A machine has 12 identical components which function independently. The probability that a
Answers
0.025 is the probability that the device will malfunction.
What do we mean by probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.So, there is a 0.2 chance that a component will malfunction.
Let x be the number of components that will fail.
That is p = 0.2 and n = 12.
Since if more than three components fail, the machine would stop functioning.
The likelihood that the device will malfunction then is:
\(\begin{aligned}&P(X > 3)=1-P(X \leq 3) \\&=1-[P(0)+P(1)+P(2)+P(3)] \\&=1-\left[{ }^{12} C_0(0.2)^0(0.8)^{12}+{ }^{12} C_1(0.2)^1(0.8)^{11}+{ }^{12} C_2(0.2)^2(0.8)^{10}+{ }^{12} C_3(0.2)^3(0.8)^9\right] \\&=1-\left[(1)(0.8)^{12}+(12)(0.2)(0.8)^{11}+\frac{12 !}{2 ! 10 !}(0.2)^2(0.8)^{10}+\frac{12 !}{3 ! 9 !}(0.2)^3(0.8)^9\right] \\&=1-(0.068719476736+0.206158430208+0.283467841536+0.23622320128) \\&=1-0.79456894976 \\&=0.20543105024 \approx 0.205\end{aligned}\)
Therefore, 0.025 is the probability that the device will malfunction.
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Complete question:
A machine has 12 identical components which function independently. The probability that a component will fail is 0.2. The machine will stop working if more than three components fail. Find the probability that the machine will stop working. A) 0.073 B) 0.795 C) 0.867 D)0.205
Related Questions
can someone help me with this asapp
Answers
Answer:
I think it's 2,1 forgive me if it's wrong
the solution of the quadratic equation x square - 4 x + 4
Answers
Answer:
\(\rm x = 2 , 2 \)
Step-by-step explanation:
A quadratic equation is given to us and we need to find the solution of the equation. The given equation is ,
\(\implies x^2 -4x + 4 = 0 \)
Now for finding the roots of the equation , let's use the quadratic formula , or by factorising out the equation . Here I would be using the factorization method , as ,
\(\implies x^2 -4x + 4 = 0\\\\\implies x^2-2x-2x+4 = 0 \\\\\implies x(x-2) -2(x-2) = 0 \\\\\implies (x-2)(x-2) = 0 \\\\\implies x = 2, 2 \)
Hence the Solution of the equation is 2,2.
Answer:
Step-by-step explanation:
x² - 4x +4 = 0
Factorization method:
Sum = -4
Product = 4
Factor = (-2) ; (-2) {-2 * -2 = 4 & (-2) + (-2) = -4}
x² -4x + 4 = 0
x² - 2x - 2x + (-2)*(-2) = 0
x(x - 2) - 2 (x - 2) = 0
(x - 2) (x - 2) = 0
x - 2 = 0 or x -2 = 0
x = 2 or x = 2
x = 2 , 2
A wind sterly component from the east) of 11 kwh and a southerly component (trom the south) of 17 km/h. Find the magnitude and the direction of the wind The magnitude of the wind is...
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The wind has a magnitude of approximately 20.25 km/h and is blowing in a direction approximately 56.31° east of south. Magnitude is the hypotenuse of a right triangle with westerly and southerly components.
To find the magnitude and direction of the wind with a westerly component of 11 km/h and a southerly component of 17 km/h, we can use the Pythagorean theorem and trigonometry.
The magnitude of the wind is given by the hypotenuse of a right triangle with legs 11 km/h and 17 km/h. Using the Pythagorean theorem, we get:
magnitude = \(\sqrt{(11^2 + 17^2)} \approx 20.25 \;km/h\)
To find the direction of the wind, we can use trigonometry. The angle θ between the wind direction and the east direction can be found using the inverse tangent function:
\(tan(\theta)\) = opposite/adjacent = 17/11
\(\theta = atan(17/11) \approx 56.31^{\circ}\)
Therefore, the wind has a magnitude of approximately 20.25 km/h and is blowing in a direction approximately 56.31° east of south.
In summary, to find the magnitude and direction of wind with given westerly and southerly components, we can use the Pythagorean theorem and trigonometry.
The magnitude is given by the hypotenuse of a right triangle with legs equal to the westerly and southerly components, while the direction is given by the angle between the wind direction and the east direction, which can be found using the inverse tangent function.
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Find the value of z.
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2z = 15
z = 7.5
PEMDAS means and what is for
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Answer: The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Step-by-step explanation: GO
Answer: PEMDAS is Parentheses, exponents, multiplication, division, addition ,subtraction
It’s for math when you have a question like this 3x(4-2)+7 the numbers are in order so do it in order and if you have parentheses you ALWAYS
do them first
Step-by-step explanation:
What are the zeros of this function?
A. x = -6 and x = -4
B. x = 0 and x = 4
C. x = -6 and x = 5
D. x = 4 and x = 6
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Answer:
D. x=4 and x=6 (A P E X)
Solve: 3a^2-4b a= -6 b= -5 If you could also leave an explanation that would be great! Thank you for your time!
Answers
Answer:
128
Step-by-step explanation:
3a² - 4b
plug in values
3(-6)² - 4(-5)
use PEMDAS and simplify (-6)² first
3(36) -4(-5)
multiply
108 + 20
add
128
hope this helps :)
the study would use a . the study would use simple random sampling because it would be easy to randomly select of . b. the study would use a . the study would use cluster sampling because the of fall into naturally occurring subgroups. c. the study would use a . the study would use stratified sampling because it would be important to have members from each segment of the population. d. the study is a , because the population is for it to be practical to record all of the responses.
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The study would use a simple random sampling because it would be easy to randomly select. The study would use cluster sampling because the of fall into naturally occurring subgroups. The study would use stratified sampling because it would be important to have members from each segment of the population.
The study is a sample survey, because the population is for it to be practical to record all of the responses.
a. The study would use a simple random sampling because it would be easy to randomly select members of the population. Simple random sampling is a type of probability sampling that is used when the population is homogenous and every member has an equal chance of being selected for the sample.
b. The study would use cluster sampling because the members of the population fall into naturally occurring subgroups. Cluster sampling is a type of probability sampling that is used when the population is heterogeneous and can be divided into naturally occurring subgroups.
c. The study would use stratified sampling because it would be important to have members from each segment of the population. Stratified sampling is a type of probability sampling that is used when the population is heterogeneous and can be divided into segments or strata based on certain characteristics.
d. The study is a sample survey, because the population is too large for it to be practical to record all of the responses. Sample survey is a type of survey that collects data from a sample of the population, rather than the entire population. This is often done when the population is too large or when it is not practical to survey the entire population.
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let a and b be events with =pa0.8 and =pb0.9. assume that a and b are independent. (a) Compute PA and B.
(b) Are A and B mutually exclusive? Explain.
(c) Are A and B independent? Explain.
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a)The probability that both A and B occur is 0.72 and b)A and B are not mutually exclusive and c)A and B are independent.
a) We have given that events a and b are independent and =pa0.8 and =pb0.9. Now, to find PA and B, we use the formula, P(A and B) = P(A) x P(B).P(A and B) = P(A) x P(B) = (0.8) x (0.9) = 0.72.
Hence, the probability that both A and B occur is 0.72.
(b) A and B cannot be mutually exclusive because if they were, the probability of their intersection would be 0. However, as we have already calculated, P(A and B) = 0.72.
Therefore, A and B are not mutually exclusive.
(c) As we have already mentioned, the events A and B are independent, which means that the occurrence of one event does not affect the probability of the other event.
We can also verify this using the formula, P(A and B) = P(A) x P(B). If we substitute the given probabilities in this formula, we get:
P(A and B) = P(A) x P(B)(0.8) x (0.9) = 0.72
This is the same value we got for P(A and B) earlier. Hence, we can say that A and B are independent.
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suppose you are standing such that a 40 foot tree is directly between you and the sun. If you were standing 35 feet away from the tree and the tree cast a 40 foot shadow, how tall could you be and still be completely in the shadow of the tree?
Answers
To determine how tall you could be and still be completely in the shadow of the tree, we need to consider the concept of similar triangles.
The ratio of the height of the tree to the length of its shadow is the same as the ratio of your height to the length of your shadow.
Given that the tree is 40 feet tall and its shadow is 40 feet long, the ratio is 40/40, which simplifies to 1.
Now, let's determine the length of your shadow. Since you are standing 35 feet away from the tree, your shadow would also be 35 feet long.
To find your maximum height, we can set up a proportion:
1/35 = x/40
By cross-multiplying, we get:
x = (1/35) * 40
Simplifying, we find that x, the maximum height you could be and still be completely in the shadow of the tree, is approximately 1.14 feet.
In conclusion, you could be up to 1.14 feet tall and still be completely in the shadow of the tree.
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I need help with this math problem please. I need help finding proofs and reasons please
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In order to prove that the angles RST and TUR are congruent, the lines 1, 2 and 3 of statements and reasons are correct.
Since triangles RST and TUR have all three sides congruent, so they are congruent triangles by case SSS.
For the line 4, the statement is "angle RST congruent to angle TUR" (what we want to prove), and the reason is "corresponding angles of congruent triangles".
HELP MEEE PLZ :( Saeed sells beaded necklaces. Each large necklace sells for 6.50 $ and each small necklace sells for4.90$ . How much will he earn from selling7 large necklaces and 6 small necklaces?
Answers
45.50 + 29.40 = 74.90
He will earn $74.90
Answer:
74.9
Step-by-step explanation:
Graph the line that passes through these points
Answers
And the line going sideways is x
The points (-2,5) and (-4,3) is
(X , Y ) so since a its -2 you would go over to -2 on the x line than from -2 go up 5 and place your point
Formal- m = (y2 - y1) / (x2 - x1)
(x1, y1) = (-2, 5)
(x2, y2) = (-4, 3)
m = (3 - 5) / (-4 - (-2)) = -2 / (-2) = 1
So the slope of the line is 1.
A median must always pass through a vertex andof the triangle.A. midpointB. another vertexc. the centerD. a side
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We want to determine a property of a triangle's median.
The median is a line drawn from the vertex to the midpoint of the opposite side.
Thus, a median must always pass through a vertex and midpoint of the triangle
Given the equation y= 2x - 8, what is the slope and the y-intercept?
Om = 2 and b= 8
O m= 2 and b= -8
m= 8 and b=2
O m= -8 and b= 2
Answers
mx+b !!
find the critical values x^2 1-a/2 and for a onfidence level and a sample size of n.
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The critical value x² for a confidence level of 1 - α/2 and a sample size of n is a statistical measure used in hypothesis testing and constructing confidence intervals.
In hypothesis testing, the critical value is compared to the test statistic to determine if there is sufficient evidence to reject the null hypothesis. In constructing confidence intervals, the critical value is used to define the range within which the true population parameter is likely to lie.
The critical value x² is based on the chi-square distribution with n - 1 degrees of freedom, where n is the sample size. The degrees of freedom represent the number of independent pieces of information available to estimate the population parameter.
To find the critical value, you need to determine the appropriate α (significance level) and locate the corresponding 1 - α/2 quantile on the chi-square distribution table with n - 1 degrees of freedom. The value obtained represents the point on the distribution below which (1 - α/2) x 100% of the data falls.
For example, if your confidence level is 95%, you would set α = 0.05. With a sample size of n, you would find the 1 - 0.05/2 = 0.975 quantile in the chi-square distribution table with n - 1 degrees of freedom.
It's important to note that the critical value is dependent on both the desired confidence level and the sample size. As the confidence level increases or the sample size changes, the critical value will vary accordingly.
In conclusion, the critical value x² for a confidence level of 1 - α/2 and a sample size of n can be found by locating the appropriate quantile in the chi-square distribution table with n - 1 degrees of freedom. This value is crucial in hypothesis testing and constructing confidence intervals.
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simplify 5^3/5^7 leaving your answer in index form
Answers
Step-by-step explanation:
\( \frac{ {5}^{3} }{ {5}^{7} } \\ \\ = {5}^{3 - 7} \\ \\ = {5}^{ - 4} \\ \\ = \frac{1}{ {5}^{4} } \)
In a normally distributed sample, 95% of people's heights are between 168 and 184 centimeters. what is the standard deviation of the sample?
A. 2
B. \(2\sqrt{2[
C. 4
D. 8
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Using the Empirical Rule, it is found that the standard deviation of the sample is of:
C. 4
By the Empirical Rule, 95% of the measures are within 2 standard deviations of the mean, that is, between 2 standard deviations below the mean and 2 standard deviations above the mean.
95% of people's heights are between 168 and 184 centimeters, hence, there are 4 standard deviations between 168 and 184 centimeters. Then:
\(4s = 184 - 168\)
\(4s = 16\)
\(s = \frac{16}{4}\)
\(s = 4\)
Hence, option C is correct.
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6. If WXYZ is a square with WZ = 27, find each measure.
X
a) ZY =
b) WY =
c) RX =
d) m2 WRZ
e) mZXYZ -
f) mZZWY =
z
Answers
b) WY= diagonal = 27 × sqrt2
c) RX= half of diagonal = (27 × sqrt2) divided by 2
d) m2 WRZ = 90 degrees
e) mZXYZ = 90 degrees
f) mZZWY = 45 degrees
Hope this helps!
what is x
1/3+3=4-x
This is too hard for me
Answers
Answer:
x = 2/3
Step-by-step explanation:
Add the numbers
\(\frac{1}{3}+3=4-x\)
\(\frac{10}{3}=4-x\)
Rearrange terms
\(\frac{10}{3}=-x+4\)
Subtract 4 from both sides of the equation
\(\frac{10}{3}-4=-x+4-4\)
Simplify
\(\frac{-2}{3}=-x\)
Divide both sides of the equation by the same term
\(\frac{-2}{3}/1=\frac{-x}{1}\)
Simplify
\(x=\frac{2}{3}\)
[RevyBreeze]
What happens to the standard error of an estimate when the sample size in a SRS decreases?A. The standard error gets smaller
B. The precision of the estimate increases
C. The standard error stays roughly the same
D. The precision of the estimate decreases
Answers
The precision of the estimate decreases when standard error of an estimate when the sample size in a SRS decreases. So, the correct answer is D).
The standard error of an estimate measures the variability of sample means around the population mean. As the sample size in a simple random sample (SRS) decreases, the sample mean becomes less representative of the population mean, resulting in more variability or less precision in the estimate.
The standard error increases as the sample size decreases because there is more uncertainty in the estimate due to the smaller sample size. Therefore, decreasing the sample size will increase the margin of error and decrease the precision of the estimate. So, the correct option is D).
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The graph shows the number of paintballs a machine launches, y, in x seconds: A graph titled Rate of Launch is shown. The x axis label is Time in seconds, and the x axis values are from 0 to 10 in increments of 2 for each grid line. The y axis label is Number of Balls, and the y axis values from 0 to 60 in increments of 12 for each grid line. A line is shown connecting points on ordered pair 2, 12 and 4, 24 and 6, 36 and 8, 48. Which expression can be used to calculate the rate per second at which the machine launches the balls? (5 points) fraction 12 over 2 fraction 2 over 12 fraction 48 over 2 fraction 2 over 48
Answers
Fraction 12 over 2 can be used to calculate the rate per second at which the machine launches the balls
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The x axis label is Time in seconds, and the x axis values are from 0 to 10 in increments of 2 for each grid line.
The y axis label is Number of Balls, and the y axis values from 0 to 60 in increments of 12 for each grid line
A line is shown connecting points on ordered pair (2, 12) and (4, 24) and (6, 36) and (8, 48)
m=24-12/4-2
m=12/2
Hence, fraction 12 over 2 can be used to calculate the rate per second at which the machine launches the balls
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You roll a fair 6-sided die.
What is P(roll an even number)?
Answers
Answer: \(\frac{3}{6}\) or 0.5
Step-by-step explanation:
It has 6 sides, {1,2,3,4,5}. So the total number of cases is 6.
Even number includes {2,4,6}. The sample space of rolling an even is 3.
The probability of rolling an even number formula is:
P(Rollinganevennumber)= \(\frac{Number of cases in the sample space}{Total number of cases}\)
The probability of an even number is \(\frac{3}{6}\) or 0.5
equilateral triangle RST is inscribed in circle O. What fraction of the circle's circumference lies between any two verticles of triangle RST
Answers
Answer:
1/3
Step-by-step explanation:
In an equilateral triangle such as the RST triangle, sides are equal or the distances between any two vertexes are equal therefore the lenght of the three pieces of the circle´s circumference are equals and, then the fraction
of the circle´s circumference is 1/3
Please help!!
I’m so confused
Answers
Answer:
A and C
Step-by-step explanation:
The distance between P and Q is 14.
With the first one the absolute value is of -8 is 8 and 8+5 is 14 so that's right.
The third one subtracting a negative is like adding a positive. So it would be 5+8 which is also 14.
The other to equal 3 and -3 which is wrong.
If f(x) = x2 2x 3, what is the average rate of change of f(x) over the interval [-4, 6]?
Answers
Answer:
see the attachment photo!
![If f(x) = x2 2x 3, what is the average rate of change of f(x) over the interval [-4, 6]?](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/VINu6GUWr99MR576ORruVbIkVdhppvf6.jpeg)
One way to establish validity of a questionnaire is my measuring:A) The correlation between the score on the questionnaire and another measure of the same conceptB) The alpha value of the reliability coefficientC) How well sunjects perform on the questionnaire at one time compared to another timeD) The consistency by which multiple sunjects are able to complete the questionnaire without error
Answers
The correct option is Option D) The consistency with which several individuals can complete the questionnaire without making an error is one technique to determine a questionnaire validity.
A questionnaire is a sort of research tool used to collect data from respondents for a survey or statistical analysis. It consists of a collection of questions (or other forms of prompts). Typically, a research questionnaire will have both closed-ended and open-ended questions. Long-term, open-ended inquiries provide the respondent the chance to go into more detail. The Statistical Society of London created the research questionnaire in 1838. Despite the fact that surveys are frequently created so that the answers may be statistically analyzed. Consequently, it may not be practical to conduct a survey using a questionnaire for some demographic groups.
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Which expression can be modeled using the number line
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The answer choice which can be modelled using the number line given in the task content is; (1/10) × 7.
Which answer choice can be modelled by the number line?It follows from the task content that the answer choice which can be modelled using the number line be identified.
Hence, since each successive threshold on the number line is 1/10 from the next. It follows that the number line best models the expression; (1/10) × 7.
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Please help me with this homework
Answers
Answer:
$3.60
Step-by-step explanation:
Solve for all Nash equilibria in pure and mixed strategies.
Include p^, q^, and each player’s expected payoff for the mixed
strategy equilibrium.
Answers
To find all Nash equilibria in pure and mixed strategies, we need to analyze the strategies and payoffs of each player. By determining the mixed strategy equilibrium and calculating the expected payoffs, we can identify the probabilities and strategies for each player.
In order to find the Nash equilibria, we need to analyze the strategies and payoffs for each player. Let's denote the strategies of Player 1 as p (probability of choosing a specific strategy) and the strategies of Player 2 as q. By analyzing the payoffs, we can determine the best responses for each player.
If both players choose pure strategies, we need to examine all possible combinations to identify any Nash equilibria. If there are no pure strategy Nash equilibria, we proceed to analyze the mixed strategy equilibrium.
In the mixed strategy equilibrium, each player assigns probabilities to their strategies. Let's denote the probabilities for Player 1 as p^ and for Player 2 as q^. By calculating the expected payoffs for each player at these probabilities, we can identify the mixed strategy equilibrium. The mixed strategy equilibrium occurs when the expected payoffs are maximized for both players given the opponent's strategy.
To provide the specific probabilities and expected payoffs for each player in the mixed strategy equilibrium, I would need more information about the strategies and payoffs of the players in the given game. Without specific details, it is not possible to determine the exact probabilities and expected payoffs.
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