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
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
PLEASE HELP!! WILL GIVE BRAINLIEST An artist has been commissioned to make a stained glass window in the shape of a regular octagon. The octagon must fit inside an 16-in. square space. Determine the length of each side of the octagon. Round to the nearest hundredth of an inch.
Work out the surface area of this cylinder.
12 cm
35 cm
Answer:
The surface area of this cylinder is 3545 cm²
∵ π =
∴ The lateral area = 24 × × 35.
∴ The area of the base = × (12)² = (144) = 452 cm²
∴ The surface area = 2640 + 2(452 ) = 3545 cm²
∴ The surface area of this cylinder is 3545 cm²
Step-by-step explanation:
Hope it is helpful.....
A rectangular prism has a length of 14ft, a height of 8ft, and a width of 15ft. What is
its volume, in cubic ft?
Answer:
37
Step-by-step explanation:
14 + 8 + 15
Answer: 1680³
Step-by-step explanation:
length x width x height
14 x 15 x 8
What is the equation of the circle with a radius of 4 and a center at (3, 2) ?
Answer:
(x - 3)^2 + (y + 2)^2 = 16
Step-by-step explanation:
(x - h)^2 + (y - k)^2 = r^2
r = radius
(h, k ) is center of circle.
The center of the circle is (3, 2) and r is 4.
(x - 3)^2 + (y + 2)^2
16
Best of luck :3
PLEASE PLEASE PLEASE HURRY!!!! I WILL GIVE BRAINLIEST!!!!!!!!!!!!! Which TWO ARE CORRECT?
Answer: D and E I'm sure
What is the 30th term of the arithmetic series 3, 7, 11, ...?
118
119
120
121
Answer:
119
Step-by-step explanation:
common different: 7-3=4
initial value =3
so x-3=(n-1)d
only 119-3=116 is divisible by 4
It's the ans cuz n-1 has to be integer
Craft project
Mariah has the pool of ribbon shown at the right and 1/2 yard of fabric for a craft project. She wants to cut the ribbon into 6 equal pieces. How long is each piece of ribbon?
Question:
6: Find the length of each ribbon piece in inches. Show your work.
Answer:
the answer is 1 over 12
The captain of the basketball team wants to determine where the team should go for their end-of-season celebration. Which of the following is a representative sample? Select all that apply.
A.
The students in her homeroom
B.
Players whose names are randomly selected from a hat
C.
The players in the starting lineup
D.
All players over 5 feet tall
E.
Every 5th player selected from an alphabetical roster of the team
The representative samples are Players whose names are randomly selected from a hat and Every 5th player selected from an alphabetical roster of the team. (Option B and E).
What is Representative Sample?A representative sample is a subset of a larger population that accurately reflects the characteristics, diversity, and distribution of the entire population. When conducting research or making decisions based on data, it is often impractical or impossible to collect information from every individual in the population. Instead, researchers or decision-makers select a representative sample to draw conclusions or make inferences about the entire population.
For a sample to be considered representative, it should be selected in a way that ensures each member of the population has an equal or proportional chance of being included. In the given problem, both options provide a fair chance for each team member to be included in the selection for the end-of-season celebration destination.
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Please help now due in 25 minutes!!!
Answer:
y=8x+1
Step-by-step explanation:
The slope is a positive 8 because the line is going upwards. Slope equals rise over run. The rise is 8 units, and the run is 1 positive unit since it is going to the right. So 8/1 is 1. There's a +1 in the equation because the y-intercept is at positive 1. The y-intercept is where the line crosses the y-axis (vertical line). Here, the line crosses it at 1.
Find the circumference of the given circle
Use 3.14 as an approximation
7 in.
Answer:
Step-by-step explanation: Determine the radius of a circle. ...
Substitute this value to the formula for circumference: C = 2 * π * R = 2 * π * 14 = 87.9646 cm .
You can also use it to find the area of a circle: A = π * R² = π * 14² = 615.752 cm² .
The circumference of the given circle is approximately 43.96 inches.
Given that a circle with radius of 7 inches, we need to find the circumference of the circle,
We know that,
In the case of a circle, the circumference is the distance around the circle.
It is the total length of the curve that forms the boundary of the shape.
To find the circumference of a circle, you can use the formula:
Circumference = 2π × radius
The radius of the circle is 7 inches, and using the approximation of π as 3.14, we can substitute these values into the formula:
Circumference = 2 × 3.14 × 7
Circumference = 43.96 inches
Therefore, the circumference of the given circle is approximately 43.96 inches.
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f(x) = 4x - 12
F1(x)=
PLEASE HELP 20 POINTS
Stephen and Chelsea want to increase the volume of this prism by 72 cubic centimeters. Chelsea wants to add eight layers, and Stephen says they only need to add four layers. Their teacher tells them they are both correct. Explain how this is possible.
Step-by-step explanation:
2.
- the volume of initial prism is 3*3*6=54 cm³;
- the number of cubics of the requested 72 cm³ is 72;
- 'Chelsea wants to add eight layers' means 72=3*3*8 cubics, then one layer in this case consists of 3x3 cubics;
- 'Stephen says they only need to add four layers' means 72=4*3*6 cubics, then one layer in this case consists of 3x6 cubics.
3.
- the volume of initial prism is 4*4*1=16 in³; it means one layer is 16 inches³;
- according to the requirement 3 layers is 16*3=48 in³; three times 16.
- according to the requirement 5 layers is 16*5=80 in³; five times 16.
- according to the requirement 7 layers is 16*7=112 in³; seven times 16.
If f ( x ) = 1 3 x − 5 , what is f ( − 6 ) ?
Answer:
-4
Step-by-step explanation:
by finding the exact value.
For each of the following four statements, indicate whether it is possible or not according to probability theory. Explain your answer. (1) The probability that a customer will buy 5 items in a single purchase is 30% ___________________________ (2) The probability that a customer will buy 3 items in a single purchase is 101% ___________________________ (3) The probability that a customer will buy 3 items in a single purchase is 99% ___________________________ (4) The probability that a customer will buy 8 item
Answer:
a) According to probability theory, the following are possible:
(1) The probability that a customer will buy 5 items in a single purchase is 30%. This represents a 0.30 chance of the customer buying 5 items.
(3) The probability that a customer will buy 3 items in a single purchase is 99% This means that there a 0.99 chance that the customer will buy 3 items.
b) According to probability theory, the following are not possible:
2) The probability that a customer will buy 3 items in a single purchase is 101%. Probability is always equal to 1 or 100%. It cannot exceed 100%.
(4) The probability that a customer will buy 8 item. This part lacks the necessary information to solve the problem.
Step-by-step explanation:
Probability describes the likelihood or chance of an event happening out of the many possible events that can take place. The sum of all probabilities for a particular event is always equal to 1. This shows that probability does not exceed 100%.
A circle has a diameter of 16 centimeters.
What is the best approximation of its area?
Use 3.14 to approximate for π.
Question 7 options:
803.84 cm2
50.24 cm2
200.96 cm2
Answer:
Step-by-step explanation:
Area of a circle=πr²
Radius = 16/2=8 Area of a circle=3.14×8×8
= 3.14×64
= 200.96cm²
= 201 cm² to the nearest unit.
What is the volume of a cylinder, in cubic inches, with a height of 13 inches and a
base diameter of 12 inches? Round to the nearest tenths place
Answer:
Rounded to the nearest integer, the volume of the cylinder is 5,878 cubic inches.
Step-by-step explanation:
Given that the volume of a cylinder is calculated using the formula Phi x Radius ^ 2 x Height, and knowing that the cylinder in question has a height of 13 inches and a base diameter of 12 inches, to calculate said volume the following calculation must be done:
Phi x (12x12) x 13 = X
Phi x 144 x 13 = X
Phi x 1,872 = X
3.14 x 1,872 = X
5,878.08 = X
Thus, rounded to the nearest integer, the volume of the cylinder is 5,878 cubic inches.
The answer is 1470.3
Uniforms are sold into packages of 8. The store's 127 employees will be given 3 uniforms. How many packages will the store need order?
Answer:
48 packages
Step-by-step explanation:
Hello There!
The first step is to find out how many uniforms they need to do so we multiply 127 and 3
3x127=381
Then we divide it by 8 ( because that's how many uniforms are sold in one package.)
381/8=47.625
you cannot have a 6th of a package so we just round to the nearest whole
so we can conclude that they will need 48 packages
~TheMathWiz
a bakerysells a cake for 250.00 pesos. the labor cost 32.50pesos per cake.flour costs 31.85pesos.other costs add up to 92.10pesos.what is bakery's profit on each cake.what is the operation to be used?
deduct one whole number from the other number
Read the sentences below. They are the first part of a summary of the article. Atoms are the building blocks of everything. They are too tiny to be seen. Atoms are made up of electrons, protons and neutrons. Which answer BEST completes the summary? A Each atom has a special number and element B Each atom has some oxygen and hydrogen. с Each atom has an atomic number of 1. D Each atom is made up of 100 elements.
Answer:
A (i think)
Step-by-step explanation:
If i'm right please mark me branliest
What is the surfsce area of the prism with 12 cm 11 cm and 10,cm
Answer:
Step-by-step explanation:
The surface area of a rectangular prism is
A=2(xy+xz+yz). where x,y,z are its dimensions, in this case
A=2(12(11)+12(10)+11(10))
A=2(132+120+110)
A=2(362)
A=724 cm^2
Answer: 724cm²
Step-by-step explanation:
The formula is: 2(lw + hl + hw). Our units are 12, 11, and 10. So, the Length, Width, and Height are,
12 is the Length.
11 is the Width
10 is the Height.
Let's solve now. Our problem will be written like this,
2 · (11 × 12) + (10 × 12) + (10 × 11)
Let's solve.
1. Multiply 11 by 12.
11 × 12 = 132
2. Multiply 10 by 12.
10 × 12 = 120
3. Multiply 10 by 11.
10 × 11 = 110
4. Add up all the products.
132 + 120 + 110 = 362
5. Multiply 362 by 2.
362 × 2 = 724
Hence, 724 is the answer.
Write the slope of a line that is parallel to the following line:
Answer:
y = 1/5x + 3
Step-by-step explanation:
To have a parralel line to another line, have the slopes of the lines be the same, just change the y- intecept. HOPE THIS HELPS!
(20 points)
What is the value of x?
☁︎
A:10
☁︎
B:20
☁︎
C:12
☁︎
D:15
Answer:
honestly I don't know 5
Step-by-step explanation:
Sighient Store
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Question 3 of 28
05056E
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Tect
0%
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IMG_90
The accompanying table contains the individual demand schedules of dark chocolate for Vanessa and Angela. Assuming
they are the only people in the market for dark chocolate, place each of their individual demand curves and the market
demand curve at the correct locations on the accompanying graph.
Price of dark
Pounds of dark chocolate Pounds of dark chocolate
chocolate
demanded by Vanessa
demanded by Angela
(per pound)
$8
1
3
%
IMG 90
00%
$1
3
5
orrect
0%
Market for Dark Chocolate
10
0%
Vanessa
Angela
Market
9
0%
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if -3x-8=16 what is the value of -2(x-7)
Answer:
-3x-8=16
-3x = 16+8
-3x = 24
x = 24/-3
x = -8
= -2(x-7)
= -2(-8-7)
= 30
Hope this helps you. Do mark me as brainliest.
The area of a rectangular field of length 12 m is 108 sq.m
Find the width of the field.
Answer:
width of rectangle is 9m
Lori wants to trade more than 3/10 but less than 4/5
Answer:
i dont know what you are asking but 3/10-8/10
Step-by-step explanation:
Diana is training for a marathon. The total miles she runs varies from week to week but follows the pattern described in the table. At the beginning of her training, Diana limited her distance so that she did not run more than 10 miles during the first three days of the week. Write an inequality you can use to find the possible distances Diana may have run on Monday during the first week of training. Solve the inequality Describe the reasonable solutions
Answer:
The inequality 3x-(x-1)>5 represents this situation. Since Diana can run more than 1 mile on tuesday and more than 6 miles on sunday.
Step-by-step explanation:
Round 117.22666 to the nearest tenths
Answer:
117.2
Step-by-step explanation:
I hope this helps a little bit.
What is the total surface area of the pyramid below?
5 ft
-
6ft
6 ft
Please I need answer!
Answer:
17 ft that's the ans
I don't know if it is correct