A sample of 3 different calculators is randomly selected from a group containing 10 that are defective and 5 that have no defects. Assume that the sample is taken with replacement. What is the probability that at least one of the calculators is defective? Express your answer as a percentage rounded to the nearest hundredth without the % sign.

1)The pdf of U is f(u) = (1/(2√u)) exp(-u/2) for u > 0 and f(u) = 0 otherwise.

2)U follows a gamma-distribution with parameter a = 3/2 or a = 1/2.

3)x = (y²/2) and dx = y dy using exponential distribution

We can rewrite the integral as:

I(1/2) = ∫₀^∞ y exp(-y²) dy

       = 1/2 ∫₀^∞ exp(-u/2) du

This is the same as the integral for f(u) when u = 1/2.

Therefore, we have:

I(1/2) = V1

(1) For U = Z², we can use the method of transformations.

Let g(z) be the transformation function such that

U = g(Z)

   = Z².

Then, the inverse function of g is given by h(u) = ±√u.

Thus, we can apply the transformation theorem as follows:

f(u) = |h'(u)| g(h(u)) f(u)

     = |1/(2√u)| exp(-u/2) for u > 0 f(u) = 0 otherwise

Therefore, the pdf of U is given by:

f(u) = (1/(2√u)) exp(-u/2) for u > 0 and f(u) = 0 otherwise.

(2) We are given that f(1/2) = VT, where V is a constant.

We can substitute u = 1/2 in the pdf of U and equate it to VT.

Then, we get:VT = (1/(2√(1/2))) exp(-1/4)VT

                            = √2 exp(-1/4)

This gives us the value of V.

Now, we can use the pdf of the gamma distribution to find the parameter a such that the gamma distribution matches the pdf of U.

The pdf of the gamma distribution is given by:

f(u) = (u^(a-1) exp(-u)/Γ(a)) for u > 0 where Γ(a) is the gamma function.

We can use the following relation between the gamma and the factorial function to simplify the expression for the gamma function:

Γ(a) = (a-1)!

Thus, we can rewrite the pdf of the gamma distribution as:

f(u) = (u^(a-1) exp(-u)/(a-1)!) for u > 0

We can now equate the pdf of U to the pdf of the gamma distribution and solve for a.

Then, we get:

(1/(2√u)) exp(-u/2) = (u^(a-1) exp(-u)/(a-1)!) for u > 0 a = 3/2

Therefore, U follows a gamma distribution with parameter

a = 3/2 or equivalently,

a = 1/2.

(3) We need to show that I(1/2) = V1.

Here, I(1) = ∫₀^∞ exp(-x) dx is the integral of the exponential distribution with rate parameter 1 and V is a constant.

We can use the change of variables y = √(2x) to simplify the expression for I(1/2) as follows:

I(1/2) = ∫₀^∞ exp(-√(2x)) dx

Now, we can substitute y²/2 = x to obtain:

x = (y²/2) and

dx = y dy

To know more about gamma-distribution, visit:

https://brainly.com/question/31733851

#SPJ11

Answer:

I cant read all of that. Im sure others ant either.

Step-by-step explanation:

Answer:

i cant read it for some reason, can you type it?

Step-by-step explanation:

Answer:

\(-\frac{3x+14}{x(x+5)(x-2)}\)  

Step-by-step explanation:

x² + 5x = x(x + 5)

x² + 3x - 10 = ( x + 5 )( x - 2 )

x² + 5x ≠ 0 , if x ≠ 0 or x ≠ - 5

x² + 3x - 10 ≠ 0 , if x ≠ - 5 or x ≠ 2

Restrictions are: x ≠ - 5, x ≠ 0, x ≠ 2

GCD is x(x + 5)(x - 2)

Given Expression = \(\frac{7(x-2)+ 2x^2 - 2x(x+5)}{x(x+5)(x-2)}\) =

\(\frac{7x-14+2x^2 -2x^2 -10x}{x(x+5)(x-2)}\) =

\(-\frac{3x+14}{x(x+5)(x-2)}\)

\(▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ { \huge \mathfrak{Answer}}▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ \)

solution is in attachment !

The binding constraints at optimality in the given mathematical formulation are Constraint B and Constraint C.

At optimality, the mathematical formulation satisfies Constraint B and Constraint C with equality. In the given mathematical problem, the objective is to minimize the expression 4X + 12Y, subject to certain constraints. The constraints are represented by equations that limit the values of X and Y. The first constraint, Constraint A (X + Y ≥ 20), states that the sum of X and Y must be greater than or equal to 20. Constraint B (4X + 2Y ≥ 60) requires that the expression 4X + 2Y be greater than or equal to 60. Constraint C (Y ≥ 5) specifies that Y should be greater than or equal to 5. Finally, Constraint D (X ≥ 0 and Y ≥ 0) sets the lower bounds for X and Y as non-negative values.

To find the optimal solution, the mathematical formulation seeks values for X and Y that minimize the objective function (4X + 12Y) while satisfying all the constraints. In this case, the binding constraints are Constraint B and Constraint C. "Binding" means that these constraints are satisfied with equality at the optimal solution, meaning their corresponding inequalities hold as equalities. In other words, the expressions 4X + 2Y = 60 and Y = 5 are both satisfied exactly at the optimal point.

Learn more about binding constraints

brainly.com/question/32070704

#SPJ11

Answer:

3/7 + 1/3 = 1621 ≅ 0.7619048

Spelled result in words is sixteen twenty-firsts.

Step-by-step explanation:

Answer:

7/21

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

Well you basically divide 3 and 1/2 by 1/6 which you would you have to simplify the 3 and 1/2 which is 7/2 and switch the denominator and numerator of the 1/6 which would be 6/1 and after you multiply(7/2 x 6/1=42/2) it would be 42/2 which you would have to simplify by dividing 42 and 2 which is 21. There you go I hope this helps.

Answer:

21.

Step-by-step explanation:

That would be  3 1/2 divided by 1/6.

= 7/2 / 1/6

= 7/2 * 6

= 42/2

= 21 glasses.

Answer:

A =338.56 units ^2

Step-by-step explanation:

The area  is now

A = (SF)^2 * s^2

where s is the side length and SF is the scale factor

A = (4)^2 (4.6)^2

A =338.56

The probability of not selecting a green marble is equal to the total number of non-green marbles in the bag divided by the total number of marbles in the bag.

To calculate the probability: there are three green marbles out of a total of twenty-five marbles, so the probability of selecting a green marble is 3/25.

The likelihood of not selecting a green marble is then 1 - 3/25 = 22/25.

This is equal to 22/25 * 100 = 88% as a percentage.

As a result, P(not green) = 88%

Probability denotes the possibility of something happening. It is a mathematical branch that deals with the onset of a random event. The value ranges from zero to one. Probability has been tried to introduce in mathematics to predict the probability of events occurring. Probability is defined as the degree to which something is likely to occur. This is the fundamental probability theory, which is also used in probability distribution, in which you will learn about the possible outcomes of a random experiment.

To know more about random event visit :-

https://brainly.com/question/15186748

#SPJ1

Answer:

314/25π inches

I hope this helps!

Answer:

See attached graph for the two functions

y = cos(x)

y = 0.5

Solution set for cos(x) i.e. the values of x for which cos(x) = 0.5 in the interval 0 < x < 2π are
{π/3, 5π/3)

or

{1.05, 5.24}  in decimal

Step-by-step explanation:

I moved the original horizontal up to y = 0.5

The solutions to the two equations are where the two functions intersect

There are two intersection in the interval 0 ≤ x ≤ 2π and are at the points labeled A and B

The two points can be obtained by setting
cos(x) = 0.5 and solving for x

cos(x) = 0.5

=> x = cos⁻¹ (0.5)

= 60° and 300° in the range 0 ≤ x ≤ 2π where 2π = 360°

In terms of π,

Since π radians = 180°, 1° = π/180 radians

60° = π/180 x 60 = π/3 radians

300° =  π/180 x 300 = 5π/3 radians

Therefore the solutions to cos(x) = 0.5 are
x = π/3 and x = 5π/3
The solution set is written as {π/3, 5π/3}

In decimal

π/3 = 1.04719 ≈ 1.05

5π/3 = 5.23598 ≈ 5.24

Solution set in decimal: {1.05, 5.24}

Hey there! :)

Answer:

15° Celsius.

Step-by-step explanation:

Begin by deriving an equation to represent the values in the table. Use the slope formula:

\(m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}\)

Plug in values from the table into the formula:

\(m = \frac{27.0 - 22.2}{15-9}\)

Simplify:

\(m = \frac{4.8}{6}\)

Reduces to:

m = 0.8. This is the slope of the equation.

Use a point from the table and plug it into the equation y = mx + b, along with the slope to calculate the y-intercept:

27 = 0.8(15) + b

27 = 12 + b

27 - 12 = b

b = 15. This represents the value when x = 0, therefore:

The engine's temperature at rest is 15° Celsius.

Answer:

15

Step-by-step explanation:

Answer:

\(\frac{x^3}{y^7}\)

Step-by-step explanation:

The key to answering this question is the exponential law that says \(a^{-n} = \frac1{a^n}$\) :

\(\frac{y^{-7}}{x^{-3}} \\ \\\to \frac{\frac1{y^7}}{\frac1{x^3}} \\ \\\to \frac1{y^7} \times \frac{x^3}1 \\ \\\to \frac{x^3}{y^7}\)

Answer:

I think it would be each girl scored 2 points, and each boy only scored one. :)

Answer:

3*4 is 12, 12*4 is 48, 48*4 is 192, so the answer is 192

If m=6, then 3×6= 18.

43-18=25

Your answer is 25.

Step-by-step explanation:

Can I have brainly please!

EVALUATE EXPRESSION

Step-by-step explanation:

43-3m=??             if m=6

substitute

43-3 * 6= 25

Answer:

293.5

Step-by-step explanation:

Harry Potter RP!!

https://brainly.com/question/20615441

The number of customers when there are 576 towers will be 12.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

Based on the information, it should be noted that the number of phone is proportional to the number of customers

The constant of proportionality will be:

= 252 / 5.25

= 48

Therefore, the customers when there are 576 towers will be:

= 576 / 48

= 12

Learn more about word problem on:

brainly.com/question/21405634

#SPJ1

The number of brownies and large cookies will be same that is 20 each.

What are inequalities ?

When two values are compared , an inequality represents whether one is greater than, less than, or not equal to the other.

It is given that the brownies cost $4 each and large cookies cost $6 each.

Let's assume the number of brownies be x and large cookies be y.

And as per the question , She is trying to make at least $200 but wants to make no more than 75 items.

So , to represent this we need an inequality which will be as follows:

Cost of x brownies = 4x

Cost of y cookies = 6y

So , inequality will be :

4x + 6y ≤ $200 --- --- --- --- --- --- --- -- - Equation 1

and

Number of brownies and cookies should not be more than 75 items. i.e.,

x + y < 75 --- --- --- --- --- --- --- -- -- -- -- -- -- Equation 2

Let's check for which value of x and y this is suitable. So , simplify equation 1 : (dividing by 2 )

2x + 3y ≤ $100

If we put x = 20 and y = 20 , then

2 × 20 + 3 × 20 = $100

$100 = $100

So , the equation is satisfied which meant the number of brownies and cookies will be equal which is 20.

Let's check it with equation 2 also :

So ,

20 + 20 < 75

40 < 75

This is also satisfied.

Therefore ,  the number of brownies and large cookies will be same that is 20 each.

Learn more about inequalities here :

brainly.com/question/25275758

#SPJ1

\(\tt\displaystyle\ 3c\underline{(p-6)}+4\underline{(p-6)}=(p-6)(3c+4)\)

Given:

One week a computer store sold a total of 36 computers and external hard drives.

Let the number of computers = x

And the number of the external hard drives = y

so, we can write the following equation:

The revenue from these sales was 29,820. If computers sold for 1180 and hard drives for 125 per unit

So, we can write the following equation:

We will solve the equations (1) and (2) to find (x) and (y):

from equation (1):

Substitute (y) from equation (3) into equation (2) and then solve for (x):

Substitute (x) into equation (3) to find (y):

So, the answer will be:

The number of computers sold = 24

The number of hard drives sold = 12

An equation of the tangent line to the curve \(x e^y+y e^x=4\) at the point (0, 4) is \(y=-(4+e^4) x+4\).

A tangent is described as a line that intersects a circle or an ellipse only at one point. If a line touches a curve at P, the point "P" is known as the point of tangency.

Now according to the question;

To obtain the tangent at a given point, we must first obtain the slope at that point by obtaining the differentiation value at that point  \(\left.y^{\prime}\right|_{x=0, y=4}\) as-

Consider the given equation;

\(x e^y+y e^x=4\)

Differentiate both side with respect to x;

\(\begin{aligned}&\frac{d}{d x}\left(x e^y+y e^x\right)=\frac{d}{d x} 4 \\&\frac{d}{d x} x e^y+\frac{d}{d x} y e^x=0\end{aligned}\)

Now apply product rule;

\(\begin{aligned}&e^y \frac{d}{d x} x+x \frac{d}{d x} e^y+e^x \frac{d}{d x} y+y \frac{d}{d x} e^x=0 \\&e^y \frac{d}{d x} x+x \frac{d}{d y} e^y \cdot y^{\prime}+e^x y^{\prime}+y \frac{d}{d x} e^x=0\end{aligned}\)

Applying exponential and power rule;

\(\begin{aligned}&e^y \cdot 1+x e^y \cdot y^{\prime}+e^x y^{\prime}+y e^x=0 \\&\left(x e^y+e^x\right) y^{\prime}=-y e^x-e^y\end{aligned}\)

Solve the value of y'

\(y^{\prime}=\frac{-y e^x-e^y}{x e^y+e^x}\)

Now, find the value of slope m.

\(m=\left.y^{\prime}\right|_{x=0, y=4}\)

\(\frac{-4 \cdot e^0-e^4}{0 e^4+e^0}=-4-e^4\)

Now, using the point-slope formula, obtain the line equation as follows.

\(\begin{aligned}&\left(y-y_1\right)=m\left(x-x_1\right) \\&(y-4)=-(4+e^4) \cdot(x-0) \\&y=-(4+e^4) x+4\end{aligned}\)

Therefore, an equation of the tangent line to the curve is   \(y=-(4+e^4) x+4\).

To know more about the tangent line, here

https://brainly.com/question/6617153

#SPJ4

Answer:

620

Explanation:

When the sample is given, the number of elk are likely to be infected is to be considered as the 620.

Calculation of the number of elk:

Since the population is 7,750.

The random sample is 50.

So here be like

= 620

hence, When the sample is given, the number of elk are likely to be infected is to be considered as the 620.

Answer:

Below

Step-by-step explanation:

Formula :     FV = PV ( 1 + i)^n      <====you just have to LEARN/KNOW this

         FV = future value = ?      PV = present value = 5000

          Periods per year 4      n = periods = 40

           interest per period in decimal form  .065/5

Plug in the values :

FV = 5000 (1 + .065/4)^40 = 9527.79 dollars

Answer:

176

Step-by-step explanation:

91/9.10=0.10

17.60/0.10=176

Answer:

176

Step-by-step explanation:

Answer:

There will be 15 2/3 cups in the mixture.

Step-by-step explanation:

3 3/5 + 2 2/3 = 3 9/15 + 2 10/15 = 5 19/15

= 6 4/15

6 4/15 × 2 1/2 = 94/15 × 5/2 = 47/3 = 15 2/3

So there will be 15 2/3 cups in the mixture.

Answer:

The slope of line d is 3/2 since the slopes of perpendicular lines are negative reciprocals of each other.

So the correct equation is

-2/3 × slope of d = -1

Answer:

3/2

Step-by-step explanation:

If a line is perpendicular to the other it's slope is the inverse reciprocal of the other slope

Queueing system can be analyzed using queueing theory to determine performance measures such as the average queue length, average waiting time, and utilization of the service channels.

The queueing system you have described can be modeled as an M/M/7 queue, where:

M represents that inter-arrival times and service times are exponentially distributed.

M represents that the arrival process is memoryless, meaning that the probability of a customer arriving at any given time does not depend on the previous arrival times or the state of the system.

7 represents the number of service channels, or lanes, available for customers to pay their toll.

The notation for this system is M/M/7, which indicates that it has an infinite queue capacity and that there is no limit to the number of customers that can be waiting in the queue.

In this queueing system, customers arrive randomly and independently, and they join the queue if all lanes are busy. They are served on a first-come, first-served basis, with the service times also being exponentially distributed.

This queueing system can be analyzed using queueing theory to determine performance measures such as the average queue length, average waiting time, and utilization of the service channels.

for such more question on Queueing system

https://brainly.com/question/16332322

#SPJ11

Answer:

thn 6<7<8 is your answer