The likelihood ratio formula follows the "Bayesian interpretation" of the data:
Pr(E|Hp)/Pr(E|Hd) = tn/t’n
tn/t’n, where tn = transfer, persistence and recovery of n amount of fibres after smothering
t’n = is the transfer, persistence and recovery of n amount of fibres are sleeping. N is the number of fibres recovered.
The numerical values to assign in my likelihood ratio formula are t410 and t’401. These numerical values were taken from the study due to a total of 401 red, cotton fibres

Answer:

3c/2y

Step-by-step explanation:

\(\frac{4c}{3} * \frac{9}{8y} = \frac{c}{3} * \frac{9}{2y} = \frac{c}{1} *\frac{3}{2y } = \frac{3c}{2y}\)

1. The server utilization is 500%.

2. The average response time in the system cannot be accurately calculated due to an overloaded and unstable system.

3. The average waiting time in the queue cannot be accurately calculated due to an overloaded and unstable system.

The server utilization can be calculated by dividing the request processing rate by the request arrival rate. In this case, the server utilization would be:

Server Utilization = Request Processing Rate / Request Arrival Rate

= 20 req/s / 4 req/s

= 5/1

= 5

Therefore, the server utilization is 5 or 500% (since it exceeds 100%).

To calculate the average response time in the system, we need to consider the queuing delay (waiting time in the queue) and the service time (time taken to process a request). In the M/M/1 queue model, the average response time is the sum of the average queuing delay and the average service time.

Average Service Time = 1 / Request Processing Rate

= 1 / 20 req/s

= 0.05 s

The M/M/1 queue model has a known formula for the average queuing delay, which is:

Average Queuing Delay = (Server Utilization²) / (1 - Server Utilization) * Average Service Time

= (5²) / (1 - 5) * 0.05 s

= 25 / -4 * 0.05 s

= -1.25 s

Since the queuing delay cannot be negative, it suggests that the server is overloaded, and the system is unstable. In this case, the average response time cannot be calculated accurately using the M/M/1 model.

Similarly, to calculate the average waiting time in the queue, we can use the formula for the average queuing delay mentioned above:

Average Waiting Time = (Server Utilization²) / (1 - Server Utilization) * Average Service Time

= (5²) / (1 - 5) * 0.05 s

= -1.25 s

Again, due to the negative value, it suggests an overloaded and unstable system, so the average waiting time cannot be accurately calculated using the M/M/1 model.

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The necessary step would be we would have to get every respondent in the population to participate if you wished to conduct a poll with a margin of error of zero.

As it is given in the description itself, if we were to conduct a poll with a margin of error of zero, we would need to recruit every responder in the population to participate.

Therefore, the necessary step would be we would have to get every respondent in the population to participate if you wished to conduct a poll with a margin of error of zero.

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Answer:

£6655

Step-by-step explanation:

Given data

Principal=  £5000

Rate= 10%

Time = 3 years

FInal Amount A=???

The expression for the compound interest is given as

A=P(1+r)^t

substitute

A=5000(1+0.1)^3

A=5000(1.1)^3

A=5000*1.331

A= £6655

Hence the final Amount is  £6655

Answer:

C

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

\(\frac{f(b)-f(a)}{b-a}\)

Here [ a, b ] = [ - 2, 2 ] , then

f(b) = f(2) = 2(2)² + 2 + 5 = 8 + 2 + 5 = 15

f(a) = f(- 2) = 2(- 2)² + (- 2) + 5 = 8 - 2 + 5 = 11 , then

average rate of change = \(\frac{15-11}{2-(-2)}\) = \(\frac{4}{4}\) = 1 → C

6(8-2x)=4x

First, apply distributive property:

6 (8)+ 6 (-2x) = 4x

48-12x =4x

Move the "x" terms to the right:

48 = 4x+12x

Combine like terms

48 = 16 x

Divide both sides of the equation by 16:

48/16 = 16x/16

3 = x

x = 3

After 2 years, the amount in the bank account will be approximately £2,121.21, considering a 3% compound interest per year.

To calculate the compound interest, we use the formula:

A = P(1 + r/n)^(n*t)

Where:

A = the final amount

P = the principal amount (initial deposit)

r = annual interest rate (in decimal form)

n = number of times interest is compounded per year

t = number of years

Given that the principal amount (P) is £2,000, the annual interest rate (r) is 3% (or 0.03 in decimal form), and the duration (t) is 2 years, we need to determine the final amount (A).

Plugging in the values, we have:

A = £2,000(1 + 0.031)^(1*2)

Simplifying the equation, we get:

A = £2,000(1 + 0.03)^2

Calculating the exponential part, we have:

A = £2,000(1.03)^2

A ≈ £2,000(1.0609)

A ≈ £2,121.21

Therefore, after 2 years, the amount in the bank account will be approximately £2,121.21 with a 3% compound interest per year.

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Answer:

RS = 18 units

Step-by-step explanation:

the 2 red strokes through RM and MS indicate they are congruent, that is

RM = MS = 9 , then

RS = RM + MS = 9 + 9 = 18 units

Answer:

P(divisor of 70) = 1/2

Step-by-step explanation:

P(divisor of 70) means what is the probability that the role results in a divisor of 70.

The divisors of 70 are: 1, 2, 5, 7, 10, 14, 35, 70

Since 1,2, and 5 are the only ones that can actually be rolled on a 6-sided die, there is a \(\frac{3}{6}\)  or \(\frac{1}{2}\) chance to roll a divisor of 70.

Answer:  5%

Step-by-step explanation:

(1), (2), 3, 4, (5), 6,

70/1 = 70.                 ( these are integers)

70/2 = 35

70/5 = 14

3 over 6 = 1 over 2 = 50%

hope this helps!!                                                                                                                                                                                      

The class width is 9.8.

We are given the following data set:43 46 52 48 64 58 42 54 58 51 48 58 54 38 51 42 44 78 39 43 39 55 68 52 46 76 43 45 55 60 47 54 46 45 54 69 40 57 30 29 54 47 58 43 48 57 41 60 40 55.The largest data value in the given data set is 78 and the smallest data value is 29. Class width is calculated by finding the difference of the largest data value and the smallest data value and dividing that difference by the desired number of classes. Largest data value - smallest data value = 78 - 29 = 49 Class width = 49/5 = 9.8

The gathering, characterization, analysis, and drawing of inferences from quantitative data are all tasks that fall under the purview of statistics, a subfield of applied mathematics. Probability theory, linear algebra, and differential and integral calculus play major roles in the mathematical theories underlying statistics. Almost all scientific fields, including the physical and social sciences, as well as business, the humanities, government, and manufacturing, use statistics. Fundamentally, statistics is a subfield of applied mathematics that emerged from the use of mathematical techniques like calculus and linear algebra in probability theory.

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Time taken to inflate the balloon to two-thirds of its maximum volume is 16 minutes.

Given the diameter of the balloon = 55 ft

Let r be the radius of the balloon. Then r = 55/2 = 27.5 ft

Rate of change of radius = 1.5 ft/min.

The maximum volume of the balloon = \(\frac{4}{3}\pi r^3\) = \(\frac{4}{3}\times3.14\times 27.5^3\)

                                                              = 87069.583 \(ft^3\)

Two- thirds of the volume = (2/3) x 87069.583 = 58046.389  \(ft^3\)

Let R be the radius of the balloon with two-thirds of its maximum volume.

Then, \(\frac{4}{3}\pi R^3\) =  58046.389

⇒          \(R^3=\frac{3}{4\times3.14}\times 58046.389\) = 13864.583

⇒            \(R=13864.583^\frac{1}{3}\)

⇒           R = 24.023 ft

Now time taken to inflate balloon to the two-third of the maximum volume = 24.023/1.5 = 16 minutes approximately.

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Answer:

A) 16 minutes

Step-by-step explanation:

Hope this helps! Pls give brainliest!

The answer is B, which is to find the common denominator.

In solving a rational equation, the first step is usually to find a common denominator for all the fractions in the equation. This allows us to combine the fractions into a single fraction and simplify the equation.

To find the common denominator, we need to identify the factors of the denominators and determine the least common multiple (LCM) of these factors. Then, we multiply each fraction by the appropriate factor(s) to get the common denominator. For example, if we have the equation:

(3/x) + (4/2x) = 1/4

The denominators are x and 2x, which have factors of x and 2. The LCM of these factors is 2x, so we need to multiply the first fraction by 2 and the second fraction by 1 to get:

(6/2x) + (4/2x) = 1/4

Then we can combine the fractions and simplify the equation to get:

(10/2x) = 1/4

From here, we can continue to solve for x by cross multiplying and manipulating the equation.

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In other words, it's 2 feet, 3 inches

=================================================

Work Shown:

Convert the 4'1" to purely inches only

4'1" = 4 ft, 1 inch

4'1" = 4 ft + 1 inch

4'1" = 48 inches + 1 inch

4'1" = 49 inches

Note how 4 ft = 4*12 = 48 inches

-------------------

Through similar steps, you should find that 1'10", aka 1 ft 10 inches, is equivalent to 22 inches

Subtracting the two quantities gets us

(4' 1") - (1' 10") = (49 inches) - (22 inches) = 27 inches

Now convert that to the format "feet,inches".

27 in = 24 in + 3 in

27 in = (24/12 ft) + 3 in

27 in = 2 ft + 3 in

27 in = 2 ft, 3 in

27 in = 2' 3"

Answer:

8000

Step-by-step explanation

Answer:

Step-by-step explanation:

5x:8=7:2

5x/8=7/2

By Cross Multiplication:

10x=56

x=56/10

x=28/5

If you need to ask any question,please let me know.

To form the smallest number, use the smallest digits first. The smaller digits are on the left. The larger digits are on the right.

Consider this smaller example of 23 vs 32.

This question is a simultaneous equation having a quadratiic equation above and a linear equation below.

substitute the value of y in equation 2 for y in equation 1

recall y = 2x + 10 ( equation 2 )

2x + 10 = x2 - 3x -4 ( since y = 2x + 10 )

Having gotten the two values of x, we see that -2 is in the x position in the options given to us but 7 was ignored. Therefore we shall use x = -2 to find the value of y in equation 2

Recall, y = 2x + 10 ( equation 2 )

thus, y = 2 ( -2 ) + 10 ( since x = -2 )

hence, y = -4 + 10 ( since 2 x -2 = _4 )

so, y = +6

finally, x = -2 and y = 6. the best coordinate is ( -2, 6 )

Answer:

It is so easy u should get this right.

First draw a circle and there is an arc that is like forming a triangle inside a circle and then ab angle is 100 degree and outside is the center of the circle. And since u try to find how much is outside it most likely means that 100-60=40

so it b 40.

Step-by-step explanation:

The number of degrees in ∠ABO is 50°. Therefore, option A is the correct answer.

Given that, in a circle whose centre is O, arc AB contains 100°.

We need to find the number of degrees in ∠ABO.

An arc of a circle is a section of the circumference of the circle between two radii. A central angle of a circle is an angle between two radii with the vertex at the centre. The central angle of an arc is the central angle subtended by the arc. The measure of an arc is the measure of its central angle.

According to the theorem ∠ABO=1/2 × arc AB.

So, ∠ABO=1/2 × 100°=50°

The number of degrees in ∠ABO is 50°. Therefore, option A is the correct answer.

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Answer:

I think it's the fourth option?

Step-by-step explanation:

Hope this is the right answer and helps!

Answer:

8x-12

Step-by-step explanation:

Distribute the 4 so 4 time 2x is 8x and 4 times 3 is 12 but the 3 is negative so negative 12

Answer:

4(2x-3) = 8x - 12

Step-by-step explanation:

4 times 2x equals 8x

4 times -3 is 12 because a negative number + a postitve = a negative

Answer:

8^2+20-30x

Step-by-step explanation:

Answer:

Hello

B. -19

Step-by-step explanation:

= (-7)+7-(19)

= (-7+7)-19

= 0-19

= -19

Answer:

C

Step-by-step explanation:

Clustered data emerge when the data from the entire sample can be grouped into a variety of different categories, refers to as clusters. Each cluster involves numerous observations, giving the data a “clustered” or “hierarchical” structure, with each observations encapsulated within the cluster.

Also, if we plot a series of numbers on a graph and we will see several of our dots gathered together, we have a cluster

From the above definition of clustered data the only option that is fitting into it is option C .

25,50,50,25,75,75

Answer:

83 degrees

Step-by-step explanation:

The angles 56 and 41 plus the one in between should add up to 180 degrees. So you do 180 - 56 - 41 = 83.

83 and x are vertical angles so they are the same measure.

<x = 83 degrees

hope this helps! :)

Answer:

-1

Step-by-step explanation:

From 10 to 8.5   is  - 1.5  

   this is -1   S.D.   below the mean

(8.5 - 10)/1.5 = -1

Answer: A.

Step-by-step explanation:

1/4 is not in fact a natural number, it's a rational number, a ratio.

The possible number of nickels that Alison would have had is given as  [14, 15, 16, 17]

We would first have to define the variables x and y. We have x as the number of pennies that she has while y is the number of nickels that she has.

We would have the inequality equation as

x + y ≤ 23

Let us define an equation

0.01x + 0.05y ≥ 0.75   ------ 1

Given that she is said to have 6 pennies then x would be = 6

6 + y ≤ 23

we would have to solve the equation above

y ≤ 23 - 6

y ≤ 17

put the value of 6 as x in the equation 1 above

0.01(6) + 0.05y ≥ 0.75

simplify the equation

0.05y ≥ 0.69

divide through by 0.05

y ≥ 13.8

y ~ 14

Hence we would have the range of values to be between  14 ≤ y ≤ 17.

This would be listed as y = [14, 15, 16, 17]

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Answer:

Step-by-step explanation:

Volume of a rectangular prism = l x w x h

I am reading the width as 12 1/2 ft

Treat the depth of the ball pit as height

Vol = l x w x h

875 = (20)(12 1/2)(h)

875 = 250(h)

875/250 = 250h/250

3 1/2 = height

depth of the ball pit is 3 1/2 ft

The ball pit is 3.5 feet deep. This can be answered by the concept Surface area.

To find the depth of the ball pit, we can use the equation: Volume = length x width x depth.

The volume of the ball pit is given as 875 cubic feet, the length is 20 feet and the width is 12.5 feet. Let d be the depth of the ball pit. Therefore, the equation we can use is:

875 = 20 x 12.5 x d

To solve for d, we can divide both sides of the equation by (20 x 12.5):

d = 875 / (20 x 12.5)

d = 3.5 feet

Therefore, the ball pit is 3.5 feet deep

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Answer:

1. x=22  2. x= 28

Step-by-step explanation:

1. The total of angles in a triangle add up to 180˚.

93+65= 158

180-158=22

This means that x = 22

2. Angles on a straight line add up to 180.

180-125=55

180-83=97

55+97=152

180-152=28

This means that x = 28

Hope that this helps you.