Answer:
a) 0.7847 = 78.47% probability that no samples are mutated.
b) 0.9769 = 97.69% probability that at most one sample is mutated.
c) 0% probability that more than half the samples are mutated.
Step-by-step explanation:
For each sample, there are only two possible outcomes. Either they are mutated, or they are not. The probability of a sample being mutated is independent of any other sample, 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.
2% of cases.
This means that [tex]p = 0.02[/tex]
12 samples are studied
This means that [tex]n = 12[/tex].
(a) No samples are mutated.
This is [tex]P(X = 0)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{12,0}.(0.02)^{0}.(0.98)^{12} = 0.7847[/tex]
0.7847 = 78.47% probability that no samples are mutated.
(b) At most one sample is mutated.
This is:
[tex]P(X \geq 1) = P(X = 0) + P(X = 1)[/tex]
Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{12,0}.(0.02)^{0}.(0.98)^{12} = 0.7847[/tex]
[tex]P(X = 1) = C_{12,1}.(0.02)^{1}.(0.98)^{11} = 0.1922[/tex]
[tex]P(X \geq 1) = P(X = 0) + P(X = 1) = 0.7847 + 0.1922 = 0.9769[/tex]
0.9769 = 97.69% probability that at most one sample is mutated.
(c) More than half the samples are mutated.
This is:
[tex]P(X > 6) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{12,7}.(0.02)^{7}.(0.98)^{5} \approx 0[/tex]
So the others(greater than 7) wil be 0 too
0% probability that more than half the samples are mutated.
\lim _{x\to 0}\left(\frac{\sqrt{1+3x+x^2}-1}{\arcsin \left(2x\right)}\right)
Step-by-step explanation:
[tex]\displaystyle \lim_{x \to 0} \left(\dfrac{\sqrt{x^2 + 3x + 1} - 1}{\arcsin 2x} \right)[/tex]
Note that as [tex]x \rightarrow 0[/tex], the ratio becomes undefined. Using L'Hopital's Rule, where
[tex]\displaystyle \lim_{x \to c} \dfrac{f(x)}{g(x)} = \lim_{x \to c} \dfrac{f'(x)}{g'(x)} [/tex]
where f'(x) and g'(x) are the derivatives of the functions f(x) and g(x), respectively. Note that
[tex]f(x) = \sqrt{x^2 + 3x + 1} \:\:\text{and}\:\: g(x) = \arcsin 2x[/tex]
[tex]f'(x) = \dfrac{2x + 3}{2(\sqrt{x^2 + 3x + 1})}[/tex]
[tex]g'(x) = \dfrac{2}{\sqrt{1 - 4x^2}}[/tex]
Therefore,
[tex]\displaystyle \lim_{x \to 0} \dfrac{f'(x)}{g'(x)} = \lim_{x \to 0} \dfrac{2x + 3}{2(\sqrt{x^2 + 3x + 1})} \times \left(\dfrac{\sqrt{1 - 4x^2}}{2} \right)[/tex]
or
[tex]\displaystyle \lim_{x \to 0} \left(\dfrac{\sqrt{x^2 + 3x + 1} - 1}{\arcsin 2x} \right) = \dfrac{3}{4}[/tex]
Bonjour, connaissez vous une app ou on peut manipuler des elastiques j'en ai besoin. Merci!
Answer:
Wow sup Comment allez-vous, je suis là pour vous aider à essayer cette application, je ne suis pas vraiment sûr de ce que vous entendez par " Rubber Band App " Mais je pense que cela pourrait aider à l'essayer Exercices de bande de résistance
Consider the following sets of sample data: A: $30,500, $27,500, $31,200, $24,000, $27,100, $28,600, $39,100, $36,900, $35,000, $21,400, $37,900, $27,900, $18,700, $33,100 B: 4.29, 4.88, 4.34, 4.17, 4.52, 4.80, 3.28, 3.79, 4.84, 4.77, 3.11 Step 1 of 2 : For each of the above sets of sample data, calculate the coefficient of variation, CV. Round to one decimal place.
Answer:
[tex]CV=0.2[/tex] ---- dataset 1
[tex]CV = 7.2[/tex] --- dataset 2
Step-by-step explanation:
Given
[tex]A: 30500, 27500, 31200, 24000, 27100,28600, 39100, 36900, 35000, 21400, 37900, 27900, 18700,[/tex][tex]33100[/tex]
[tex]B: 4.29, 4.88, 4.34, 4.17, 4.52, 4.80, 3.28, 3.79, 4.84, 4.77, 3.11[/tex]
Required
The coefficient of variation of each
Dataset A
Calculate the mean
[tex]\mu = \frac{\sum x}{n}[/tex]
[tex]\mu = \frac{30500+ 27500+31200+24000+ 27100+28600+ 39100+ 36900+ 35000+ 21400+ 37900+ 27900+ 18700+33100}{14}[/tex][tex]\mu = \frac{418900}{14}[/tex]
[tex]\mu = 29921.43[/tex]
Next, calculate the standard deviation using:
[tex]\sigma = \sqrt{\frac{\sum(x - \mu)^2}{n}}[/tex]
So, we have:
[tex]\sigma= \sqrt{\frac{(30500 - 29921.43)^2 +.................+ (18700- 29921.43)^2 + (33100- 29921.43)^2}{13}}[/tex]
[tex]\sigma= \sqrt{\frac{487723571.42857}{14}}[/tex]
[tex]\sigma= \sqrt{34837397.959184}[/tex]
[tex]\sigma= 5902.32[/tex]
So, the coefficient of variation is:
[tex]CV=\frac{\sigma}{\mu}[/tex]
[tex]CV=\frac{5902.32}{29921.43}[/tex]
[tex]CV=0.2[/tex] --- approximated
Dataset B
Calculate the mean
[tex]\mu = \frac{\sum x}{n}[/tex]
[tex]\mu = \frac{4.29+ 4.88+ 4.34+ 4.17+ 4.52+ 4.80+ 3.28+ 3.79+ 4.84+ 4.77+ 3.11}{11}[/tex]
[tex]\mu = \frac{46.79}{11}[/tex]
[tex]\mu = 4.25[/tex]
Next, calculate the standard deviation using:
[tex]\sigma = \sqrt{\frac{\sum(x - \mu)^2}{n}}[/tex]
[tex]\sigma = \sqrt{\frac{(4.29 - 4.25)^2 + (4.88- 4.25)^2 +.........+ (3.11- 4.25)^2}{11}}[/tex]
[tex]\sigma = \sqrt{\frac{3.859}{11}}[/tex]
[tex]\sigma = \sqrt{0.35081818181}[/tex]
[tex]\sigma = 0.593[/tex]
So, the coefficient of variation is:
[tex]CV=\frac{\sigma}{\mu}[/tex]
[tex]CV = \frac{4.25}{0.5903}[/tex]
[tex]CV = 7.2[/tex] -- approximated
Estimate 9272 - 28 by first rounding each number so that it has only 1 nonzero digit.
Answer:
8970
Step-by-step explanation:
In order to round 9272 so that it has only 1 nonzero digit, look at the hundred digit, If the number is greater or equal to 5, add 1 to the thousand figure. If this is not the case, add zero
The hundred digit is 2 which is less than 5, so 0 is added to 9. the number becomes 9000
In order to round 28 so that it has only 1 nonzero digit, look at the units digit, If the number is greater or equal to 5, add 1 to the tens figure. If this is not the case, add zero
The units digit is greater than 5, so 1 would be added to tens digit. the number becomes 30
9000 - 30 = 8970
Derek sold her house for $541,600, which was 140% of the amount she paid for it.
Calculate the amount she paid for the property.
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Answer:
$386,857.14
Step-by-step explanation:
You have ...
sold = 140% × paid
Dividing by 140% gives ...
paid = sold/1.40 = $541,500/1.40 = $386,857.14
Derek paid $386,857.14 for the property.
A study was done on the batting averages for two baseball players: Hitmore and Bunter. Data were collected over a period of time for baseball parks that are natural and artificial turf. It was found that Hitmore does better overall (.e., has a better batting average). However, for both natural and artificial turf separately, Bunter does better. Which of the following is correct?
This is an example of a negative association between variables.
This is an example of Simpson's Paradox.
"Turf" is a lurking variable in this example
Both (B) and (C) are correct
This situation is mathematically impossible
Answer:
Both (B) and (C) are correct
Step-by-step explanation:
Explaining in simple terms, The Simpson's paradox simply describes a phenomenon which occurs when observable trends in a relationship, which are obvious during singular evaluation of the variables disappears when each of this relationships are combined. This is what played out when hitmire appears to d well on both of natyraknamd artificial turf when separately compared, but isn't the same when the turf data was combined. Also, performance may actually not be related to the turf as turf may Just be. a lurking variable causing a spurious association in performance.
What is the median of the following set of numbers?
1 5
12 1 121
1
121
13
O A. 27
ОВ.
COIN
OC. .
12
OD.
1 5
12 1 121
1
121
13
O A. 27
ОВ.
COIN
OC. .
12
OD. ????????????????
Median of the given data is 8.5.
What is median?In statistics, the median is the middle value of the given list of data in order. Data or observations can be sorted in ascending or descending order.
Given data,
1 , 5, 12, 1, 121, 1, 121, 13
Arranging in ascending order
1, 1, 1, 5, 12, 13, 121, 121
Number of elements N = 8
When number of elements is odd
Median = (N/2 th term + (N/2)+1 th term)/2
Median = (8/2 th term + (8/2)+1 th term)/2
Median = (4th term + 5th term)/2
Median = (5+12)/2
Median = 17/2
Median = 8.5
Hence, 8.5 is the median of the given data.
Learn more about median here:
https://brainly.com/question/28060453
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Chester has less than $25 to spend at the county fair. The entrance fee is $5, and each ride costs $3. The number of rides, r, that Chester can go on is represented by the inequality 3r + 5 < 25. Select the most amount of rides Chester can go on without overspending
Answer:
6 rides
Step-by-step explanation:
3r+5<25
3r<20
r<6.67
rides=6
check answer
3r+5<25
3(6)+5<25
18+5<25
23<25
For what value of x is the rational expression below equal to zero?
20+2x
5-x
O A. -10
O B. -5
C. 10
O D. 5
Answer:
A.-10 should be the answer to the question..
The rational expression is zero at x = -10.
What is rational expression?The ratio of two polynomials is known as a rational expression.
The given rational expression can equate to zero
[tex]\frac{20+2X}{5-X} =0[/tex]
Then, 20+2x=0
Therefore, x = (-20/2) = -10.
At x = -10, the given rational expression is zero.
To learn more about rational expression, use the link given below:
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evaluate the given expression if w= 17, x= 29, and a =8 w+(1/x)+(1/z) a. 17.18 b.8.11 c. 94.13 d. 46.15
Answer:
a. 17.18
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
Identify
w = 17
x = 29
z = 8
w + (1/x) + (1/z)
Step 2: Evaluate
Substitute in variables: 17 + (1/29) + (1/8)Add: 3981/232Divide: 17.1595Express in roster form. Set of B is the set of all elements x such that x is an element of natural numbers and x is a multiple of 8
=========================================================
Explanation:
The set of natural numbers is {1,2,3,...} basically anything positive and a whole number.
Any multiple of 8 is of the form 8x. Since x is a natural number, the smallest it can be is x = 1 which corresponds to 8x = 8*1 = 8. So 8 is the first multiple of the set. Then 16 is next because 8x = 8*2 = 16, and so on.
That's how we end up with {8, 16, 24, 32, ...}
The three dots, or ellipses, tell the reader that the pattern goes on forever. This set is infinitely large. We wouldn't stop at 800 because we could plug in say x = 200 to get 8x = 8*200 = 1600 and that's a multiple of 8.
Find the Value of x
Answer:
42
Step-by-step explanation:
(adjacent straight angles sum up to 180)
3x+54=180
x=42
A small town experienced an explosive population increase Originally the town had population 170 within 3 years the town's population increased by 400% what is the town current population
Answer:
Step-by-step explanation:
We need to first find out how much 400% of 170 is and then add that increase to the original 170 people.
4(170) = 680 and
680 + 170 = 850 people after 3 years.
PLEASE HELP!
Determine which of the following lists is in order from smallest to largest.
1. -3,131,0, (-3)^2
2. (-3)^2,-3,0, |3|
3. -3,0,|3|, (-3)^2
4. 0,-3,|3|, (-3)^2
Answer:
3. -3,0,|3|, (-3)^2
Step-by-step explanation:
Answer:
answer would be option 3
Step-by-step explanation:
help this helps
find the quotient of 8 divided by one-third, multiply 8 by
A:1/8
B:1/3
C:3
D:8
are the possible answers
Answer:
find the quotient of 8 divided by one-third, multiply 8 by
A:1/8
B:1/3( true
C:3
D:8
are the possible answers
For the equation, complete the solution. 7x + y = −18
Answer:
x= - 18/7 - 1/7y, y
or if you are solving for y= -18-7x, x
( SEE OTHER IMAGE)
Step-by-step explanation:
See image below:)
Answer:
[tex]x= \frac{- 18 - y }{7}[/tex]
y = - 18 - 7x
Step-by-step explanation:
7x + y = - 18
7x + y - y = - 18 - y
7x = - 18 - y
[tex]\frac{7x}{7}= \frac{- 18 - y }{7}[/tex]
[tex]x= \frac{- 18 - y }{7}[/tex]
7x + y = - 18
7x - 7x + y = - 18 - 7x
y = - 18 - 7x
In a study, researchers wanted to measure the effect of alcohol on the hippocampal region, the portion of the brain responsible for long-term memory storage, in adolescents. The researchers randomly selected 23 adolescents with alcohol use disorders to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of 9.02 cm3. An analysis of the sample data revealed that the hippocampal volume is approximately normal with no outliers and x=8.16 cm3 and s=0.7 cm3. Conduct the appropriate test at the α=0.01 level of significance.
Answer:
We do not reject the Null Hypothesis
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=23[/tex]
Population mean [tex]\mu=9.02cm^3[/tex]
Sample mean [tex]\=x=8.16[/tex]
Standard deviation [tex]\sigma=0.7cm^3[/tex]
Significance level [tex]\alpha =0.01[/tex]
Generally the Null and and alternative Hypothesis are as follows
[tex]H_0:\mu=9.02cm^3[/tex]
[tex]H_a:\mu<9.02cm^3[/tex]
Therefore t critical Value is
[tex]t\ critical\ Value=(\alpha,df)[/tex]
[tex]t\ critical\ Value=(0.01,22)[/tex]
Where
[tex]df=n-1\\\\df=23-1=>22[/tex]
Therefore
From t Table
[tex]t value=-2.8[/tex]
Generally the equation for Z Critical is mathematically given by
[tex]t=\frac{\=x-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]
[tex]t=\frac{8.16-9.02}{\frac{0.7}{\sqrt{23} } }[/tex]
[tex]t=-5.89[/tex]
Therefore
Since the t test statistics is greater than the Critical value
Hence,we do not reject the Null Hypothesis
Use the graph of the function to find its domain and range. Write the domain and range in interval notation.
Answer:
Domain = -6 < x < 3
range = -6 < x < -4
Step-by-step explanation:
The domain is the input values along the x-axis. According to the graph, the x values are within the interval;
Domain= -6 < x < 3
The range is the output values along the y-axis. According to the graph, the y values are within the interval;
range = -6 < x < -4
Which rules of exponents will be used to evallate this expression? Select three options.
Software Solution (SOS) helps subscribers solve software problems. All transactions are made over the telephone. For the year 2018, 10 engineers, most of whom are recent graduates, handled 119,000 calls. The average yearly salary for software engineers was $58,000. Starting in 2019, the firm retained and hired only software engineers with at least 2 years of experience. SOS raised the engineers’ salary to $73,000 per year. In 2019, eight engineers handled 127,000 calls.
Required:
1. Calculate the partial operational productivity ratio for both years.
2. Calculate the partial financial productivity ratio for both years. (Round your answers to 4 decimal places.)
Answer:
a. 11900, 15875
b. 0.2052, 0.2175
Step-by-step explanation:
number of engineers in 2018 = 10
calls handled in 2018 = 119000
average salary in 2018 = 58000
number of engineers in 2019 = 8
calls handled = 127000
salary = 73000
a.) operational productivity = output/input
in year 2018 = 119000/10= 11900
in year 2019 = 127000/8 = 15875
b.) ratio for both years = output/amount spent
in year 2018 = 119000/10*58000 = 0.2052
in year 2019 = 127000/8*73000 = 0.2175
A pen costs $2 and a ruler costs 50 cents. Write down an expression in dollar for the cost of p pen and r ruler.
Answer:
.50r + 2p
Step-by-step explanation:
cost of ruler * number of rules + cost of pens * number of pens
.50 *r + 2 *p
.50r + 2p
Two parallel lines, e and f, are crossed by two transversals.
What is the measure of <15
m<15 = 77°
m< 15 = 83°
m<15 = 93°
m<15= 97°
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Answer:
∠15 = 97°
Step-by-step explanation:
At any given transversal of parallel lines, all obtuse angles are congruent, and all acute angles are congruent. Obtuse angle 15 is congruent to the one market 97°.
∠15 = 97°
Hallar la ecuación de la recta (2,3) y (1,-2)
Answer:
[tex]y=5x-7[/tex]
Step-by-step explanation:
A right triangle has side lengths 7, 24, and 25 as shown below. Use these lengths to find cos B, tanB, and sin B.
Answer:
cosB = 7/25 = 0,28
tanB = 24/7 = 3,428571429
sinB = 24/25 = 0,96
an isosceles triangle has one angel that measure 30 degree what is the measure of the other two angles that are equal?
WILL MARK YOU IF YOU HELP ME !!!!
Answer:
Perpendicular bisector
Answer:
perpendicular bisector
A searchlight is shaped like a parabola. If the light source is located 3 feet from the base along the axis of symmetry and the depth of the searchlight is 4 feet, what should the width of the opening of the searchlight be?
9514 1404 393
Answer:
8√3 ≈ 13.86 ft
Step-by-step explanation:
The light source is usually placed at the focus, so the focus-vertex distance is p=3 ft. The equation for the parabola with its vertex at the origin is ...
y = 1/(4p)x^2
y = 1/12x^2
The opening for some y-value extends ±x from the axis of symmetry, so is a total of 2x in width.
For y=4, the corresponding value of x is ...
4 = 1/12x^2
48 = x^2
√48 = x = 4√3
Then the width of the searchlight opening is ...
2(4√3 ft) = 8√3 ft ≈ 13.86 ft
Alejandro used a mathematical property to create two equivalent expressions.
6(x + 2) = 6x + 30
Which of the following is the missing term?
O 24
Х
O 5x
6
5
Find the area of the sector in
terms of pi.
120°
24
Area = [?] π
Enter
WILL MARL BRAINLIEST IF YOU HELP
Answer:
C.
Step-by-step explanation:
In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
A.
9 + 9 = 18
18 < 22
No triangle
B.
7 + 3 = 10
10 = 10
No triangle
C.
5 + 6 = 11 and 11 > 9 good
5 + 9 = 14 and 14 > 6 good
9 + 6 = 15 and 15 > 5 good
There is a triangle.
Answer: C.