one and point two correct?
so im just gonna try and guess what the equation might be ^-^

14 devided by 2=?
26 devided by 8=?
then multiply the two answers to get the final answer.

(note im not trying to take points im just trying to help out a friend so im sorry if its wrong chika)

There are a multitude of ways to solve this, but to help you visualize it, we can use a graph to plot these points, and then form a line. Once we have a line, we can simply get the equation of the line to answer our question.

How do we plot the points?

We should obviously start out with a graph. We only need Quadrant I. We will let our x-axis (the horizontal axis) contain the number of boxes of cookies, and our y-axis (the vertical one) contain our prices.

We put our number of boxes on the x-axis because it is the independent variable, while the price per box goes on the y-axis because it is the dependent variable.

At this "point," we should be able to plot our numbers at the proper points. We can simply line up our "dot" (point) with the information given, so that Point 1 is (2 , 14) and Point 2 is (8 , 26). We know that information from the prompt.

Now, we simply need to draw a line that connects these 2 points.

Once we have done that, we need to remember the equation for a line. This is "y=mx+b" where "m" is our slope and "b" is our y-intercept. Our slope is going to be in a fraction with the format [tex] \frac{rise}{run}[/tex], or the change in the y-value over the change in the x-value.

When we work this out, we will find that the equation for this is y=2x+10.

Below, I have attached an image of the graph that we should make while doing this. Note that this graph "goes by 2s." The red point represents 2 boxes for 14 dollars. The blue point represents 8 boxes for 26 dollars. The green line represents the relationship between them.

The measure of an angle and the measure of its supplement are equal. find the measure of each of the supplementary angles

Answers

each angle is 90° because 90°=90°. 90°+90°=180°

Answer:

Step-by-step explanation:

Sorry, here are the problems:

160: 20 degrees

90: 90 degrees

X: ____

the current value of a baseball card is 80 times its original value the baseball card is worth $36 write and solve an equation to find the original value of the baseball card

Answers

Final answer:

To find the original value of a baseball card that is now worth 80 times its original value, you divide the current value of $36 by 80, resulting in an original value of $0.45.

Explanation:

The student wants to find the original value of a baseball card that is currently worth 80 times its original value and has a present worth of $36. We set up the equation: original value multiplied by 80 equals current value (80 × original value = $36). To find the original value, we divide the current value by 80.

Write the equation: 80 × original value = $36.Divide both sides of the equation by 80 to isolate the original value. So, original value = $36 ÷ 80.Calculate the result: original value = $0.45.

The original value of the baseball card was $0.45.

Alan drove 756 miles in 12 hours. at the same rate, how many miles would he drive in 8 hours?

Answers

First find the unit rate, or how many miles he drives per hr.
756 mi/12 hrs= 63 mph

Multiply the speed by time to get distance.
63 mph* 8 hrs= 504 mi

Final answer: 504 mi

Final answer:

Alan would drive 504 miles in 8 hours.

Explanation:

To find out how many miles Alan would drive in 8 hours, we can set up a proportion using the information given. Since Alan drove 756 miles in 12 hours, we can write the proportion as:

12 hours / 756 miles = 8 hours / x miles.

To solve for x, we can cross-multiply and then divide:

12 * x = 8 * 756

x = (8 * 756) / 12

x = 504

Therefore, Alan would drive 504 miles in 8 hours.

Learn more about Miles driven in a given time here:

https://brainly.com/question/4676946

#SPJ2

How do i solve for x 30x - 60 = 20x

I already know x equals 6, but i dont know how to get the answer

Answers

First, subtract 30x from each side to get:
-60 = -10x
Then, divide each side by -10 to get:
x = 6
Now, plug back in to check your answer:
30(6) - 60 = 20(6)
180 - 60 = 120
120 = 120

Hope this helps!! :)

The real number -16 belongs to which sets of numbers?

Answers

counting numbers or natural numbes are like 1,2,3,4,5,6, etc

whole numbers include counting numbers, but with 0, so 0,1,2,3,4, 5, etc

integers include the negatives, so -4,-3,-2,-1,0,1,2,3,4, etc

rational numbers are numbers that can be written in form a/b where a and b are integers and b≠0

irrational numbers can't be written as a rational numer

so -16 is an integer and ratinoal number

-16 is an integer and rational number.

What are natural numbers, rational numbers, integers and irrational numbers?

Natural numbers are: 1, 2, 3, ....

Integer numbers are: ...., -2, -1, 0, 1, 2, ... (so it includes positive and negative natural number, and 0 )

Irrational numbers are those real numbers which are not rational numbers.

Know that all natural numbers are integers, all integers are rational numbers. That means natural numbers are not irrational.

The counting numbers or natural numbers are like 1,2,3,4,5,6, etc

Note that whole numbers include counting numbers, but with 0, so 0,1,2,3,4, 5, etc

Also rational numbers are numbers that can be written in form a/b where a and b are integers and b≠0

so -16 is an integer and rational number

Learn more about numbers here;

https://brainly.com/question/3151755

#SPJ2

How to find slope of any given line segment?

Answers

Best Answer: I'll make one up and explain how to do it.

Lets say your two points are (2,6) and (-4,7)

To start with you need to use the point-slope formula which is y2-y1/x2-x1

Remember (x,y), Thus we have

7-6/-4-2 = 1/-6; So out slope is -1/6

Now lets use the following equation y = mx+b to solve for b which is the y-intercept. By substitution of either order pair we can solve for b

6 = 2(-1/6)+b; distribute the 2
6 = -2/6+b; add 2/6 to each side to isolate b
6+2/6 = b; put 6 over 1
6/1+2/6 = b; get a common denominator between 6/1 and 2/6 which is 6
6(6/1)+2/6 = b ; distribute
36/6+2/6 = b; add these up
38/6 = b; reduce to lowest terms by dividing by 2 to each
19/3 = b

So our final equation is y = -1/6x+19/3

Need help! Please. It could be a integer or a decimal

Answers

It could be a integer

True or false? if the sample mean of a random sample from an x distribution is relatively small, then the confidence interval for Î¼ will be relatively short

Answers

false is the answer that's right

Prove that a triangle with sides n^2 1, n^2 - 1 and 2n (for n > 1) is a right triangle

Answers

Hello,

You have lost a sign "+".
[tex](n^2-1)^2+(2n)^2\\ =n^4-2n^2+1-4n^2\\ =n^4+2n^2+1\\ =(n^2+1)^2 [/tex]

Theorem of Pythagore is verified in this case: the triangle is a right one

Give an example of an open equation

Answers

an example would be x+4=8

one example would be x - 7 = -3 or 2x = 28

How to simplify 8x2+7x-3+4x-8

Answers

hello :
8x²+7x-3+4x-8 = 8x² +(7x+4x) +(- 3 - 8)=8x²+7x - 11

An airplane descend 1.5 miles to an elevation of 5.25 miles. Find the elevation of the plane before its descent.

Answers

Just add them together

The clean up hitter on a baseball tean batted 1/3 of the runs the team scored. The hitter batted in 3 runs. Select the equation that represents the number of n of runs the team scored. Then solve the equation:

A.1/3n=3
B.n/3=1/3
C.3n=1/3
D.3n=9

Answers

The number of runs the team scored is n. The clean up hitter batted in 1/3 of the runs. The clean up hitter batted in 3 runs. We can use this information to set up an equation. 1/3 (number of runs) = 3 1/3 (n) = 3 n = 9 The team scored 9 runs. The correct answer is A. 1/3 (n) = 3

I need math help. Look at the attachment. No multiple choice.

Answers

there are 4 quarters per year

if annual rate = 8%

quarterly rate would be 8%/4 = 2%

so the (1+r) beomes (1+0.02) = 1.02

if a 40-foot tree casts a 12-foot shadow,find the length of a shadow cast by a 23-foot tree

Answers

ratio and proportion

shadow:length=12:40=3:10

if length is 23 then
3:10=?:23
3/10=?/23
multiply both sides by 23
69/10=?
6.9=?

6.9ft is the shadow length

The length of the shadow cast by the 23 feet tree is 6.9 feet

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

Given data ,

Let the height of the tree A = 40 feet

The height of the shadow of the tree A = 12 feet

Now ,

The height of the tree B = 23 feet

Let the height of the shadow of the tree B = x

So , the proportion equation is

height of the shadow of the tree A / height of the tree A = height of the shadow of the tree B / height of the tree B

And the proportion will be ,

12 / 40 = x / 23

Multiply by 23 on both sides , we get

x = ( 12 × 23 ) / 40

x = ( 3 × 23 ) / 10

x = 69 / 10

x = 6.9 feet

Therefore , the value of x is 6.9 feet

Hence , The length of the shadow cast by the 23 feet tree is 6.9 feet

To learn more about proportion click :

https://brainly.com/question/7096655

#SPJ2

Write an equation for the line through p that is parallel to l and perpendicular to l

Answers

well the equation can't be paralle and perpendicular to I at the same tjme

The sum of 5 consecutive even numbers is 505 What is the third number in this sequence?

Answers

The answer 101. 99+100+101+102+103 = 505

you can't have 5 even numbers add to 505

even numbers can only add up to an even number.

To add a value 1 to variable x, you write ________.

Answers

1+x you can not add them because they are not like terms

The correct expression after adding a value 1 to variable x is 1 + x.

Used the concept of expression that states,

A mathematical expression is defined as the collection of numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that,

Add a value of 1 to variable x.

Here, the number is 1 and the variable is x.

Hence add the number 1 and x is written as,

1 + x

So, the expression is, 1 + x

To learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ5

What can you infer about elements that are in the same group?
a. they will have the same atomic mass
b. they will display similar chemical and physical properties
c. they will contain the same number of protons
d. they will emit x rays of similar frequency

Answers

b.

Elements of the same group in the Periodic Table will have similar chemical and physical properties.

Answer:

b.They will display similar chemical and physical properties.

Step-by-step explanation:

We have to find about the elements that are in the same group.

In modern periodic table

Elements are arranged in group according to similar properties.

The elements which have same properties are placed in the same group and mass of different elements are different in the group.

The outer electronic configuration of every element in the same group are same.

Therefore, the physical and chemical properties of the elements are same in the group.

Hence, option B is true.

Answer:b.They will display similar chemical and physical properties.

What is the general process for solving an equation with one variable

Answers

Thanks for the question!

First, make sure all the variable are on one side and all the numbers are on the other. Then, combine like terms. If necessary, isolate the variable.

Hope this helps!

The general process is by grouping like term I. E the unknown to the left hand side while value to the right hand side

Which ordered pairs are solutions to the inequality 4x+y>−6?

Select each correct answer.

(2, 0)

(−3, 6)

(4, −20)

(0, −9)

(−1, −1)

Answers

Answer:

(2,0) , (4,-20) and (-1,-1)

Step-by-step explanation:

[tex]4x+y>-6[/tex]

WE need to select an ordered pair that is solution to our inequality

Lets check with each option

(2,0) , plug in 2 for x and 0 for y

[tex]4x+y>-6[/tex]

[tex]4(2)+0>-6[/tex]

[tex]8>-6[/tex] True

(−3, 6), plug in -3 for x and 6 for y

[tex]4x+y>-6[/tex]

[tex]4(-3)+6>-6[/tex]

[tex]-6>-6[/tex] False

(4, −20) , plug in 4 for x and -20 for y

[tex]4x+y>-6[/tex]

[tex]4(4)-20>-6[/tex]

[tex]-4>-6[/tex] True

(0, −9) , plug in 0 for x and -9 for y

[tex]4x+y>-6[/tex]

[tex]4(0)-9>-6[/tex]

[tex]-9>-6[/tex] False

(-1, −1) , plug in -1 for x and -1 for y

[tex]4x+y>-6[/tex]

[tex]4(-1)-1>-6[/tex]

[tex]-5>-6[/tex] True

Final answer:

The ordered pairs that are solutions to the inequality 4x+y>-6 are (2, 0), (4, -20), and (-1, -1) as they satisfy the condition when substituted into the inequality.

Explanation:

To determine which ordered pairs are solutions to the inequality 4x+y>-6, we need to plug the x and y values from each ordered pair into the inequality.

For the pair (2, 0), we substitute x = 2 and y = 0 into the inequality: 4(2) + 0 > -6, which simplifies to 8 > -6. This is true, so (2, 0) is a solution.For the pair (-3, 6), we substitute x = -3 and y = 6: 4(-3) + 6 > -6, which simplifies to -12 + 6 > -6. This gives -6 > -6, which is not true, so (-3, 6) is not a solution.For the pair (4, -20), we substitute x = 4 and y = -20: 4(4) - 20 > -6, which simplifies to 16 - 20 > -6. This gives -4 > -6, which is true, so (4, -20) is a solution.For the pair (0, -9), we substitute x = 0 and y = -9: 4(0) - 9 > -6, which simplifies to -9 > -6. This is not true, so (0, -9) is not a solution.For the pair (-1, -1), we substitute x = -1 and y = -1: 4(-1) - 1 > -6, which simplifies to -4 - 1 > -6. This gives -5 > -6, which is true, so (-1, -1) is a solution.

The correct solutions to the inequality are the ordered pairs (2, 0), (4, -20), and (-1, -1).

Kim estimates that the faucet in her kitchen drips at a rate of 1 drop every 2 seconds. Erik wants to know how many times the faucet drios in a week

Answers

302400. the amount of seconds in a week divided by 2

Other Questions

To calculate density, both _____ must be measured.length and volumelength and massvolume and mass What causes different liquids to form layers when they are poured into a container? Which characteristic is not true of epics? A.The hero goes on a journey. B.The heroes are usually flawed in some critical way. C.Battles are fought against gods and monsters. D.They tend to be very long Which situation would result in a theory being replaced rather than revised? If x , y and z Are whole numbers greater than 2 and If xyz2 = 735 What is the value of x+ y+z Tissue found in the ____________ that contains ____________ cells is called nervous tissue. How are Taoism and Legalism different?A) Taoism emphasizes letting go. Legalism is centered on constant and total control.B) Taoism teaches a person to be patient. Legalism pushes a person to achieve success at any cost.C) Taoism is useful for running a government. Legalism applies to all areas of life.D) Taoism teaches us to accept the natural flow of the universe. Legalism proposes that we can change our reality. How many xenon atoms are contained in 2.36 moles of xenon? 3.92 x 1024 xenon atoms 2.55 x 1023 xenon atoms 1.42 x 1024 xenon atoms 7.91 x 1025 xenon atoms 1.87 x 1026 xenon atoms? Which feature do the viol and the violin have in common? The rock had a mass of 500g and a density of 10 g/cm3. What is the volume of the rock Which discovery did scientists make when they arranged elements in order of increasing atomic mass? A. a repeating pattern of properties B. a puzzling series of numbers C. alphabetical arrangement of the names of elements D. a complex code of patterns and relationships Why is editing always the final stage of the writing process is mixing salt and pepper physical or chemical change ? _______ is an energy carrier molecule that shuttles some of the energy from glycolysis. Which of the following is a complex sentence. a. I had tea and coffee.b. I had tea because there was no coffee left. c. I had tea that was strong and bitter. d. I had tea but she had coffee . What did noble women contribute to medieval warrior society If y is directly proportional to x and if y=50 when x=25, find k, the constant of proportionality. The metric system was devised by _____. sophocles moses the romans the french Escolha a alternativa correcta: a.o controle de qualidade pertence ao grupo de processos de execuo do projecto. b.um produto com grau inferior geralmente constitui um problema. c.no se deve entregar ao cliente funcionalidades extras, alm das que ele solicitou. d.a garantia da qualidade pertence ao grupo de processos de controle do projecto. A collection of 30 coins worth $5.50 consists of nickels, dimes and quarters. There are twice as many dimes as nickels. How many quarters are there? Steam Workshop Downloader