Answer:
hi
Step-by-step explanation:
The rope is originally 100 ft. long. The first piece is 32 ft., leaving 100–32, or 68 ft.
Let n be the second piece, and n-30 be the third piece. Then:
n+n-30=68
2n=98
n=49
n-30=19
The second piece is 49 ft. long; the third piece is 19 ft. long ……..
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
Jamie wants to treat some friends to lunch. He has $40 and knows the lunch will cost about $7 per person p. How many people can Jamie buy lunch for.
Answer:
5 people
Step-by-step explanation:
40/7=5.71
Thats not enough for 6 people so you go down to 5 people, you can't have 5.71 of someone
Factor the algebraic expression.
12a+9
In ΔMNO, m = 55 inches, n = 48 inches and o=59 inches. Find the measure of ∠O to the nearest 10th of a degree.
Answer: 69.5 degree
PLZ HELP DUE IN 8 MINS PLZ HELP
Answer: for number 1 its negative 14
Step-by-step explanation:
PART A: is this a proportional relationship?
PART B: if this is a proportional relationship, what is the constant?
PART C: if this is a proportional relationship, write a direct proportional equation.
Please help please thank
Answer:
3/4 of an hour
Step-by-step explanation:
the longest is 1 hour. the shortest is 1/4 of an hour. 1 minus 1/4 is 3/4
Please help
A 136
B 208
C 352
D 576
Answer im not in grade
Step-by-step explanation:
A small jar of peanut butter sells for 0.08 per ounce. A large jar of peanut butter sells for $1.20 per pound. Which is the better buy and by how much (in cents per pound)?
Answer:
a small jar of penuts buteer sells for 0.08 per ounce
A large jar of penut buttter sells for $1.20 per pound
the answer is :
hope it will help you
look at pic
14 points
Answer:
The Second One I Think
Step-by-step explanation:
By what I understand that would be the one that is in standard form
What is the distance of -a and a?
Step-by-step explanation:
Distance = positive value
a + a = 2a
Answer:
I think its 0
Step-by-step explanation:
becuase if you add the same number but on is negative and the other is positve it is always a 0.
Example:
10 + (-10) = 0
7. Bella scored 8 points in the second round. This
made her total score 39. How many points did she
score in the first round?
In a certain town there were 348 robberies last year. This year the number of robberies has gone down 40%. How many robberies were there this year, to the nearest whole number?
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.
Number of robberies this year= 60% of 348 = 60/100 × 348 = 208.8
To the nearest whole number = 209
There are 209 robberies this year.
I hope this help.
Pls help due tomorrow if correct ill give brailiest
Answer:
Add 3 each term inside the parentheses, then use inverse operations to solve.
Step-by-step explanation:
Answer this correctly I'll give brainalist + 10 points
Answer:
x=90-73=17
Step-by-step explanation:
Answer:
I think it might be 17... sorry if u get ir wrong
in a major study by the statistics classes at Washington High School, city parking spaces were examined for compliance with the requirement to put money in the parking meters. Overall, the students found that 76% of metered parking places had meters that had NOT expired, and 24% had meters that were expired. If the traffic officer in charge of ticketing cars with expired meters checks meters at random, what is the probability he will find an expired meter BEFORE the 3rd one
Answer:
0.4224 = 42.24% probability he will find an expired meter BEFORE the 3rd one
Step-by-step explanation:
For each car, there is a 24% probability that it had expired parking meters.
What is the probability he will find an expired meter BEFORE the 3rd one?
Three possible outcomes:
Two expired(each with 24% probability)
First expired(24% probability) and second not(76% probability)
First not(76% probability) and second expired(24% probability). So
[tex]p = 0.24^2 + 2*0.24*0.76 = 0.4224[/tex]
0.4224 = 42.24% probability he will find an expired meter BEFORE the 3rd one
A school earns $70 from selling 50 tickets for the school play. Each ticket costs the same price.
How much does the school earn for one ticket ??
Find the area of the parallelogram.
The area of the parallelogram is [a] in2.
Answer:
A = 117in²
Step-by-step explanation:
A = bh
A = 9×13
A = 117in²
13
×9
117
Since it's a parallelogram where going to do the formula b×h.
Answer:
117in²
Step-by-step explanation:
Expressions can be written using a combination of numbers and letters. Those values can also be described using words. Choose ALL expressions that are correctly described in words.
which is it
Answer:
A: 3a + 9: the sum of three times a and nine
C:15b − 10: ten less than the product of fifteen and b
Step-by-step explanation:
I just answer this question in US, and I got C right but choose the wrong answer for A.
These are the right answers.
A share of ABC stock was worth $60 in 2000 and worth $1920 in 2005.
Write an exponential function that models the value of the stock starting
from 2005.
Answer:
A share of ABC stock was worth $60 in 2005 and only worth $45 in 2010. ... diftolence b. Write an exponential function that ...
Answer this correctly I’ll give brainalist + 10 points
Answer: 118
Step-by-step explanation:
These angles are a linear pair. They sum to 180 degrees.
62 + x = 180
-62 -62
X= 118
Which expression is equivalent to the expression below?
g + g+g+g+g+g
Answer:
6 x g
Step-by-step explanation:
Answer:
[tex]g^{6}[/tex]
Step-by-step explanation:
Given a and b are numbers, and a + b = 180, which
statements also must be true?
a = 180 - 6
a - 180 = b
360 = 2a + 2b
a = 90 and b = 90
round 0.50062 to 2 significant figures
Answer:
0.50
Step-by-step explanation:
Count figures after the decimal
Keeping it simple by asking for more help. Question 10.
Answer: I will go with A or you can choose d if you want
Step-by-step explanation:
Brainliest stars
21)
In which container is the probability of randomly selecting a red ball on one draw 3/7?
Answer: Your answer is going to be C)
Here is my explanation, very simple! So if you count all the balls together in answer's A) B) and D) there aren't 3 balls in each, so for example answer A) has 4 red ball's. B) only has 1 red ball, D) also has 1 ball, so C) is your only reasonable answer because although all the containers have a total of 7 ball's there is not enough for your probability. being said your container/answer is C!
Answer: c
Step-by-step explanation: the girl up there said it
How do I answer this ? (1 + 3x)º
44°
Answer:
132x+44
Step-by-step explanation:
(1+3x)(44)
=(1+3x)(44)
=(1)(44)+(3x)(44)
=44+132x
=132x+44
How do savings account differ from checking accounts
- they’re not offered at banks
- they typically pay interest
- the funds are easier to get
-you have to keep the money in for a long
Answer:
Savings accounts typically pay interest.
Step-by-step explanation:
1 1/4 x 2 1/4 = ? i need help plzzz
Answer:
2,13/16
Step-by-step explanation: you can put it in the calculator and the answer given would be 2 13/16 hope it helps!
Answer:
2 13/16 or 45/16
There are 24 students in a class. Only -- of the students remembered to bring their hat and mittens to class.
How many students forgot to bring their hat and mittens?
Answer:
6
Step-by-step explanation:
Answer:
22?
Step-by-step explanation:
24-2=22?????