2. A manufacturer produces light bulbs at a Poisson rate of 300 per hour. The probability that a light bulb is defective is 0.012. During production, the light bulbs are tested, one by one, and the defective ones are put in a special can that holds up to a maximum of 50 light bulbs. On average, how long does it take until the can is lled

Answers

Answer 1

Answer:

On average it will take 13 hrs 53 minutes before the van is filled

Step-by-step explanation:

The first thing we need to do here is to find find the number of defective light bulbs

Using the poisson process, that would be;

λ * p

where λ is the poisson rate of production which is 300 per hour

and p is the probability that the produced bulb is defective = 0.012

So the number of defective bulbs produced within the hour = 0.012 * 300 = 3.6 light bulbs per hour

Now, let X be the time until 50 light bulbs are produced. Then X is a random variable with the parameter (r, λ) = (50, 3.6)

What we need to find however is E(X)

Thus, the expected value of a gamma random variable X with the parameter (x, λ) is;

E(X) = r/λ = 50/3.6 = 13.89

Thus the amount of time it will take before the Can will be filled is 13 hrs 53 minutes


Related Questions

In football seasons, a team gets 3 points for a win, 1 point for a draw and 0 points for a

loss. In a particular season, a team played 34 games and lost 6 games. If the team had a

total of 70 points at the end of the season, what is the difference between games won and lost​

Answers

Answer:

The difference between the games won and lost = 21 - 6 =15

Step-by-step explanation:

According to the question In a football season a team gets 3 points for a win, 1 point for a draw and 0 points for a loss.

A particular season a team played 34 games and lost 6 games . Finding the difference between game won and game lost simply means we have to know the number of game lost and game won.

The team played a total of 34 games.

Total games played = 34

Out of the 34 games played they lost 6 games. That means the remaining games is either win or draw. Therefore,

34 - 6 = 28 games was won or draw

Let

the number of games won = x

the number of game drew = y

3x + y = 70.............(i)

x  + y = 28................(ii)

x = 28 - y

insert the value of x in equation(i)

3(28 - y) + y = 70

84 - 3y + y = 70

84 - 70 = 3y -y

14 = 2y

divide both sides by 2

y = 14/2

y = 7

insert the value of y in equation(ii)

x + y = 28

x = 28 - 7

x = 21

The team won 21 games , drew 7 games and lost 6 games.

The difference between the games won and lost = 21 - 6 =15


Complete the point- slope equation of the line through (8, -8 and (9, 8). Y - 8 =

Answers

The point slip form would be: y+8=16(x-8). Not sure if that’s what you were looking for.

What is the approximate length of minor arc LM? Round to
the nearest tenth of a centimeter.
12.4 centimeters
15.7 centimeters
31.4 centimeters
36.7 centimeters

Answers

Answer:its 15.7

Step-by-step explanation:

Answer:

15.7

Step-by-step explanation:

HELP...it has timer​

Answers

Answer:

lily has a larger ratio

Step-by-step explanation:

A researcher conducts two studies on the effectiveness of a peer mentoring program. Self-evaluation ratings among participants before, during, and after the program were measured in both studies. In Study 1, 12 participants were observed, and in Study 2, 16 participants were observed. If Fobt = 3.42 in both studies, then in which study will the decision be to reject the null hypothesis at α= 0.05 level of significance?

Answers

Answer:

Study 2

Step-by-step explanation:

Okay, so in this question we are given the data or parameters or information Below;

=>" two studies were conducted on the effectiveness of a peer mentoring program."

=> "Self-evaluation ratings among participants before, during, and after the program were measured in both studies."

=> In Study 1, 12 participants were observed"

=> "Study 2, 16 participants were observed."

=> " If Fobt = 3.42 in both studies"

Say Vo = study 2 and V1 = study 1.

Hence, Vo: not effective.

V1 = effective.

The study in which the decision will be to reject the null hypothesis at α= 0.05 level of significance is the STUDY 2.

This is because the value of F > f-critical.

You have already a 1000 cash on your hand. You have also a 1000 cash in bank and you withdraw half of 500, so, it means you withdraw 250. Now, you have a 1000 cash on hand plus 250 that you have been withdraw from the bank, all in all you have 1250 now in your hand.

Answers

Answer: At the end, you have $750 remaining in the bank.

Step-by-step explanation:

I guess you want to know how much is left in the bank.

initially

Hand : $1000

Bank: $1000

you withdraw $250 from the bank:

Hand: $1000 + $250 = $1250

Bank: $1000 - $250 = $750

Please help. I’ll mark you as brainliest if correct!

Answers

Answer:

[tex]\sqrt{-6} \sqrt{-384}=\sqrt{(-6)(-384)}=\sqrt{2304}=48\\ a=48\\b=0[/tex]

or

[tex]a=-48\\b=0[/tex]

both solutions are correct because root square has two solutions, one positive and one negative.

Answer:

a= -48

b=0

Step-by-step explanation:

[tex]\sqrt[]{-6} = i\sqrt{6}[/tex]

[tex]\sqrt{-384} =i\sqrt{384}[/tex]

[tex](i\sqrt{6} )(i\sqrt{384} )[/tex]

[tex]i^{2} \sqrt{2304}[/tex]

(-1)(48) = -48

a + bi

a= -48

b= 0

42,000 as a multipul of a power of 10

Answers

Answer:

[tex] 4.2 \times {10}^{4} [/tex]

Step-by-step explanation:

[tex]42000 = 4.2000 \times \times {10}^{4} \\ = 4.2 \times {10}^{4} [/tex]

A random sample pulled 43 catfish from a large lake. They were marked and released. A second sample pulled out 88 catfish. Seventeen had been marked. Calculate the estimated population

Answers

Answer: 114

Step-by-step explanation: You have 43 new catfish then you catch 88 but 17 of them have already been marked so you do not want to count those in the estimated population again because they have already been counted so you take 88 minus 17 and you get 71 new fish. So then you add the first new sample of fish 43 and then you add the second new sample of fish 71 and then you get 114

average of a data set was 40, and that standard deviation was 10, what else could you derive from that information.

Answers

Answer:

[tex] \bar x = 40, s =10[/tex]

And from these values we can estimate the sample variance like this:

[tex] s^2 = 10^2 =100[/tex]

And we can also estimate the coeffcient of variation given by:

[tex] \hat{CV} =\frac{s}{\bar x}[/tex]

And replacing we got:

[tex] \hat{CV} = \frac{10}{40}= 0.25[/tex]

And this coefficient is useful in order to see the variability in terms of the mean for this case since is lower than 1 we can conclude that this variation around the mean is low.

Step-by-step explanation:

For this case we have the following info given:

[tex] \bar x = 40, s =10[/tex]

And from these values we can estimate the sample variance like this:

[tex] s^2 = 10^2 =100[/tex]

And we can also estimate the coeffcient of variation given by:

[tex] \hat{CV} =\frac{s}{\bar x}[/tex]

And replacing we got:

[tex] \hat{CV} = \frac{10}{40}= 0.25[/tex]

And this coefficient is useful in order to see the variability in terms of the mean for this case since is lower than 1 we can conclude that this variation around the mean is low.


please help me on this work please !

Answers

The second one I beileve is the answer to your question

When writing expressions for complex numbers, what does i represent?

Answers

Answer:

see below

Step-by-step explanation:

i is the imaginary number and it represents the square root of -1

Let:T : ℝ3→ℝ3 be the transformation that projects each vector x=​(x1​,x2​,x3​)onto the plane
x2=0​,
so
​T(x​)=​(x1​ ,​0 ,x3​). Show that T is a linear transformation.
The first property for T to be linear is
​T(0​) =_________________________________________________
Check if this property is satisfied for T.T​(x1​, x2​, x3​) =​(x1​, ​0,x3​)
​T(0,0,0) = ( _____ ,_____, _,_______) ,
​So, is the first property​ satisfied?
Yes 0r No
The second property for T to be linear is ​T(cu​+dv​)=______(see choices below)___________________________________________for all vectors(u and v)i n the domain of T and all scalars​ c, d
cT(u)+dT(v)
dT(u)+cT(v)dT(u)−cT(v)
cT(u)−dT(v)
for all vectors
u​,
v in the domain of T and all scalars​ c, d.
Check if this property is satisfied for T. Let u=​(u1​, u2​, u3​) and v =​(v1​, v2​, v3​).
T(cu+dv)=​(cu1+dv1​, ​0, cu3+dv3​) =​(cu1​, _______, _________) +​(dv1​, ________, _________)
Factor out the scalar in each ordered triple.
T(cu+dv) = ____​(u1​, ​0, u3) + ______​(v1​, ​0,v3​)
Further simplify the previous equation.
T(cu+dv) = c

(choices pick one)
T(v)
T(u)+d

(choices for the arrow above pick one)
T(v)
T(u)
​So, is the second property​ satisfied?
Yes
No
​Thus, T ▼
is
is not
linear.

Answers

Answer:

Step-by-step explanation:

A linear transformation must satisfy the following properties.

- T(0) = 0.

- For vector a,b then T(a+b) = T(a) + T(b).

- For a vector a and a scalar r, it must happen that T(ra) = rT(a)

In this case we have that T(a,b,c) = (a,0,c).

Note that T(0) = T(0,0,0) = (0,0,0) = 0. So, the first property holds.

Let [tex] a=(a_1,a_2,a_3), b=(b_1,b_2,b_3) [/tex]. Then

[tex]T(a+b) = T((a_1+b_1,a_2+b_2,a_3+b_3)) = (a_1+b_1,0,a_3+b_3) = (a_1,0,a_3)+(b_1,0,b_3) = T(a) + T(b)[/tex]

So the second property holds.

Finally, let r be a scalar and let [tex] a=(a_1,a_2,a_3)[/tex]. Then

[tex] T(ra) = T((ra_1,ra_2,ra_3)) = (ra_1,0,ra_3) = r(a_1,0,a_3)= rT(a)[/tex]

So, the three properties hold, and therefore, T is a linear transformation.

It is true that T represents a linear transformation

How to determine if T is a linear transformation

A linear transformation is such that have the following properties

T(0) = 0.If u and v are vectors, then T(u+v) = T(u) + T(v).If u is a vector and r is a scalar, then T(ru) = rT(u)

For the first property, we have:

T(x1,x2,x3) = (x1,0,x3)

The above property becomes

T(0) = T(0,0,0)

T(0) = (0,0,0)

T(0)= 0.

So, we can conclude that the first property of the linear transformation is satisfied

For the second property, we make use of the following:

u = (u1, u2, u3) and b = (v1,v2,v3)

The above property becomes

T(u + v) = T(u1 + v1, u2 + v2, u3 + v3)

Expand

T(u + v) = T(u1 + v1, 0, u3 + v3)

Expand

T(u + v) = (u1,0,u3) + (v1, 0, v3)

Simplify

T(u + v) = T(u) + T(v)

The above means that the second property is also satisfied

Recall that:

u = (u1, u2, u3)

So, we have:

T(ru) = (ru1, ru2, ru3)

Where r is a scalar

Expand

T(ru) = (ru1, 0, ru3)

Further, expand

T(ru) = r(u1, 0, u3)

So, we have:

T(ru) = rT(u)

The above means that, the third property is also satisfied

Hence, T represents a linear transformation

Read more about linear transformation at:

https://brainly.com/question/15213874

Find the diameter and radius of a circle with a circumference of 65.98 Please help ​

Answers

Answer:

21 and 10.5 respectively

Step-by-step explanation:

Remember circumference of a circle is given as;

C= 2×π×r; r is raduis

r = C / 2×π

=65.98/(2×3.142)= 10.50

D= 2× r = 2× 10.50= 21.0( D represent diameter)

Note π = 3.142 a known constant

The perimeter of the rectangle is below 76 units. Find the length of side AD. AB on rectangle 3y + 3 CB 2y

Answers

Answer:

14 units

Step-by-step explanation:

The perimeter of a figure is the sum of the lengths of all the sides.

Here, we know that ABCD is a rectangle, so by definition, AB = CD and AD = BC. We also are given that AB = 3y + 3 and BC = 2y, which means that:

AB = CD = 3y + 3

AD = BC = 2y

Adding up all the side lengths and setting that equal to the perimeter, which is 76 units, we get the expression:

AB + CD + AD + BC = 76

(3y + 3) + (3y + 3) + 2y + 2y = 76

10y + 6 = 76

10y = 70

y = 7

We want to know the length of AD, which is written as 2y. Substitute 7 in for y:

AD = 2y = 2 * 7 = 14

The answer is thus 14 units.

~ an aesthetics lover

Answer:

14

Step-by-step explanation:

The perimeter of a rectangle is found by

P = 2 (l+w)

P = 2( 3y+3+2y)

Combine like terms

P = 2(5y+3)

We know the perimeter is 76

76 = 2(5y+3)

Divide each side by 2

76/2 = 2/2(5y+3)

38 = 5y+3

Subtract 3 from each side

38-3 = 5y+3-3

35 = 5y

Divide each side by 5

35/5 = 5y/5

7 =y

We want the length of AD = BC = 2y

AD = 2y=2*y = 14

1) Ethan, Amir, Victoria, and Kayla share
3 apples equally. What fraction of an
apple does each friend get?​

Answers

Answer:

3 apples / 4 people

3/4

to check divide fractions

Multiply reciprocal

3/1 x 4/1

3/1 / 1/4 = 3/4

3/4 x 4 = 12/4 = 3 apples

3/4 is the answer

Hope this helps

Step-by-step explanation:

simplify 2x+x+x+2y times 3y times y

Answers

Answer:

12 x y² + 6 y³

Step-by-step explanation:

Step(i):-

Given ( 2 x + x + x + 2 y ) times 3 y times y

( 2 x + x + x + 2 y ) × 3 y × y = ( 4 x + 2 y) × 3 y × y =  ( 4 x + 2 y) 3 y²

By applying Distributive property

( a + b ) c = a . c + b . c

               = 4 x . 3 y² + 2 y . 3 y²

               = 12 x y² + 6 y³

Final answer:-

( 2 x + x + x + 2 y ) times 3 y times y =  12 x y² + 6 y³

Please help


Convert 200 cm to cm

Answers

Answer:

to cm it's still 200 if you mean to metre 2m

Step-by-step explanation:

Answer:

It would still be 200

Step-by-step explanation:

A professor gives her 100 students an exam; scores are normally distributed. The section has an average exam score of 80 with a standard deviation of 6.5. What percentage of the class has an exam score of A- or higher (defined as at least 90)? Type your calculations along with your answer for full credit; round your final percentage to two decimal places.

Answers

Answer:

6.18% of the class has an exam score of A- or higher.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 80, \sigma = 6.5[/tex]

What percentage of the class has an exam score of A- or higher (defined as at least 90)?

This is 1 subtracted by the pvalue of Z when X = 90. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{90 - 80}{6.5}[/tex]

[tex]Z = 1.54[/tex]

[tex]Z = 1.54[/tex] has a pvalue of 0.9382

1 - 0.9382 = 0.0618

6.18% of the class has an exam score of A- or higher.

how do you add 9 in 1 6 + 2 1/12​

Answers

Step-by-step explanation:

9 + 1/6 + 2 1/12

9 + 2.25

11.25

Identify the exponential function for this graph. (Be sure to look at the scales
on the x- and y-axes.)

Answers

On the x axes thi nk I really don’t know

The required  exponential function will be F(x)= [tex]4(0.5)^{x}[/tex]

Hence, Option A is the correct.

What is function?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

From the assumption graph as shown in attached figure, we can determine that when x = 0  then y = 4.

Also, we can closely observe that the graph represents decay  

exponential function.

The reason is that when the value of x   increases, the graph of the particular function decreases.

But, the rate of decay must be less than 1 for decay exponential function because if it is greater than 1, then it would represent  the exponential growth function.  

Hence, the option B and D should be completely ruled out as these values represent the exponential growth.  

And from graph, it is clear that when  x = 0 then y = 4

The exponential function will be F(x)= [tex]4(0.5)^{x}[/tex]

To learn more about function visit:

https://brainly.com/question/8892191

#SPJ7

Express the following ratio in its simplest form.
4:12

Answers

Answer:

3:12

Step-by-step explanation:

Answer:

1:3

Step-by-step explanation:

Think 4:12 as a fraction for a moment, it would be 4/12. Now completely simplify 4/12, you get 1/3. Now put 1/3 as a ratio, it would be 1:3.

Please mark BRAINLIEST, thanks!

In the western region of the state the times of all boys running in this event are normally distributed with standard deviation 12 seconds, but with mean 5 minutes 22 seconds. Find the proportion of boys from this region who qualify to run in this event in the state meet. (Hint: normalcdf)

Answers

Here is the full question.

The average finishing time among all high school boys in a particular track event in a certain state is 5 minutes 17 seconds. Times are normally distributed with standard deviation 12 seconds.

A.  The qualifying time in this event for participation in the state meet is to be set so that only the fastest 5% of all runners qualify. Find the qualifying time in seconds (round it to the closest second). (Hint: Convert minutes to seconds.)  

B. In the western region of the state the times of all boys running in this event are normally distributed with standard deviation 12 seconds, but with mean 5 minutes 22 seconds. Find the proportion of boys from this region who qualify to run in this event in the state meet. (Hint: normalcdf)

Answer:

a. x ≅ 337 seconds.

b. P(x > 337 )  = 0.1056

Step-by-step explanation:

A.

Given that ;

Mean [tex]\mu =[/tex] 5 minutes 17 seconds =( (60× 5)+17  ) seconds  = 317 seconds   ( since 60 seconds make 1 minute.

Standard deviation: [tex]\sigma[/tex] = 12 seconds.

Only the fastest 5% of all runners qualify

The objective is to determine the qualifying time in seconds

Let's look for the Z-score of 0.95;

The Z-score is 1.645 from the tables

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

[tex]x = ( 12 * 1.645 ) + 317 \\ \\x = 336.74[/tex]

x ≅ 337 seconds.

B. Given that the standard deviation = 12 seconds

Mean = 5 minutes 22 seconds = (5 × 60 + 22 )seconds = 322 seconds

he objective is  to find P(x > 337 )   i.e the proportion of boys from this region who qualify to run in this event in the state meet.

we are using command normalcdf   (SEE THE ATTACHED FILE BELOW FOR THE COMPUTATION)

we have  P(x > 337 )  = 0.1056

Evaluate the function h(t) =|t +2| + 3; find h(6)

Answers

Answer:

11

Step-by-step explanation:

h(t) =|t +2| + 3

Let t=6

h(6) =|6 +2| + 3

       = |8| +3

        =8+3

         = 11

What’s the correct answer for this question ?

Answers

Answer:

C

Step-by-step explanation:

It closely resembles to a sphere.

If y varies directly as x, and y is 48 when x is 6, which expression can be used to find the value of y when x is 2?

Answers

Answer:

When x is 2, y is 16

Step-by-step explanation:

If y is 48 and x is 6, then y is 8 when x is 1.

Because of this, when x is 2, y will be 16.

Please mark Brainliest

..
..................​

Answers

[tex]1. \: (x - y) {2} \\ = {x}^{2} - 2xy + {y}^{2} \\ 2. \: (a + b) ^{2} \\ = {a}^{2} + 2ab + {b}^{2} \\ 3. \: (2x + 3y) ^{2} \\ = {(2x)}^{2} + 2.2x.3y + (3y) ^{2} \\ = {4x}^{2} + 12xy + {9y}^{2} \\ 4.(3x - 2y) ^{2} \\ = (3x) ^{2} - 2.3x.2y + (2y) ^{2} \\ = {9x}^{2} - 12xy + {4y}^{2} \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]

Answer:

a) x^2−2xy+y^2

b) a^2 -ab+b^2

c)4x^2+12xy+9y^2

d)9x^2 -12xy+4y^2

Step-by-step explanation:

a) x^2−2xy+y^2

b) a^2 -ab+b^2

c)4x^2+12xy+9y^2

d)9x^2 -12xy+4y^2

We rewrite (x-y)^2 as (x-y) (x-y) to show and always see + sign at start for question a ) and question b)

a) x*x+x(−y)−yx−y(−y) = x^2−2xy+y^2

b) a^2 becomes a^2 -ab as a^2 -ab+b^2

c) As shown in notes attached and this will help you most.

d) the reasons we keep +4y is because -2y becomes -2y-2y and creates a plus.

2y + 5x – z = 4y + 6x solve for y

(show work)

Answers

Answer:

y = -z/2 - x/2

Step-by-step explanation:

2y + 5x – z = 4y + 6x

-5x. -5x

2y - z = 4y + x

+z. +z

2y = 4y + z + x

-4y -4y

-2y = z + x

÷-2. ÷-2

y = -z/2 - x/2

outline the procedure for finding the probabilities of any given compound event​

Answers

Explanation:

We will discuss the probability of any given Compound event under two broad heading. Exclusivity and Dependence.

Two or more events are mutually exclusive if they cannot occur at the same time.

In mutually excusive events,

[tex]P(A \cap B)=0[/tex]

The probability of two mutually exclusive events is given as:

P(A or B)=P(A)+P(B)

If however the two events can occur at the same time, they are mutually inclusive and: [tex]P(A \cap B)\neq 0[/tex].

For mutually inclusive events A and B,

[tex]P(A or B)=P(A)+P(B)-P(A \cap B [/tex].

Two events are independent if the outcome of one does not affect the outcome of the other.

For two independent events, the probability of A and B,

[tex]P(A \cap B)=P(A) \times P(B)[/tex].

Two events are not independent if the outcome of one affect the outcome of the other.

For two dependent events, if A is dependent of B, we say that the probability of A given B,

[tex]P(A|B)=\dfrac{P(A) \cap P(B)}{P(B)}[/tex].

no guess please explain

Answers

No, is not a function because for the same value of X it has two different values of y, that’s not the definition of function.

Other Questions
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