A certain type of aluminum screen has, an average, one flaw in a 100-foot roll. Assume the flaw distribution approximately follows the Poisson distribution. (a) Find the probability that a 100-foor roll has at most 2 flaws. (b) Suppose that I bought 10 200-foot rolls, find the probability that there are exactly 3 rolls that have no flaws in them. (c) Suppose that a store had many 200-foot rolls in storage, a clerk is doing inspections. What is the probability that the 15th roll he inspected was the 3rd one that have no flaws in it

Answers

Answer 1

Answer:

a) 0.9197 = 91.97% probability that a 100-foor roll has at most 2 flaws.

b) 0.1074 = 10.74% probability that there are exactly 3 rolls that have no flaws in them.

c) 0.0394 = 3.94% probability that the 15th roll he inspected was the 3rd one that have no flaws in it.

Step-by-step explanation:

To solve this question, we need to understand the Poisson and the Binomial distribution.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

(a) Find the probability that a 100-foor roll has at most 2 flaws.

A certain type of aluminum screen has, an average, one flaw in a 100-foot roll, which means that [tex]\mu = 1[/tex]. Only one roll means that the Poisson distribution is used.

This is:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

In which

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-1}*1^{0}}{(0)!} = 0.3679[/tex]

[tex]P(X = 1) = \frac{e^{-1}*1^{1}}{(1)!} = 0.3679[/tex]

[tex]P(X = 2) = \frac{e^{-1}*1^{2}}{(2)!} = 0.1839[/tex]

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.3679 + 0.3679 + 0.1839 = 0.9197[/tex]

0.9197 = 91.97% probability that a 100-foor roll has at most 2 flaws.

(b) Suppose that I bought 10 200-foot rolls, find the probability that there are exactly 3 rolls that have no flaws in them.

Two parts.

Probability that a single 200-foot roll has no flaw.

This is [tex]P(X = 0)[/tex], Poisson(single 200-foot roll) when [tex]\mu = \frac{200*1}{100} = 2[/tex]. So

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-2}*2^{0}}{(0)!} = 0.1353[/tex]

0.1353 probability that a single 200-foot roll has no flaw.

Probability that on 10 200-foot rolls, 3 have no flaws.

Multiple 200-foot rolls means that we use the binomial distribution.

0.1353 probability that a single 200-foot roll has no flaw means that [tex]p = 0.1353[/tex]

10 200-foot rolls means that [tex]n = 10[/tex]

We want [tex]P(X = 3)[/tex]. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{10,3}.(0.1353)^{3}.(0.8647)^{7} = 0.1074[/tex]

0.1074 = 10.74% probability that there are exactly 3 rolls that have no flaws in them.

(c) What is the probability that the 15th roll he inspected was the 3rd one that have no flaws in it.

0.1353 probability that a single 200-foot roll has no flaw means that [tex]p = 0.1353[/tex]

2 with flaws in the first 14, which is [tex]P(X = 2)[/tex] when [tex]n = 14[/tex]

The 15th has no flaw, with probability of 0.1353. So

[tex]P = 0.1353*P(X = 2) = 0.1353*(C_{14,2}.(0.1353)^{2}.(0.8647)^{12}) = 0.1353*0.2911 = 0.0394[/tex]

0.0394 = 3.94% probability that the 15th roll he inspected was the 3rd one that have no flaws in it


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Answers

Answer:

C

Step-by-step explanation:

area of circle is found by [tex]\pi[/tex][tex]r^{2}[/tex]

r=4 so 4*4=16

so A=16[tex]\pi[/tex]

we are finding area of shaded part so 45/360(16[tex]\pi[/tex])

The area of the shaded sector is (45/360)16π square units if Henry constructed circle A with a radius of 4 units option (C) is correct.

What is a circle?

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

It is given that:

Henry constructed circle A with a radius of 4 units.

Henry then created a sector as shown in the figure below.

As we know, the area of the sector can be find using the formula:

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Here, θ is the central angle

r is the radius

π = 3.141

r = 4 units

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Step by step explanation
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Leave a like and brainliest!

What value of x is in the solution set of 2x - 3> 11 - 5x?
0 -3
O 0
O2
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Answers

Answer:

The answer is x>2, x has to be greater than 2,

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34. CONSTRUCTION A construction worker is working on the roof of a
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Answers

Answer:

t = 6.77 s

Step-by-step explanation:

Given that,

A drop of paint falls from a rafter that is 225 feet above the  ground.

We need to find the time when the paint hit the ground. Let the time be t.

Using the second equation of kinematics i.e.

[tex]s=ut+\dfrac{1}{2}at^2[/tex]

Where

u = 0 (initial velocity is 0 as it was at rest)

a = g

So,

[tex]225=\dfrac{1}{2}\times 9.8t^2\\\\t=\sqrt{\dfrac{2\times 225}{9.8}} \\\\t=6.77\ s[/tex]

So, it will hit the ground at 6.77 s.

Josiah bought two pounds of strawberries for $9.60. What is the price, in dollars per ounce of strawberries? 1 pound = 1 pound= 16 ounces 16 ounces Before you try that problem, answer the question below. How many ounces of strawberries did Josiah buy?

Answers

Answer:

$0.30 per ounce

Step-by-step explanation:

16 ounces per pound

16 x 2 = 32 ounces per 2 pounds

9.60/32 = $0.30 per ounce


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Answer:

True

Step-by-step explanation:

Hope this helps you

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Answers

Answer:

height = 184.7 feet

Step-by-step explanation:

sin 38 = height/300

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height = 184.7 feet

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Answers

Answer:

209 robberies

Step-by-step explanation:

Robberies last year =348

Robberies has reduced by 40% which means there are (100-40)% = 60% robberies this year.

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There are 209 robberies this year.

I hope this help.  

Easy brainliest for correct answer 100%

Answers

Answer:

B) A/l

Step-by-step explanation:

Isolate the variable, w. Note the equal sign, what you do to one side, you do to the other.

Divide l from both sides of the equation:

A = l * w

(A)/l = (l)/l * w

w = A/l

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~

the answer is (B) = 4/I .

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Answers

Answer:

Option 3

Step-by-step explanation:

[tex]\left(x+3\right)^{\frac{1}{3}}+3[/tex]

Answer:

option 4 on edg

Step-by-step explanation:

y=3(x+3) +3

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Answers

Answer: You have the correct answer. It's choice A.

Explanation:

You can verify this by plugging each root into the equation.

So for instance, plug in x = -2 and we get

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f(-2) = -3*(0)*(-2-sqrt(3))*(-2-4)

f(-2) = 0

This verifies x = -2 is a root.

All that matters is that zero buried in there in the second to last step. Multiplying 0 by anything leads to 0. The other roots are verified in the same manner. The -3 out front is the leading coefficient.

----------------

Extra info:

Choice B is eliminated because (x+3) being a factor implies that x = -3 is a root. But this isn't listed in the instructions.Choice C is a similar story to choice BChoice D is eliminated since -sqrt(3) is not one of the listed roots, so (x+sqrt(3)) is not a factor.
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Answers

Answer:

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732

Step-by-step explanation:

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Answers

It would be a right angle

Answer:

A right angle.

Step-by-step explanation:

Hope this helps! Have a great rest of your day!

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Answer:

C is the answer according to me

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Answer:

no, they are not.

Step-by-step explanation:

3z means a number multiplied by 3

so if z is 2, 3(2) = 6

but z^3 means z multiplied by z, and then multiplied by z again.

so if z is 2, it's 2x 2 = 4 x 2 = 8

let me know if you have questions

The two expressions are not equivalent to each other.

What are equivalent expressions?

Equivalent expressions are expressions that are equal and synonyms to each other when used differently with various mathematical concepts.

From the expressions given:

z^33z

The first expression is a variable (z) raised to a power of 3. The power is also called an exponent.The second expression is a variable(z) that has a coefficient of 3

Let us assume that:

z^3 = 3z

Now, let's replace 2 for the value of z on both sides, we have:

(2)^3 = 3(2)

8 ≠ 6

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i believe it is 1.5. just divide 3 by two to solve the equation.

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Answers

Answer:

9 + 22h

Explanation:

The question is incomplete as Gordon's height is not given. To solve further, we will represent this height with h

So, we have:

nine more than the [tex]product[/tex] of 22 and [tex]Gordons\ height[/tex]

More than, in this case means plus (+)

nine + the [tex]product[/tex] of 22 and [tex]Gordons\ height[/tex]

Rewrite nine as 9 and substitute h for Gordons height

9 + the [tex]product[/tex] of 22 and h

product, in this case means multiplication (*)

9 + 22 * h

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9 + 22h

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Answers

Answer: 98.1%

Explanation:

A 10% sale means that the post-sale price of the item is now 90%, or 0.9 of the original cost of the item. We then apply 9% sales tax by multiplying the 0.9 by 109%, or 1.09. 0.9 * 1.09 = .981, so the total cost of the item is 98.1% of the original pre-sale sticker price.

For percentage problems that do not deal with a specific starting number, it is always helpful to plug in 100 for the starting number. Here, we would then have a post-sale price of 90 dollars, and if we calculate the sales tax for the 90-dollar item it would be 90 * 0.09 = $8.10. THis gives us a total cost of 90 + 8.10 = $98.10, or 98.1% of the original 100-dollar price.

Answer: 98.1 % (other answer above got it as well but hope this helps anyway :)

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Answers

Answer:

6.25 ft

Step-by-step explanation:

The smaller flag width is 5. And the larger flag is not that big in size. So the close answer is 6.25

Answer:

6.25ft

Step-by-step explanation:

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Answers

Answer: 3sqm

Step-by-step explanation:

Solve for x.
(Round to the nearest hundredth)

Answers

Answer:

Step-by-step explanation:

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What would you call the expression 2x -5y - 7?

Answers

Answer:

Trinomial

Step-by-step explanation:

Its called a Trinomial since it has 3 terms in it                                                                                                                                

Hope its helps!

The graph of f(x)shown below resembles The graph of g(x)x^4,But it has been vertically compressed. Which of the following could be the equation of f(x)? 
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B f(x)2x^4
C F(x)=-1/2x^4
D f(x)=1/2x^4
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A!!!!!!!!!!!!!!!!!!!

Help me plzzzzzzzzzz.z.z.z.z.z.z..z.z.z.z

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Answer:

Area of rectangle = 10 in.²

Area of triangle = 0.5 in.²

Square inches of plastic in bookmark = 9.5 in.²

Step-by-step explanation:

✔️Area of rectangle = Length × Width

Length = 5 in.

Width = 2 in.

Area of rectangle = 5 × 2 = 10 in.²

✔️Area of Triangle = ½*bh

b = 1 in.

h = 1 in.²

Area of triangle = ½*1*1

Area of triangle = 0.5 in.²

✔️Square inches of plastic in bookmark = area of rectangle - area of triangle

= 10 - 0.5 = 9.5 in²

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