Answer:
The true statements Include
A) The length of a confidence interval can be determined if you know only the margin of error.
B) The margin of error can be determined if you know only the length of the confidence interval.
D) The confidence interval can be obtained if you know only the margin of error and the sample mean.
G) The margin of error can be determined if you know only the confidence level, population standard deviation, and sample size.
F) The confidence level can be determined if you know only the margin of error, population standard deviation, and sample size.
The false statements include
C) The confidence interval can be obtained if you know only the margin of error.
E) The margin of error can be determined if you know only the confidence level.
F) The confidence level can be determined if you know only the margin of error.
Step-by-step explanation:
Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample mean) ± (Margin of error)
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
The critical value is obtained using the confidence level (and sample size for t-distributions).
Standard Error of the mean = (Standard deviation)/[√(sample size)]
Standard error of the mean = σₓ = (σ/√n)
Taking each of the statements one at a time
a) The length of a confidence interval can be determined if you know only the margin of error.
According to the mathematical expression of the confidence interval, the length of the confidence interval is 2 × Margin of error. Hence, the length of the confidence interval can be truly obtained from only the margin of error.
This statement is true.
b) The margin of error can be determined if you know only the length of the confidence interval.
This is another way of phrasing statement A. The margin of error is half of the length of the confidence interval.
Hence, this statement is also true.
c) The confidence interval can be obtained if you know only the margin of error.
The confidence interval can be obtained from an expression that involves the sample mean and margin of error.
Confidence Interval = (Sample mean) ± (Margin of error)
The confidence interval cannot be obtained from just the margin of error. Hence, this statement is false.
d) The confidence interval can be obtained if you know only the margin of error and the sample mean.
Like o stated in (c) above, the confidence interval can be obtained from an expression that involves the sample mean and margin of error.
Confidence Interval = (Sample mean) ± (Margin of error)
Hence, this statement is true.
e) The margin of error can be determined if you know only the confidence level.
To obtain the margin of error, if the confidence interval isn't used, an expression involving the critical value and the standard error of the mean is used.
Margin of Error = (Critical value) × (standard Error of the mean)
The critical value is obtained using the confidence level, but the margin of error cannot be obtained from just that, we still need the standard error of the mean.
Hence, this statement is false.
f) The confidence level can be determined if you know only the margin of error.
This is another way of phrasing statement E. Hence, this statement too is false.
g) The margin of error can be determined if you know only the confidence level, population standard deviation, and sample size.
This is true as these is all that is required to obtain the margin of error.
h) The confidence level can be determined if you know only the margin of error, population standard deviation, and sample size.
This can be a bit stressful to obtain, but it is true. It is easy to see this from all the explanation from the beginning to this point.
Hope this Helps!!!
A company is planning a four-year project, with an initial cost of $1.67 million. This investment cost is amortised to zero over four years on a straight-line basis. However, the asset could be disposed of for $435,000 in four years. The project requires $198,000 in working capital initially and is fully recoverable after the project is completed. The project generates $1,850,000 in sales and $1,038,000 in costs each year. If the tax rate is 21% and the required return rate is 16.4%, what is NPV?
Answer:
The Net Present Value = $451180.733
Step-by-step explanation:
Given that:
the initial cost of the project is $1670000
the initial increase in working capital is $198000
The total investment will be ; initial cost of the project + initial increase in working capital
The total investment = $1670000 + $198000
The total investment = $1868000
So, This investment cost is amortised to zero over four years; This implies that the project will depreciate in four years;
Now; lets determine the rate of the annual depreciation
The annual depreciation = [tex]\dfrac{Initial \ cost \ of \ project }{life \ of \ project}[/tex]
The annual depreciation = [tex]\dfrac{1670000}{4}[/tex]
The annual depreciation = $417500
Over to the annual operating cash flow; the annual operating cash flow can be calculated as follows:
annual operating cash flow = (sales - cost) × (1 - tax rate )+ (annual depreciation × tax rate )
Given that the tax rate = 21% = 0.21
annual operating cash flow = (1850000 -1038000)×(1-0.21)+(417500× 0.21)
annual operating cash flow = 812000 × 0.79 + 87675
annual operating cash flow = 641480 + 87675
annual operating cash flow = $729155
So; let's calculate the after tax salvage value for the project
We know that the sales values for the project in four years is $435,000 (i.e the disposal rate of the asset after four years)
Thus; the book value is zero
The after tax salvage value for the project can now be determined by the relation:
after tax salvage value = sale value - tax (sale value - book value)
after tax salvage value = 435000 - 0.21 (435,000 -0)
after tax salvage value = 435000 - 91350
after tax salvage value = $343650
Similarly; given that the recovering rate of the project is $198000;
The cash flow in year 4 will be: annual operating cash flow + after tax salvage + recovery working capital
cash flow in year 4 = $(729155 + 343650 + 198000)
cash flow in year 4 = $ 1270805
This implies that the cash flow from year one to three is : 729155
the cash flow in year four is : 1270805
Given that the Required return rate = 16.4% = 0.164
We can therefore determine the Present cash inflows by using the relation:
[tex]Present \ Value = \dfrac{c_1}{(1+r)^1}+ \dfrac{c_2}{(1+r)^2}+ \dfrac{c_3}{(1+r)^3}+ \dfrac{c_4}{(1+r)^4}[/tex]
[tex]Present \ Value = \dfrac{729155}{(1+0.164)^1}+ \dfrac{729155}{(1+0.164)^2}+ \dfrac{729155}{(1+0.164)^3}+ \dfrac{1270805}{(1+0.164)^4}[/tex]
[tex]Present \ Value = \dfrac{729155}{1.164^1}+ \dfrac{729155}{1.164^2}+ \dfrac{729155}{1.164^3}+ \dfrac{1270805}{1.164^4}[/tex]
Present Value = $(626421.8213 + 538163.0767 + 462339.413+692256.4225)
Present Value = $2319180.733
Finally, The net present value = Present Value - Total Investment
Net Present Value = $(2319180.733 - 1868000)
Net Present Value = $451180.733
Therefore; The Net Present Value = $451180.733
A trapezoid was broken into two congruent triangles and a rectangle. A trapezoid is broken into 2 triangles and 1 rectangle. The triangles both have a base of 3 centimeters and a height of 12 centimeters. The rectangle has a height of 12 centimeters and a width of 14 centimeters. What is the base length, b, of one of the triangles? 3 cm 4 cm 6 cm 7 cm
complete question:
The picture below is the complete question.
Answer:
base of the triangles = 3 cm
Step-by-step explanation:
The trapezoid was broken into 2 congruent triangles and a rectangle. The 2 triangle have a height of 12 cm . The rectangle has a height of 12 cm and width of 14 cm .
The base length of the triangle can be computed as follows.
Note a congruent triangle have exactly the same three sides and exactly the same three angles.
area of a triangle = 1/2 × base × height
From the area of the trapezoid one can calculate the sides of the triangle.
area of the trapezoid = 1/2 × (a + b)h
where
a = top side
b = base side
h = height
area of the trapezoid = 1/2 × (a + b)h
area of the trapezoid = 1/2 × (14 + 20)12
area of the trapezoid = 1/2 × 34 × 12
area of the trapezoid = 34 × 6
area of the trapezoid = 204 cm²
204 = area of the triangles + area of the rectangle
204 =2 (1/2bh) + lw
where
b = base of triangle
h = height of triangle
l = length of rectangle
w = width of rectangle
204 = bh + (14 × 12)
204 = 12b + 168
12b = 204 - 168
12b = 36
divide both sides by 12
b = 36/12
b = 3 cm
base of the triangles = 3 cm
Answer:
3
Step-by-step explanation:
I got 4cm wrong in the unit test and it showed me that the answer was 3cm
Are the two figures necessarily similar? Type "yes" or "no".
Two rhombuses =
Two circles =
Two isosceles triangles =
Two regular hexagons =
Answer:
Two rhombuses are not necessarily similar , No
Two circles are always similar , Yes
Two isosceles are similar , Yes
Two regular hexagons will be similar , Yes
The similar figures are Circle, Isosceles triangle and regular hexagons.
Geometric shapes are the figures which demonstrate the shape of the objects we see in our everyday life. In geometry, shapes are the forms of objects which have boundary lines, angles and surfaces. There are different types of 2d shapes and 3d shapes.
Two rhombuses are not necessarily similar: NoTwo circles are always similar: YesTwo isosceles are similar: YesTwo regular hexagons will be similar: YesTherefore the similar figures are Circle, Isosceles triangle and regular hexagons.
To Learn more about, Geometric shapes, refer:
https://brainly.com/question/16176111
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Matt bought 4 pie molds at a cost of $0.53 per mold. He also bought 4 pre-
made crusts at a cost of $0.72 per crust. How much did Matt spend on pie
molds? Do not include $ in your answer.
Answer:
2.12
Step-by-step explanation:
He spent 4*0.53 on pie molds.
4*0.53=2.12
The diagram shows the scores given by the panel of judges
during a dancing competition.
a) Which score was the mode?
8
7
6
b)
Frequency
There were 5 judges.
They each gave one score in each
round of the competition.
3
2
How many rounds were there?
+
o
0 1 2 3 4 5
Score
Note: Please make sure your final answer says ... rounds.
Answer:
a) 4b) 6 roundsApply the distributive property to create an equivalent expression. 4(3+1/4c-1/2d)??
Answer:16/16c-4/8d
Step-by-step explanation:
Evaluate the expression 6•14-(9+8)2
Answer:
50
Step-by-step explanation:
First things first, use PEMDAS.
Parenthesis is first.
(9+8) is in parenthesis. 9+8 is obviously 17.
The equation now looks like this:
6 x 14 - 17 x 2
There is no exponents, but there is multiplication. 6 x 14 is 84 and 17 x 2 is 34. They both are multiplication equations.
The equation now looks like this:
84 - 34
84-34 is 50. 50 is your answer.
Element X decays radioactively with a half life of 8 minutes. If there are 980 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 43 grams?
y=a(.5)^t/h
Answer:
[tex]t \approx 36.1\,min[/tex]
Step-by-step explanation:
The time constant for the isotope decay is:
[tex]\tau = \frac{8\min}{\ln 2}[/tex]
[tex]\tau \approx 11.542\,min[/tex]
Now, the decay of the isotope is modelled after the following expression:
[tex]m (t) = m_{o}\cdot e^{-\frac{t}{\tau} }[/tex]
The time is now cleared with some algebraic handling:
[tex]\frac{m(t)}{m_{o}} = e^{-\frac{t}{\tau} }[/tex]
[tex]t = -\tau \cdot \ln \frac{m(t)}{m_{o}}[/tex]
Finally, the time need for the element X to decay to 43 grams is:
[tex]t = - (11.542\,min)\cdot \ln\left(\frac{43\,g}{980\,g} \right)[/tex]
[tex]t \approx 36.1\,min[/tex]
Academic Advising: In 2014, the Community College Survey of Student Engagement reported that 32% of the students surveyed rarely or never use academic advising services. Since then, a local California community college that participated in the survey hired several new academic counselors and focused on outreach efforts to increase student awareness of available services. The counseling office staff then conducted a survey of 500 randomly selected students at the college, and 26% of those students said that they rarely or never use academic advising services. Campus administrators want to know whether the hiring and outreach efforts increased student use of academic advising. Which alternative hypothesis is appropriate?
Answer:
The alternative hypothesis is that the proportion of the students surveyed that rarely or never use academic advising services is less than 32% or 0.32. That is the students use of academic advising has increased.
Ha: p < 0.32
Step-by-step explanation:
The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.
For the case above;
Let p represent the proportion of the students surveyed that rarely or never use academic advising services.
The null hypothesis is that the proportion of the students surveyed that rarely or never use academic advising services is equal to 32% or 0.32.
H0: p = 0.32
The alternative hypothesis is that the proportion of the students surveyed that rarely or never use academic advising services is less than 32% or 0.32. That is the students use of academic advising has increased.
Ha: p < 0.32
Does consuming beer attract mosquitoes? A study done in Burkino Faso, Africa, about the spread of malaria investigated the connection between beer consumption and mosquito attraction.1 In the experiment, 25 volunteers consumed a liter of beer while 18 volunteers consumed a liter of water. The volunteers were assigned to the two groups randomly. The attractiveness to mosquitoes of each volunteer was tested twice: before the beer or water and after. Mosquitoes were released and caught in traps as they approached the volunteers. For the beer group, the total number of mosquitoes caught in the traps before consumption was 434 and the total was 590 after consumption. For the water group, the total was 337 before and 345 after. 1Lefvre T, Gouagna L-C, Dabir KR, Elguero E, Fontenille D, et al. 2010 Beer Consumption Increases Human Attractiveness to Malaria Mosquitoes. PLoS ONE 5(3): e9546. doi:10.1371/journal.pone.0009546 (a) State the null and alternative hypotheses for a test to see if, after consumption, the average number of mosquitoes is higher for the volunteers who drank beer. Let group 1 be the people who drank beer and let group 2 be the people who drank water. SHOW HINT (b) Compute the average number of mosquitoes per volunteer before consumption for each group. Round your answers to two decimal places. Beer group: Water group: Are the two sample means different? Do you expect that this difference is just the result of random chance? SHOW HINT (c) Compute the average number of mosquitoes per volunteer after consumption for each group. Round your answers to two decimal places. Beer group: Water group: Are the two sample means different? Do you expect that this difference is just the result of random chance? SHOW HINT (d) If the difference in part (c) is statistically significant, do we have evidence that beer consumption increases mosquito attraction?
Answer:
Take u1 = average number of mosquitoes attracted after drinking beer
u2 = average number of mosquitoes attracted after drinking water
a) The null and alternative hypotheses:
H0 : u1 = u2
H1 : u1 > u2
b) i) The average number of mosquitoes per volunteer before drinking (beer group) :
[tex] x'1 = \frac{x_1}{n} = \frac{434}{25} = 17.36 [/tex]
Sample mean for mosquitoes attracted before consumption for beer group is 17.36
The average number of mosquitoes per volunteer before drinking (water group) :
[tex] x'2 = \frac{x_2}{n} = \frac{337}{18} = 18.72 [/tex]
Sample mean for mosquitoes attracted before consumption for water group is 18.72
The two means are different.
The difference in the two means are as a result of random choice.
c) i) The average number of mosquitoes per volunteer after drinking (beer group) :
[tex] x'1 = \frac{x_1}{n} = \frac{590}{25} = 23.60 [/tex]
Sample mean for mosquitoes attracted after consumption for beer group is 23.60
ii) The average number of mosquitoes per volunteer after drinking (water group) :
[tex] x'2 = \frac{x_2}{n} = \frac{345}{18} = 19.17[/tex]
Sample mean for mosquitoes attracted after consumption for water group is 19.17
The two sample means are different.
This difference here is likely not to be as a result of random choice, because the mean difference here is greater than the mean difference before consumption.
d) A statistically significant difference provides evidence that beer consumption increases mosquito attraction, as the average number of mosquitoes attracted when drinking beer is higher than the mean number of mosquitoes attracted when drinking water.
Carrie rolls 2 fair dice and adds the results from each. Work out the probability of getting a total of 9
Answer:
Probability of a sum of 9 = 0.111111
OR
Probability of a sum of 9 = 1/9
Step-by-step explanation:
Carrie rolls 2 fair dice and adds the results from each.
The total sample space = 36
Gotten from 6²= 36
The probability of getting a total of 9
Now let's look at the possible sum to give us a 9 (3 and 6, 4 and 5) twice.
So we gave number of occurrence of 9 to be four.
Probability of a sum of 9 = 4/36
Probability of a sum of 9 =1/9
Probability of a sum of 9 = 0.111111
The probability of getting a total of 9 is 0.111111 and this can be determined by using the concept of probability.
Given :
Carrie rolls 2 fair dice and adds the results from each.
The sample space is equal to [tex]6^2[/tex] that is 36. The numbers require on both the dices to get the sum equal to 9 are 4 and 5 or 6 and 3.
So, there is a total of 4 numbers in 36 sample size in order to get the sum of 9.
Now, the probability of getting a total of 9 is given by:
[tex]\rm P=\dfrac{4}{36}[/tex]
Further, simplify the above expression.
[tex]\rm P = \dfrac{1}{9}[/tex]
P = 0.111111
So, the probability of getting a total of 9 is 0.111111.
For more information, refer to the link given below:
https://brainly.com/question/23017717
A clown has a silly string that is a 52cm long and magic scarf that is 28cm long.
How long are the clown's silly string and magic scarf combined?
Answer:
you asked about Telugu movies I see Telugu moviesI am from India telangana
What's the present value of $11,000 discounted back 5 years if the appropriate interest rate is 4.5%, compounded semiannually?
Select the correct answer.
a. $7,083.20
b. $7,025.60
c. $7,040.00
d. $7,068.80
e. $7,054.4
Answer:
Step-by-step explanation:
A = P[1 + (r/n)]^(nt)
Look the formula up online to find out what each variable represents if needed.
We are solving for P, which is the principal amount 5 years back.
Substitute 11,000 for A (total amount), 4.5% for r(rate), 2 for n(number of times -- in this case, semiannually), and 5 for t(time -- 5 years).
11000 = P[1+(0.045/2)]^(2x5)
11000 = P (1.0225)^10
11000 = P (1.2492) approx.
Divide both sides by 1.2492 to find P.
P = $8805.64 (approx)
I know that the answer I got is not an option listed. However, I feel that my workings may help other people to answer this question or give them inspiration to answer similar questions. Therefore, I will leave this answer up.
Thanks, and sorry I couldn't do much.
find the complete factored form of the polynomial 48m^5+8n^2
Answer:
8 ( 6 m 5^ + n 2^ )
Answer:
8( 6m^5 + n^2)
Step-by-step explanation:
48m^5+8n^2
Factor out 8
8* 6m^5 + 8 * n^2
8( 6m^5 + n^2)
To save money for a sabbatical to earn a master’s degree, you deposit $2000 at the end of each year in an annuity that pays 7.5% compounded annually. a) How much will you have saved at the end of five years? b) Find the interest.
Answer:
The amount he will have at the end of five years is $11,616.8
Interest on the amount is $1,616.8
Step-by-step explanation:
Kindly check the attached picture for explanation.
6 times a number plus 22 is greater than 7
Answer: A
Step-by-step explanation: A is the correct answer because once you do the math (6*5/2+22) it gives you the correct amount. You also need to pay attention to the greater then and less than signs so that you don’t get confused.
If you found this answer helpful, give it a five star rating and a thanks!
(Even a brainliest if you want ;D)
Answer:a
Step-by-step explanation:
Please answer this correctly
Answer:
5 cm
Step-by-step explanation:
Use lenght times wight times height
So, you need to do 4 times 4 times ________ is 80
An urn contains 78 slips of paper. Each slip bears a number from 1 to 26. Each number appears on 3 different slips. A child selects two slips of paper at random and without replacement. Find the probability that the drawn slips have the same number. Write your answer as a reduced fraction.
Answer:
2 / 77
Step-by-step explanation:
Each number appears 3 times in the urn.
After picking any number, the number picked will appear only two more times in the urn, and the total slips of paper will be 77.
So for any first number we pick, the probability of the second number picked being the same number as the first pick is the number of times the same number appears in the urn (2) over the total number of slips in the urn (77):
Probability = 2 / 77
Find the value of MP! Need help!
Answer:
c) 118°
Step-by-step explanation:
PN is the diameter of the given circle.
[tex] \purple {\bold {\therefore m(\widehat{PMN}) = 180°}}.... (1)\\[/tex]
Now, by inscribed angle theorem:
[tex] m\widehat {MN} = 2\times m\angle MPN\\
\therefore m\widehat {MN} = 2\times 31°\\
\red{\bold {\therefore m(\widehat {MN}) = 62°}}....(2) \\\\[/tex]
Now,
[tex] \because m(\widehat{MP}) + m(\widehat{MN}) =m(\widehat{PMN})\\
\therefore m(\widehat{MP}) + 62° =180°\\
\therefore m(\widehat{MP}) =180°-62°\\
\huge \orange {\boxed {\therefore m(\widehat{MP}) =118°}} \\[/tex]
2.34−1.7*0.2 = I am very confused
Answer:
2.34-1.7*0.2=2
Step-by-step explanation:
Well to solve this, we need to use PEMDAS:
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Multiplication comes first before subtraction. You can do long multiplication for this and multiply 1.7 and 0.2 together. Once done that, the product of those 2 numbers are 0.34.
Now 2.34-0.34=2.00
Our answer is 2.
Answer:
2
Step-by-step explanation
1.7 x 0.2 = 0.34
2.34-0.34=2
What’s the correct answer for this question?
Answer:
21/100
Step-by-step explanation:
By looking at the table, we can find the box that has information on people who have dogs but do not walk. The number is 21. The total number of people is 100. To find probability, divide 21 by 100.
21/100
This fraction is in its simplest form and cannot be simplified any further.
Rathaus thinks all the factors of even numbers are even which explains wether Rathan is correct
Answer:
Incorrect
Step-by-step explanation:
It is incorrect because all even numbers have a factor of 1.
That is odd.
Answer:
False
Step-by-step explanation:
even numbers has odd & even factors
6 is an even number
Factors of 6 = 2 , 3
Where 3 is a odd number
What is the value of x?
65°, 79° , X
Answer:
x=36 degrees
Step-by-step explanation:
Remember that all angles of a triangle must add up to 180 degrees due to the Angle Addition Postulate. So let's plug it in! x+65+79=180
Now you solve, x=180-79-65
x=36!
x=36 degrees
Answer:
Option B
Step-by-step explanation:
All interior angles of a triangle add up to 180°.
[tex]79+65+x=180\\144+x=180 \\144-144+x=180-144\\\boxed {x=36}[/tex]
The missing angle is 36°.
Option B should be your correct answer.
Please Help I will mark as brainliest
Answer:
A. True
B. True
C. False
D. True
Step-by-step explanation:
A) To find the probability of the letters spelling CAT go to the letter C, then A, and finally T. there is only one sequence that does this, so the numerator will be 1. There are 6 outcomes overall, so the denominator will be 6. The probability of the letters spelling CAT would be 1/6. The answer is true.
B) To find the probability of T being the first letter go to the letter T. All sequences after the letter T will all be included in the answer. TAC and TCA are both possible solutions, this means there are 2 correct outcomes, so 2 is the numerator. Again, there are 6 outcomes overall, so the denominator will be 6. The probability of T being the first letter is 2/6, which is equal to 1/3. The answer is true.
C) To find the probability of A being the first letter go to the letter A. All sequences after the letter A will all be included in the answer. ACT and ATC are both possible solutions, this mean there are 2 correct outcomes, so 2 is the numerator. Again, there are 6 outcomes overall, so the denominator will be 6. The probability of A being the first letter is 2/6. The answer is false.
D) To find how many total outcomes are possible go to the tree diagram and look to the far right. Go down each of the rows to find all of the outcomes, there is T,C,T,A,C, and A. That means there are six possible outcomes. The answer is true.
A single card is drawn at random from a standard 52 card deck. Work out in its simplest
Answer:
1/52
Step-by-step explanation:
Consider writing onto a computer disk and then sending it through a certifier that counts the number of missing pulses. Suppose this number X has a Poisson distribution with parameter μ = 0.2. (Round your answers to three decimal places.)
Required:
a. What is the probability that a disk has exactly one missing pulse? (Round to four decimal places)
b. What is the probability that a disk has at least two missing pulses? (Round to four decimal places)
c. If two disks are independently selected, what is the probability that neither contains a missing pulse?(Round to four decimal places)
Answer:
a) 0.164 = 16.4% probability that a disk has exactly one missing pulse
b) 0.017 = 1.7% probability that a disk has at least two missing pulses
c) 0.671 = 67.1% probability that neither contains a missing pulse
Step-by-step explanation:
To solve this question, we need to understand the Poisson distribution and the binomial distribution(for item c).
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
[tex] e = 2.71828[/tex] is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Binomial 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.
Poisson mean:
[tex]\mu = 0.2[/tex]
a. What is the probability that a disk has exactly one missing pulse?
One disk, so Poisson.
This is P(X = 1).
[tex]P(X = 1) = \frac{e^{-0.2}*0.2^{1}}{(1)!} = 0.164 [/tex]
0.164 = 16.4% probability that a disk has exactly one missing pulse
b. What is the probability that a disk has at least two missing pulses?
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
In which
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!} [/tex]
[tex]P(X = 0) = \frac{e^{-0.2}*0.2^{0}}{(0)!} = 0.819[/tex]
[tex]P(X = 1) = \frac{e^{-0.2}*0.2^{1}}{(1)!} = 0.164 [/tex]
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.819 + 0.164 = 0.983[/tex]
[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.983 = 0.017[/tex]
0.017 = 1.7% probability that a disk has at least two missing pulses
c. If two disks are independently selected, what is the probability that neither contains a missing pulse?
Two disks, so binomial with n = 2.
A disk has a 0.819 probability of containing no missing pulse, and a 1 - 0.819 = 0.181 probability of containing a missing pulse, so [tex]p = 0.181[/tex]
We want to find P(X = 0).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{2,0}.(0.181)^{0}.(0.819)^{2} = 0.671[/tex]
0.671 = 67.1% probability that neither contains a missing pulse
find the equation in standard form of the line passing through the points (2, negative 3) and (4, 2)
A.5x-2y=16
B.2x-3y=9
C.y=5/2x+8
D.5x+2y=16
Answer:
Step-by-step explanation:
(2 + 3)/(4 - 2)= 5/2
y + 3 = 5/2(x - 2)
y + 3 = 5/2x - 5
y = 5/2x - 8
2y = 5x - 16
5x - 2y = 16
Answer with Explanation please! Thank you!
Answer:
B)
Step-by-step explanation:
Slope = -3
Y-intercept = 3
So
Equation is
y = mx+b
Where m is slope and b is y-intercept
y = -3x+3
omar has 5 liters of water he divides the water evenly between 4 buckets. how many milliters does omar pour in each bucket
Answer:
1250 milliliters
Step-by-step explanation:
Omar has 5 liters of water. He divides evenly between 4 buckets.
5/4 = 1.25
He pours 1.25 liters in each bucket.
Convert 1.25 liters into milliters.
1.25 × 1000
1250 milliliters.
Omar pours 1250 milliliters in each bucket.
4. Candice leaves on a trip driving at 25 miles per hour. Four hours later, her sister
Liz starts from the same location driving at 50 miles per hour. How long after Liz
leaves home will she catch up to Candice?
A 9 hours
B 4 hours
C 8 hours
D 7 hours
Answer: B. 4 hours
Step-by-step explanation:
