A boxcar contains six complex electronic systems. Two of the six are to be randomly selected for thorough testing and then classified as defective or not defective.
a. If two of the six systems are actually defective, find the probability that at least one of the two systems tested will be defective. Find the probability that both are defective.
b. If four of the six systems are actually defective, find the probabilities indicated in part (a).

Answers

Answer 1

Answer:

Step-by-step explanation:

Number of electronic systems = 6

(a) Number of defected systems = 2

Probability of getting at least one system is defective

1 defective and 1 non defective + 2 defective

= (2 C 1 ) x (4 C 1) + (2 C 2) / (6 C 2)

= 3 / 5

(b) four defective

Probability of getting at least one system is defective

2 defective and 2 non defective + 3 defective and 1 non defective + 4 defective  

= (4 C 2 ) x (2 C 2) + (4 C 3 )(2 C 1) + (4 C 4) / (6 C 4)

= 1

Answer 2

Answer:

(a)P(At least one defective)[tex]=0.6[/tex]

P(Both are defective)[tex]=0.067[/tex]

(b)P(At least one defective)[tex]=14/15[/tex]

P(Both are defective)[tex]=0.4[/tex]

Step-by-step explanation:

We are given that

Total number of complex electronic system, n=6

(a)Defective items=2

Non-defective items=6-2=4

We have to find the  probability that at least one of the two systems tested will be defective.

P(At least one defective)=[tex]\frac{2C_1\times 4C_1}{6C_2}+\frac{2C_2\times 4C_0}{6C_2}[/tex]

Using the formula

[tex]P(E)=\frac{favorable\;cases}{total\;number\;of\;cases}[/tex]

P(At least one defective)[tex]=\frac{\frac{2!}{1!1!}\times \frac{4!}{1!3!} }{\frac{6!}{2!4!}}+\frac{\frac{2!}{0!2!}\times \frac{4!}{4!}}{\frac{6!}{2!4!}}[/tex]

Using the formula

[tex]nC_r=\frac{n!}{r!(n-r)!}[/tex]

P(At least one defective)[tex]=\frac{2\times \frac{4\times 3!}{3!}}{\frac{6\times 5\times 4!}{2\times 1\times 4!}}+\frac{1}{\frac{6\times 5\times 4!}{2\times 1\times 4!}}[/tex]

P(At least one defective)[tex]=\frac{2\times 4}{3\times 5}+\frac{1}{3\times 5}[/tex]

P(At least one defective)[tex]=\frac{8}{15}+\frac{1}{15}=\frac{9}{15}[/tex]

P(At least one defective)[tex]=\frac{3}{5}=0.6[/tex]

Now, the probability that both are defective

P(Both are defective)=[tex]\frac{2C_2\times 4C_0}{6C_2}[/tex]

P(Both are defective)=[tex]\frac{\frac{2!}{0!2!}\times \frac{4!}{4!}}{\frac{6!}{2!4!}}[/tex]

P(Both are defective)[tex]=\frac{1}{\frac{6\times 5\times 4!}{2\times 1\times 4!}}[/tex]

P(Both are defective)[tex]=\frac{1}{3\times 5}[/tex]

P(Both are defective)[tex]=0.067[/tex]

(b)

Defective items=4

Non- defective item=6-4=2

P(At least one defective)=[tex]\frac{4C_1\times 2C_1}{6C_2}+\frac{4C_2\times 2C_0}{6C_2}[/tex]

P(At least one defective)[tex]=\frac{\frac{4!}{1!3!}\times \frac{2!}{1!1!} }{\frac{6!}{2!4!}}+\frac{\frac{4!}{2!2!}\times \frac{2!}{2!}}{\frac{6!}{2!4!}}[/tex]

P(At least one defective)[tex]=\frac{2\times \frac{4\times 3!}{3!}}{\frac{6\times 5\times 4!}{2\times 1\times 4!}}+\frac{\frac{4\times 3\times 2!}{2!\times 2\times 1}}{\frac{6\times 5\times 4!}{2\times 1\times 4!}}[/tex]

P(At least one defective)[tex]=\frac{2\times 4}{3\times 5}+\frac{2\times 3}{3\times 5}[/tex]

P(At least one defective)[tex]=\frac{8}{15}+\frac{6}{15}=\frac{8+6}{15}[/tex]

P(At least one defective)[tex]=\frac{14}{15}[/tex]

P(Both are defective)[tex]=\frac{4C_2\times 2C_0}{6C_2}[/tex]

P(Both are defective)[tex]=\frac{\frac{4\times 3\times 2!}{2\times 1\times 2!}\times \frac{2!}{2!}}{\frac{6\times 5\times 4!}{2\times 1\times 4!}}[/tex]

P(Both are defective)[tex]=\frac{\frac{4\times 3\times 2\times 1}{2\times 1\times 2\times 1}}{3\times 5}[/tex]

P(Both are defective)[tex]=\frac{6}{15}=0.4[/tex]

P(Both are defective)[tex]=0.4[/tex]


Related Questions

12 workers take 4 hours to complete a job. How long would it take 15 workers to complete the job?

Answers

Answer:

3.75

Step-by-step explanation:

Park Hyatt Philadelphia at the Bellevue, located at Walnut and Broad in downtown Philadelphia has a capacity of 240 king rooms. Customers of Hyatt are typically either leisure travelers or business customers. Hyatt charges a discount fare of $125 for a midweek stay (but requires booking a week in advance) which contrast the regular fare of $275. Typically, business customers book in the last minute, and are willing to pay the regular fare, if they can be guaranteed accommodation. Suppose we are interested in the bookings in Park Hyatt on August 6th (the day of our final exam). Hyatt knows that there are plenty of leisure travelers, willing to pay the low fares. However, all else being equal, Hyatt would like to fill those rooms with the high-fare travelers. The objective of Hyatt is to maximize the sum of revenue from both sections of the travelers. If Hyatt followed the ‘booking limit policy’, by reserving some rooms for last-minute business customers, how many rooms should it reserve? Assume that there is ample demand of leisure customers willing to pay the discount fare, and the number of business customers is normally distributed, with mean 50 and standard deviation 26. (6 points)

Answers

Answer:

[tex]X=53[/tex]

Step-by-step explanation:

From the question we are told that:

Regular fare R= $275

Discount fare of $125

Mean [tex]\=x =50[/tex]

Standard deviation [tex]\sigma= 26.[/tex]

Generally, the equation for Critical Fraction is mathematically given by

[tex]C=\frac{Pf-Pd}{Pf}[/tex]

[tex]C=\frac{275-125}{275}[/tex]

[tex]C=0.5[/tex]

From Z Distribution Table

[tex]Z=0.1131[/tex]

Therefore

Reservation  made is give as for High fare travellers is

[tex]X = \=x+(z* \sigma)[/tex]

[tex]X = 50 + (0.1131 * 26)[/tex]

[tex]X=53[/tex]

find x and y on triangle
Also the degree is 30 and the other thing is 7sqrt3​

Answers

Answer:

y =7

x =14

Step-by-step explanation:

Since this is a right triangle we can use trig functions

tan 30 = opp /adj

tan 30 = y/ 7 sqrt(3)

7 sqrt(3)  tan 30 = y

7 sqrt(3) * 1/ sqrt(3) =t

7 =y

sin 30 = opp/ hyp

sin 30 = 7/x

x sin 30 =7

x = 7/ sin 30

x = 7 / 1/2

x = 14

A certain positive integer has exactly 20 positive divisors.

What is the largest number of primes that could divide the integer?

thx for the help in advance

Answers

9514 1404 393

Answer:

  3

Step-by-step explanation:

20 has at most 3 proper factors greater than 1: 2×2×5. Each of these can represent a prime factor of the number of interest, and is 1 more than that prime's power. That is, the number of interest (n) will have at most 3 prime factors p, q, r, and will be ...

  n = p·q·r^4

_____

For some prime factorization ...

  [tex]\displaystyle n=\prod_{k=1}^m{p_k^{q_k}}[/tex]

The total number of divisors of n is ...

  [tex]\displaystyle\prod_{k=1}^m{(q_k+1)}[/tex]

Help please! it’s due soon

Answers

Answer:

33. That means (A) can be any number and b times any number wilo get 0 so any numbr will do

34.It is wrong because if x equals 40 anything multiply that will be more than that and so isnt a good reasoning

A building 51 feet tall casts a shadow 48 feet long. Simultaneously, a nearby statue casts a shadow of 16 feet. How tall is the statue? Choose an answer

Answers

Answer: 17 feet

Step-by-step explanation:

51/48 = x/16

(51)(16)/48

The statute is 17 feet tall.

What are the similar triangles?

Similar triangles are the triangles that have the same shape, but different sizes. The corresponding angles are congruent and the sides are in proportion.

What is the ratio of any two corresponding sides of similar triangles?

The ratio of any corresponding sides in two equiangular triangles is always the same.

Let's visualize the situation according to the given question.

AB is the building ,whose height is 51f

BC is the shadow of the building AB, whose length is 48ft.

QR is the shadow of the tower statue, whose length is 16feet.

Let the height of the statue PR be h feet.

In triangle ACB and triangle PRQ

∠ACB = ∠PRQ = 90 degrees  

( the objects and shadows are perpendicular to each other)

∠BAC = ∠QPR

( sunray falls on the pole and tower at the same angle, at the same time )

ΔACB similar to ΔPRQ   ( AA criterion)

Therefore, the ratio of any two corresponding sides in equiangular triangles is always same.

⇒ AC/CB = PR/RQ

⇒[tex]\frac{51}{48} =\frac{h}{16}[/tex]

⇒ h = [tex]\frac{(51)(16)}{48}[/tex]

⇒ h = 17 feet.

Hence, the statute is 17 feet tall.    

Learn more about the similar triangle here:

brainly.com/question/25882965

#SPJ2

find the slope of the joining pairs of points (1/a, 1/b) (b,a)

Answers

Answer: m = 1/b

Step-by-step explanation: Unfortunately, I can't give you a picture of the slope, but take that formula I gave you and enter it into a graphing calculator and it will show you the slope. I recommend desmos online calculator, good luck

the answer is








1/b i believe

r-(-4x - (y + y)); use x = -4, and y = -3 evaluate ​

Answers

Answer:

insert values of x and y

r - ( -4(-4) - ( -3-3))

r - ( 16 +6 )

r - 22

Doneeeeeeeeeeeeeeeeee3

Find the minimum turning point of y = x^2 + x - 12

Answers

Answer:

(x+4)(x-3)

Step-by-step explanation:

x^2+x-12

=x^2+(4-3)x-12

=x^2+4x-3x-12

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

=(x+4)(x-3)

Answer:x=6

Step-by-step explanation:

A research report claims that 20% of all individuals use Firefox to browse the web. A software company is trying to determine if the proportion of their users who use Firefox is significantly different from 0.2. In a sample of 200 of their users, 26 users stated that they used Firefox.

Required:
Using this data, conduct the appropriate hypothesis test using a 0.01 level of significance.

Answers

Answer:

Reject H0

Step-by-step explanation:

Z  = -2.474873734

 

survey (positive) 26

n (total) 200

p 0.2

 

p /point est. 0.13

POPULATION(min) 4000

np        >= 5 ? YES 40

n(1-p)  >= 5 ? YES 160

Sample is valid  

Confidence Level - "P" values  

99% 2.58

Confidence Interval - "P" values  

(0.0686 , 0.1914 )  

Reference=0.2 Reject H0

Multiple Choice
Which statement is an example of the Identity Property of Multiplication?
A. 8.0 = 0
B. 8. 1 = 8
C. 8.-1 = -8
D. -8.-1 = 8

Answers

Answer:

I think that the answer is - 8.-1=8

A football team has a probability of 0.76 of winning when playing any of the other four teams in its conference. If the games are independent, what is the probability the team wins all its conference games

Answers

Answer:

0.33362176

Step-by-step explanation:

Probability is the ratio of the number of possible outcomes to the number of total outcomes.

Given that a football team has a probability of 0.76 of winning when playing any of the other four teams in its conference, the probability that the team wins all its conference games

= 0.76 * 0.76 * 0.76 * 0.76

= 0.33362176

This is the probability that the teams wins the 4 matches played against the other teams in the conference.

88%
19. What is the solution X in this equation? 2(3x - 7) + 4(3x + 2) = 6(5x+9) + 3

Answers

[tex]\\ \sf\longmapsto 2(3x-7)+4(3x+2)=6(5x+9)+3[/tex]

[tex]\\ \sf\longmapsto 6x-14+12x+8=30x+54+3[/tex]

[tex]\\ \sf\longmapsto 6x+12x-14+8=30x+57[/tex]

[tex]\\ \sf\longmapsto 18x+6=30x+57[/tex]

[tex]\\ \sf\longmapsto 30x-18x=6-57[/tex]

[tex]\\ \sf\longmapsto 12x=51[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{51}{12}[/tex]

Find the greatest number of students to whom 45 soccer balls and 60 tennis balls can be equally divided.

Answers

Answer:

15 students

Step-by-step explanation:

Find GCF of 45 and 60:

45 = 3*3*560 = 2*2*3*5

GCF(45,60) = 3*5 = 15

Soccer balls=45Tennis balls=60

Find Greatest common multiple or GCF

[tex]\\ \sf\longmapsto 45=3\times 3\times 5[/tex]

[tex]\\ \sf\longmapsto 60=2\times 2\times 3\times 5[/tex]

Now

[tex]\\ \sf\longmapsto GCF=3\times 5=15[/tex]

An automobile manufacturer has given its car a 46.7 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this car since it is believed that the car has an incorrect manufacturer's MPG rating. After testing 150 cars, they found a mean MPG of 46.5. Assume the population standard deviation is known to be 1.1. A level of significance of 0.05 will be used. State the null and alternative hypotheses.

Answers

Answer: See explanation

Step-by-step explanation:

The null hypothesis H0: The null hypothesis states that there is no relationship between the two things that are being considered.

The alternative hypothesis is contradictory to H0 and it explains that there is a relationship between the two selected variables.

Based on the question, the null hypothesis H0 is that the rating of car is equal to 46.7 miles per gallon. μ = 46.7 MPG

The alternative hypothesis Ha is that the rating of the car is not equal to 46.7 Miles per gallon. μ ≠ 46.7 MPG

a company has decreased the weight of its boxes of macaroni by 8 %. if the new weight of the box is 13.1ounces, what was the original weight of the​ box?

Answers

Answer:

실례합니다 ?

Step-by-step explanation:

이것이 무엇을 의미하는 질문입니까?

회사는 마카로니 상자의 무게를 8% 줄였습니다. 상자의 새 무게가 13.1온스인 경우 상자의 원래 무게는 얼마였습니까? 오른쪽 ?

Answer:

x*0.92 = 13.1

x = 14.24

Step-by-step explanation:

SOVE, REDUCE TO LOWEST TEERMS SIMPLIFY IMPROPER FRACTIONSAS MIXED FRACTIONS

Answers

I don’t see a picture

I WILL GIVE BRAINLEST FAST PLEASE ANSWER THE QUESTION IN THE IMAGE

Answers

Answer:

Cannot be determined

Step-by-step explanation:

We only know one angle and we could only compare one set of sides.

We do not have enough information to determine if the triangles are similar

Answer: D. Cannot be determined

Complete the function table.
Input (n) Output (n-2)

Answers

Answer:  Choice C

This is because the input n = 2 leads to the output n-2 = 2-2 = 0

As another example: the input n = 4 leads to the output n-2 = 4-2 = 2

Whatever the input is, subtract 2 from it to get the output.

1+9+40-40+40+10x2 equals what?

Answers

Answer:

70

Step-by-step explanation:

1+9+40-40+40+10*2

----------------------- 20

10+40-40+40+20

50 (-40+40 cancels out to 0) +20

50+20= 70

(Following PEMDAS)

Multiply, add, subtract.

if you were to instead go through it left to right, you would get 120, which is incorrect.

The number of unique visitors to the college website can be approximated by the formula N(t)=410(1.32)t where t represents the number of years after 1997 when the website was created. Approximate to the nearest integer the number of unique visitors to the college website in the year 2020.

Answers

Answer:

243212

Step-by-step explanation:

Substitute the given value of t into the given formula. To find t, subtract 1997 from 2020.

2020−1997=23

Now substitute 23 into the equation for t and calculate.

N(t)N(23)==≈410(1.32)t410(1.32)23243,212

The number of unique visitors to the college website in the year 2020 was approximately 243,212.

(a) If y varies directly as x, and y=24 when x=16, find y when x=12.

(b) In a formula, z varies inversely as P. If Z is 200 when P is 4, find z when P is 10.

Answers

Answer:

(a) 18

(b) 80

Step-by-step explanation:

(a) let y=kx

so, 24=16k

or, k=24/16 or, k=3/2

now, putting x=12

y=kx

or, y=(3/2)×12

or, y=3×12/2

or, y=36/2

or, y=18

(b) let P=k/z

so, 4=k/200

or, k=800

when P = 10

P=k/z

or, 10=800/z

or, z=800/10

or, z=80

Write the quadratic function f(x) = x2 - 2x - 8 in factored form.
A) f(x) =(x - 4)(x - 2)
B) f(x) =(x + 4)(x - 2)
C) f(x) =(x - 4)(x + 2)
D) Rx) =(x + 4)(x + 2)

Answers

Answer:

Hello,

answer C

Step-by-step explanation:

[tex]f(x)=x^2+2x-8\\\\=x^2-4x+2x-8\\\\=x(x-4)+2(x-4)\\\\=(x-4)(x+2)\\\\Answer\ C[/tex]

Some one please help with question 10!!!

Answers

Answer:

Choice A.

[tex]2 {x}^{ \frac{2}{5} } \times y ^{ \frac{2}{3} } [/tex]

It can be shown that the line with intercepts (a, 0) and (0, b) has the following equation:
x/a + y/b= 1, a ≠ 0, b ≠ 0.

Use this result to write an equation of the line.

Point on line:

(−2, 4)

x-intercept: (a, 0)

y-intercept: (0, a)

(a ≠ 0)

Answers

The equation of the straight line is [tex]x+y=2[/tex].

Given:

The line with intercepts (a,0) and (0,b) has the equation [tex]\frac{x}{a} +\frac{y}{b} =1, a\neq 0, b\neq 0[/tex] Point on the line: (-2, 4)x-intercept: (a, 0)y-intercept: (0, a)[tex]a\neq 0[/tex]

To find: The equation of this line

It is given that a line with intercepts (a,0) and (0,b) has the equation [tex]\frac{x}{a} +\frac{y}{b} =1, a\neq 0, b\neq 0[/tex]

Now, it is given that the referred line has intercepts (a, 0) and (0, a). Then, using the above statement, the equation of this line can be written as,

[tex]\frac{x}{a} +\frac{y}{a}=1[/tex]. It is already given that [tex]a\neq 0[/tex]. So, we need not mention it again.

It is also given that the point (-2, 4) lies on this line. Then, the coordinates of this point must satisfy the equation of the line.

This implies that,

[tex]\frac{-2}{a} +\frac{4}{a} =1[/tex]

[tex]\frac{2}{a} =1[/tex]

[tex]a=2[/tex]

Now, put [tex]a=2[/tex] in the equation of the line, [tex]\frac{x}{a} +\frac{y}{a}=1[/tex] to get,

[tex]\frac{x}{2} +\frac{y}{2} =1[/tex]

[tex]x+y=2[/tex]

So, the equation of the line is [tex]x+y=2[/tex].

Learn more about equations of straight lines here:

https://brainly.com/question/18879008

Please help!!
A) In a movie, a mad scientist enlarges a cow to 100 times its normal size. How much stronger would its legs be than a normal cow?
B) How many times more would it weigh than a normal cow?
C) Can you see how results A and B would yield a cow that would collapse under its own weight?

Answers

Answer:

100 times everything.

Step-by-step explanation:

If the cow is 100 times larger than its normal size, obviously everything else should be 100 times stronger and heavier.

Please help me, by completing this proof!

Answers

Answer:

Step-by-step explanation:

                 Statement                                                 Reasons

1). Line PQ is an angle bisector of ∠MPN       D). Given

2). ∠MPQ ≅ ∠NPQ                                           A). Definition of angle bisector

3). m∠MPQ = m∠NPQ                                      F). Definition of congruent

                                                                               angles.

4). m∠MPQ + m∠NPQ = m∠MPN                    C). Angle addition postulate

5). m∠MPQ + m∠MPQ = m∠MPN                   G). Substitution property of

                                                                                equality

6). 2(m∠MPQ) = m∠MPN                                 B). Distributive property

7). m∠MPQ = [tex]\frac{1}{2}(m\angle MPN)[/tex]                               E). Division property of equality  

Please help me please! I really need it! Thank you so much!!!!!!!!!!! Sorry Quality is really bad

Answers

Answer:

 7[tex]\frac{5}{6}[/tex]

Step-by-step explanation:

- 2[tex]\frac{1}{3}[/tex] - ( - 10[tex]\frac{1}{6}[/tex] ) = - 2[tex]\frac{1}{3}[/tex] + 10[tex]\frac{1}{6}[/tex] = - 2[tex]\frac{2}{6}[/tex] + 10[tex]\frac{1}{6}[/tex] = ( 10 - 2 ) + ( [tex]\frac{1}{6}[/tex] - [tex]\frac{2}{6}[/tex] ) = 8 - [tex]\frac{1}{6}[/tex] = 7 + ( [tex]\frac{6}{6}[/tex] - [tex]\frac{1}{6}[/tex] ) = 7[tex]\frac{5}{6}[/tex]

3/4 + 20 (2/5 x 4/7) ​

Answers

Answer:

i believe the answer is 5.3

Which shows the image of rectangle ABCD after the rotation () (W)?
13
VA
1
V

Answers

Answer:

Graph (1)

Step-by-step explanation:

Given rule for the rotation of a figure is,

A(x, y) → A'(-y, x)

This rule defines the rotation of point A by 90° counterclockwise about the origin.

Coordinates of point A → (-2, 0)

Coordinates of point C → (-1, 0)

Following the rule of rotation,

A(x, y) → A'(-y, x)

A(-2, 0) → A'(0, -2)

C(-1, 4) → C'(-4, -1)

Now search the image points from the graphs attached,

Graph (1) will be the answer.

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