Answer:
a) 0.0486 = 4.86% probability that exactly two of the four components last longer than 1000 hours.
b) 0.9996 = 99.96% probability that the subsystem operates longer than 1000 hours.
Step-by-step explanation:
For each component, there are only two possible outcomes. Either they last more than 1,000 hours, or they do not. Components operate independently, which means that the binomial probability distribution is used to solve this question.
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.
One subsystem has eight identical components, each with a probability of 0.1 of failing in less than 1,000 hours.
So 1 - 0.1 = 0.9 probability of working for more, which means that [tex]p = 0.9[/tex]
a. exactly two of the four components last longer than 1000 hours.
This is P(X = 2) when [tex]n = 4[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{4,2}.(0.9)^{2}.(0.1)^{2} = 0.0486[/tex]
0.0486 = 4.86% probability that exactly two of the four components last longer than 1000 hours.
b. the subsystem operates longer than 1000 hours.
The subsystem has 8 components, which means that [tex]n = 8[/tex]
It will operate if at least 4 components are working correctly, so we want:
[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]
In which
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{8,0}.(0.9)^{0}.(0.1)^{8} \approx 0[/tex]
[tex]P(X = 1) = C_{8,1}.(0.9)^{1}.(0.1)^{7} \approx 0tex]
[tex]P(X = 2) = C_{8,2}.(0.9)^{2}.(0.1)^{6} \approx 0[/tex]
[tex]P(X = 3) = C_{8,3}.(0.9)^{3}.(0.1)^{5} = 0.0004[/tex]
Then
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0 + 0 + 0 + 0.0004 = 0.0004[/tex]
[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.0004 = 0.9996[/tex]
0.9996 = 99.96% probability that the subsystem operates longer than 1000 hours.
Popcorn at the Movies - Exit Slip
You and a friend go to the movies and decide to share a large bucket of popcorn. Write a story to describe the graph.
A 7 sided die is rolled. What is the probability a number greater than 5 or an odd number is rolled?
Answer:
5/7
Step-by-step explanation:
5,6,7,1, and 3 would have to be rolled, which is 5 out of the 7 numbers that can possibly be rolled
Determine the least common multiple (LCM) of 48 and 16.
A. 16
B. 24
C. 36
D. 48
Answer:
16
since it's the least that can be divided by both
Answer:
a) 16
Step-by-step explanation:
Determine the least common multiple (LCM) of 48 and 16.
A. 16
please help me with this dont guess pls!
Answer:
B
Step-by-step explanation:
Answer:
3357
Step-by-step explanation:
Square ABCD has a side length of 10 centimeters. Find the area of the square. Type a numerical answer in the space provided. Do not include units or spaces in your answer.
Answer:
100
Step-by-step explanation:
Multiply two of the side lengths
10×10 = 100
1. In the diagram below which expression represents x, the measure of the exterior angle shown?
Answer:
a) a + b
Step-by-step explanation:
The value of the exterior angle x will be (a+b).
What is an exterior angle?The angle made by the two lines of the figure which lie on the outside of the closed figure is called the exterior angle.
The exterior angle is the sum of the two opposite internal angles of any figure.
The exterior angle in the given figure will be equal to x = a+b the sum of the two opposite interior angles.
Therefore the value of the exterior angle x will be (a+b).
To know more about exterior angles follow
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Me jay bought a television for 9560, he used it for some years and later sold it at a profit of 1439. Find his selling price
Answer:
10999
Step-by-step explanation:
9560 + 1439 = 10999
Thenks and mark me brainliest :)
NO LINKS PLS
The ratio of hot dogs to hamburgers on a barbeque table is 5:4. If there are 36 hamburgers on the table then how many hot dogs must be there?
Step-by-step explanation:
let the ratio be x
then, 5x, 4x is the ratio of hotdog and hamburger
According to question,
5x+3x=36
8x=36
x=36÷8
x=4
therefore, no, of hotdogs are= 5x
=5×4
=20
Need help ASAP!! Plssss
Answer: b that is too easy
Step-by-step explanation:
Help can someone find the zeros for
F(x) = x^2 -25x + 24
Answer:
Variable form: x=24 and x=1
Point form: (24,0) and (1,0)
Step-by-step explanation:
f(x) = x² - 25x + 24
0 = x² - 25x + 24
0 = (x-24)(x-1)
0 = x - 24 and x - 1 = 0
24 = x and x = 1
Therefore, the zeroes of the function are (24,0) and (1,0)
Can someone help please will give brainliyist
Answer:
slope is 3/4 or .75
Step-by-step explanation:
Equation of line is
y= .75 + 1.5
hope this helps :)
Help please thank you
Answer:
no
yes
yes
0.92 cents
4.72
9.26
Step-by-step explanation:
The foot, the pound, and the gallon are all example of ______ units. This system of measurement was first devised in England
Drag each graph to show if the given data has a positive correlation, a negative correlation, or no correlation.
The solution is:
the first graph is positive correlation
The second is No correlation
The third is positive correlation
The fourth is negative correlation.
Here, we have,
each correlation would mean:
A positive correlation : As one variable increases, so does the other
In other words, the line would be going 'up'
A negative correlation : As one variable increases, the other decreases
In other words, the line would be going 'down'
No correlation : there is no connection between the two
In a visual way, you won't be able to see a 'line'.
so, from the given graph we get,
Therefore, the first graph is positive correlation
The second is No correlation
The third is positive correlation
The fourth is negative correlation.
learn more on correlation :
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What are the mean absolute deviation and population standard deviation of this data set? Round to the nearest tenth if necessary. 2, 4, 6, 9, 14
Answer:
For a data set of N elements:
{x₁, x₂, ..., xₙ}
The mean is:
[tex]M = \frac{x_1 + x_2 + ... + x_n}{N}[/tex]
The mean absolute deviation is:
[tex]MAD = \frac{|x_1 - M| + ... + |x_n - M|}{N}[/tex]
And the population standard deviation is:
[tex]PSD = \frac{\sqrt{|x_1 - M|^2 + ... + |x_n - M|^2} }{\sqrt{N}}[/tex]
In this case, our set has 5 elements, and the set is:
{2, 4, 6, 9, 14}
The mean of this set is:
[tex]M = \frac{2 + 4 + 6 + 9 + 14}{5} = 7[/tex]
The mean absolute deviation is:
[tex]MAD = \frac{|2 - 7| + |4 - 7| + |6 - 7|+ |9 - 7| + |14 - 7| }{5} = 3.6[/tex]
And the population standard deviation is:
[tex]PSD = \sqrt{\frac{|2 - 7|^2 + |4 - 7|^2 + |6 - 7|^2+ |9 - 7|^2 + |14 - 7|^2 }{5}} = 4.2[/tex]
Please help giving brainliest please
Answer:
$87025
Step-by-step explanation:
Net worth is assests minus liabilities
What is the constant rate of change for the relationship shown in the table?
Answer:
3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
The first year Eleanor organized a fund-raising event,
she invited 30 people. For each of the next 5 years,
she invited double the number of people she had
invited the previous year. If f(n) is the number of
people invited to the fund-raiser n years after
Eleanor began organizing the event, which of the
following statements best describes the function f?
To serve 1 person at a local restaurant it takes 10 minutes. To serve 5 people it takes 18 minutes. Using the points (1, 10) and (5, 18), find the slope between the two points. The formula for slope is m =y2 - y1/x2 - x1
(a) m=2
(b) m= -2
(c) m= -5
9514 1404 393
Answer:
(a) m = 2
Step-by-step explanation:
The formula tells you the slope is ...
m = (18 -10)/(5 -1) = 8/4
m = 2
which of the following shows the numbers in the box shown below listed in the increasing order
PLEASE HELP ME ITS MULTIPLE CHOICE
Answer:
Step-by-step explanation:
The answer is class D so number 4
The mathematics faculty at a college consists of 11 professors, 12 associate professors, 7 assistant professors, and 6 instructorsIf faculty member is selected , find the probability of choosing a professor or an instructor
Answer:
The probability of choosing a professor or an instructor is 47.22%.
Step-by-step explanation:
Given that the mathematics faculty at a college consists of 11 professors, 12 associate professors, 7 assistant professors, and 6 instructors, if a faculty member is selected, to find the probability of choosing a professor or an instructor the following calculation must be performed:
11 + 12 + 7 + 6 = 100
11 + 6 = X
36 = 100
17 = X
17 x 100/36 = X
1700/36 = X
47.22 = X
The probability of choosing a professor or an instructor is 47.22%.
Solve the equation.
3(x−9)=30
Answer:
19
Step-by-step explanation:
3(x-9)= 3x-27
3x-27=30
3x=57
x=19
please help me with this
Answer:
.38 or 38%
Step-by-step explanation:
I divided 44 by 116 then rounded
Answer: 38% of boys play an instrument.
Step-by-step explanation:
They are asking for the percentage of boys that play an instrument.
44 ÷ 116 = 0.379310...
Round to the nearest hundredth
0.38
Find the percentage
0.38 × 100 = 38 or 38%
speeeeeeeedddddddddddddddddddddddddddddddd
Answer:
I would be ...
75/8
multiple 9 by 8 and then add 3
Hope this helps!
Step-by-step explanation:
;)
Answer:
75/8!
Step-by-step explanation:
(25 points)
What is the value of k?
Please explain your answer
Answer:
que?
Step-by-step explanation:
Danielle is trying to solve the equation 7^x = 22 . Explain in detail how Danielle should solve this problem. Then solve it step by step showing all your work and tell Danielle what the answer should be.
Answer:
Step-by-step explanation:
7^x=22
take log of both sides
[tex]log(7)^x=log 22\\x log 7=log22\\x=\frac{log 22}{log7} \approx ~1.59[/tex]
PLZ Hlp extra credit imma fail no link!!!
Answer:
B, C, and F
Step-by-step explanation:
You can double check my answers and it'll make sense.
2 to the power of 4 means you multiply 2 by itself 4 times.
The answer of that would be 16.
4 x 4 also equals 16 so therefore those three answers are equivalent.
Answer:
a and c
Step-by-step explanation:
it says equivalent to
What is the simplest form of the radical expression?
4 - v2x+6 v2X
free branliest! come come comeeee get it!
Answer:
thanks i appreciate it
Answer:
Thank you Do you Have a question Or?