Find the product of 2x2(6x + 3)

The probability that the average length of a bundle of steel rods chosen at random is less than 124.5 cm.

P(M < 124.5) = 0.0603.

P(M 169.3 cm 168.3 cm) = 0.7724

Given that,

Steel rods are produced by a firm. The lengths of the steel rods have a mean of 125.2 cm and a standard deviation of 2.3 cm, and they are regularly distributed. 25 steel rods are packaged together for shipping.

We have to determine the probability that the average length of a bundle of steel rods chosen at random is less than 124.5 cm.

P(M < 124.5-cm) =

We know that,

Mean =μ= 125.2

Standard deviation=σ=2.3

n=25

P(M<124.5)= P[(M-μ)/σ< 124.5-125.2/0.46]

=P(z<-1.522)

Using the z-table,

=0.0603

Therefore, The probability that the average length of a bundle of steel rods chosen at random is less than 124.5 cm.

P(M < 124.5) = 0.0603.

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Try reducing your annealing temperature by a few degrees and repeat the PCR.

What is the principle of PCR machine ?

The PCR technique is based on the enzymatic replication of DNA. In PCR, a short segment of DNA is amplified using primer mediated enzymes. DNA Polymerase synthesis new strands of DNA complementary to the template DNA.

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0.27 = 0.0027% probability that this bulb was produced by factory B.

Given,

In the question:

Three factories produce light bulbs to supply the market. Factory a produces 20%, 50% of the tools are produced in factory B and 30% in factory C. 2% of the bulbs produced in factory A, 1% of the bulbs produced in factory b and 3% of the bulbs produced in factory C are defective.

We use the conditional probability formula to solve this question. It is

P(A|B) = P(A∩B) / P(A)

In which,

P(B|A) is the probability of event B happening, given that A happened.

P(A∩B) is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Bulb is defective.

Event B: Produced by factory A.

Probability of a bulb being defective.

2% of 20%(factory A)

1% of 50%(factory B)

3% of 30%(factory C). So

P(A) = 0.02 x 0.2 + 0.01 x 0.5 + 0.03 x 0.3

P(A) = 0.018

Defective and from factory B:

1% of 50%. So

P(A∩B) = 0.01 x 0.5 = 0.005

What is the probability that this bulb was produced by factory B?

P(A|B) = P(A∩B) / P(A)

P(A|B) = 0.005/ 0.018

P(A|B) = 0.27

Hence, 0.27 = 0.0027% probability that this bulb was produced by factory B.

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There are 4 different 12-bit strings possible that begin with 0101, end with 1100 or have 0110 as the four middle bits.

We have to find the number of 12-bit strings that are starting with 0101, end with 1100 or have 0110 in the middle bits.

So, the first four position are reserved for 0101 and we have two options for the middle four bits and the end four positions.

So, we can write here,

Total possible different positions for 1100 and 0110 is,

= 2 x 2

= 4

Because, the two combination can appear simultaneously or they can appear one by one.

So, the total different 12-bit strings possible that have 0101 in the start, 1100 in the end or 0101 in the middle are 4.

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The probability that the average fracture strength of 100 randomly selected pieces will be equal to 33.19%.

In order to find the probability first we find the Z score. The Z score related the standard deviation and the mean of any data as

Z = X - μ/σ where Z is the Z score, X is the random variable, μ is the mean and σ is the standard deviation.

The standard deviation of the randomly selected 100 variables will be given as

s = σ/√n where n = 100 and σ = 2

s = 2/√100

s = 0.2

Now, the Z score for this data will be

Z = X - μ/s where X = 13.8, and μ = 13.5 and the value of s = 0.2

Z = 13.8 - 13.5/0.2

Z = 1.5

Now, for Z = 1.5 the p value will be 0.66807

The probability will be P = 1 - 0.66807 = 0.33193 that is 33.19%

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Since the scooter is rented for $1 and the firm charges $0.15 per minute, the necessary expression is 1+0.15m.

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.

Here,

rent of scooter=$1

rent of scooter per minute=$0.15

The expression,

=1+0.15m

The required expression is 1+0.15m as rent of scooter is $1 and per minute rent charged by company is $0.15.

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Answer:

-6

Step-by-step explanation:

-(-3)²+3

-9 + 3

-6

Three problems would arise if the frequency of scrum was lowered to every two or three days.

(A) There may be missed opportunities to examine and amend the sprint backlog.

(B) The Sprint strategy deteriorates; barriers are raised and taken down more slowly.

(C) Too much time is spent updating the scrum board prior to meetings.

Scrum is a project management framework that was initially focused on software development, while it has now been applied to other areas such as research, sales, marketing, and cutting-edge technology.

It is intended for groups with ten or fewer members who divide their work into tasks that can be finished in sprints, which are time-boxed iterations that can be done in as little as one month and most frequently two weeks.

If the frequency was reduced to every two or three days, there would be three issues.

(A) The chances to review and modify the Sprint Backlog may be missed.

(B) The Sprint plan becomes imprecise; obstacles are raised and removed more slowly.

(C) Too much time is spent before meetings updating the scrum board.

Therefore, three problems would arise if the frequency was lowered to every two or three days.

(A) There may be missed opportunities to examine and amend the sprint backlog.

(B) The Sprint strategy deteriorates; barriers are raised and taken down more slowly.

(C) Too much time is spent updating the scrum board prior to meetings.

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Step-by-step explanation:

of course there is an explanation. and a correct answer (not just a wild guess).

f(x) = 2x

g(x) = 2x² - 1

f(g(x)) means that x is first processed by g, and then the result of that is processed by f.

in other words, the whole functional expression of g becomes the input argument for f.

therefore,

f(g(x) = 2(2x² - 1) = 4x² - 2

so, the correct answer is light blue.

Answer:

(2,-1)

Step-by-step explanation:

The 3360 possible four-digit numbers are greater than 2999.

What is the combination?

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.

We know it has to be a four-digit number,

The first digit has to be between 3 and 9 (inclusive) so there are 7 options.

The unit digit can be any number so there are 10 options.

The answer will be 7 * (# of possible middle digit combos) * 10.

There are 7*48*10 = 3360 possible four-digit numbers.

Hence, the 3360 possible four-digit numbers are greater than 2999.

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In a book, a study of analysis with four groups is recommended to include a maximum of four prepared research topics.

These projects give you and your students the chance to research watershed-related subjects outside of the regular chemical water testing every three weeks. They give your pupils the chance to hone their research and scientific method skills, examine issues related to waterways that interest them, and analyze data and solve problems. For a study with four groups, a book can only prescribe a maximum of four planned research topics.

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Bradon is 24 years old and Micheal is 72 years old.

Michael is 3 times as old as brandon. 18 years ago, michael was 9 times as old as brandon

Let m represent Michael

Let b represent Brandon

Then,

m = 3b                    <-----------"Michael is 3 times as old as Brandon."

m - 18 = 9(b - 18)    <-----------"18 years ago, Michael was 9 times as old as Brandon."

3b - 18 = 9b - 162

-18 = 6b - 162

144 = 6b

b = 24     <-------This is Brandon's age.

3b = m

3(24) = 72 <------This is Michael's age.

Therefore, Michael is 3 times as old as Brandon. Also, 18 years ago, Brandon would have been 6 and Michael would have been 54

Now, Bradon is 24 years old and Micheal is 72 years old.

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Answer:

radius = 6.5

Step-by-step explanation:

the equation of a circle centred at the origin is

x² + y² = r² ( r is the radius )

x² + y² = 42.25 ← is the equation of a circle centred at the origin

with r² = 42.25 ( take square root of both sides )

r = [tex]\sqrt{42.25}[/tex] = 6.5

Answer:

Step-by-step explanation:

Given equation,

→ y = 3x + 5

The value of y when x is 10,

→ y = 3x + 5

→ y = 3(10) + 5

→ y = 30 + 5

→ [ y = 35 ]

The value of y when x is -10,

→ y = 3x + 5

→ y = 3(-10) + 5

→ y = (-30) + 5

→ [ y = -25 ]

So, these are the values of y.

The correct conclusion for "it was expected that the hourly wage in October 2019 would increase, and the p-value associated with the hypothesis test is .001" is "the average wage is not increased."

A hypothesis is described in statistics as a formal statement that explains the relationship between two or more variables belonging to the specified population. It aids the researcher in converting the stated issue into an understandable justification for the study's findings. A strong hypothesis outlines the predicted link between the dependent and independent variables and is succinct and straightforward. It is best to be as specific and testable as possible when describing this relationship.

The answer to the statement "it was predicted that the hourly wage in October 2019 would grow, and the p-value associated with the hypothesis test is.001" should be "the average wage is not raised."

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Answer:

 122°

The measure of the central angle is twice the measure of the inscribed angle that subtends the same arc.

 ∠ABC = 2×∠ADC = 2×61°

 ∠ABC = 122°

Step-by-step explanation:

More than twice as many roast beef sandwiches as the deli sold over the course of five months.

Let the tuna sandwich sold by deli be 'x'

Then, tuna sandwich for 5 months-

1st month - x1

2nd month - x2

3rd month - x3

4th month - x4

5th month - x5

Then,

Selling of roast beef sandwich is 3 times more than tuna sandwich.

Then, roast beef sandwich for 5 months-

1st month -3x1

2nd month - 3x2

3rd month -3x3

4th month - 3x4

5th month - 3x5

Thus, the difference is-

Difference = (3x5 + 3x4 + 3x3 +  3x2 + 3x1) - (x1 + x2 + x3 + x4 + x5)

Difference  = 2x1 + 2x2 + 2x3 + 2x4 + 2x5

Thus, more than twice as many roast beef sandwiches as the deli sold over the course of five months.

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Answer:

Step-by-step explanation:

The relative humidity of the parcel at sea level on the leeward side is 58% that is option D

The amount of water vapour in an air-water mixture relative to the maximum amount is known as relative humidity (RH). RH is a comparison between the humidity of a specific water-air mixture and the saturation humidity ratio at a particular temperature (dry-bulb)

By deducting the temperature on the wet-bulb thermometer from the temperature on the dry-bulb thermometer and utilizing a relative humidity chart, one may determine the relative humidity.

The relative humidity of the parcel at sea level on the leeward side is 58%

Option d is the correct answer

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Circle A will be enlarged by a scale factor of 2 to assist demonstrate how circle A and circle B are comparable.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle).

The equation of a circle with the center and radius r

( x − a )² + ( y − b )² = r²

The equation of circle A,

(x-(-2))²+(y-(-1))²=2²

x²+4+4x

The equation of circle B,

(x-1)²+(y-2)²=4²

Thus, circle A will be enlarged by a scale factor of 2 to assist demonstrate how circle A and circle B are comparable.

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The value of d is 0.05.

What is cohen?

A standardized effect size called Cohen's d is used to compare the means of two groups. It's frequently applied when contrasting a treatment with a control group. It may be an acceptable effect size to include with the findings of the t-test and the ANOVA. Cohens d is often used in psychology.

Here, we have

Given

Mean = 5

Standard deviation = 100

We have to find the value of d

So, we apply here formula for d

Cohen d = mean / standard deviation      ........................1

Now, we put the value of mean and  standard deviation and we get

Cohen d = 5 / 100

Cohen d = 0.05

Hence, the value of d is 0.05

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a) SS = {HHH, THH, HTH, HHT, THT, TTH, HTT,  TTT} i) P(1 head) = 0.375 ii) P(at least 2 heads) = 0.5 iii) P(no heads) = 0.125.

Suppose that a coin is tossed three times and the side showing face up on each toss is noted. Suppose also that on each toss heads and tails are equally likely. Let HHT indicate the outcome heads on the first two tosses and tails on the third, THT the outcome tails on the first and third tosses and heads on the second, and so forth.

Given that

a) A coin is tossed three times and the side showing face up on each toss is noted.

The total number of possible outcome are 2³ = 8

The sample space is given by

SS = {HHH, THH, HTH, HHT, THT, TTH, HTT,  TTT}

b) Write each of the following events as a set, in set-roster notation, and find its probability.

(i)The event that exactly one toss results in a head.

In this case we need to include only those outcomes where we have exactly on head,

E(1 head) = {THT, TTH, HTT}

So there are 3 such outcomes, the probability is

P(1 head) = no. of desired outcomes/total number of outcomes

P(1 head) = 3/8

P(1 head) = 0.375

(ii) The event that at least two tosses result in a head

In this case we need to include only those outcomes where we have at least two heads which means two or greater than two,

E(at least 2 heads) = {HHH, THH, HTH, HHT}

So there are 4 such outcomes, the probability is

P(at least 2 heads) = 4/8

P(at least 2 heads) = 0.5

(iii) The event that no head is obtained.

In this case we need to include only those outcomes where we have no heads at all.

E(no heads) = {TTT}

So there is only 1 such outcome, the probability is

P(no heads) = 1/8

P(no heads) = 0.125

Hence the answer is a) SS = {HHH, THH, HTH, HHT, THT, TTH, HTT,  TTT} i) P(1 head) = 0.375 ii) P(at least 2 heads) = 0.5 iii) P(no heads) = 0.125.

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A scatter plot or scatter gram chart can highlight the distribution patterns or demonstrate and compare the two data sets.

What is scatter plot ?

Dots are used to indicate values for two separate numeric variables in a scatter plot . The values for each data point are shown by the position of each dot on the horizontal and vertical axes.

Scatter plot shows the relationships between variables are visualized using scatter plots.

The given data can highlight the distribution patterns or demonstrate two sets of rainfall data for two different time periods in the same location.

From the given data, it is observed that the given data is observed in the scatter plot.

Hence, a scatter plot or scatter gram chart can highlight the distribution patterns or demonstrate and compare the two data sets.

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The sample mean versus desired mean is not a type of comparison one would anticipate for a two-sample test to be performed. Therefore, the option C holds true.

A sample test can be referred to or considered as the test that includes the conducting of an activity to determine the nearest possible outcome of a much larger set of observations. The purpose of conducting such a test is testing that two population means are the same in a set of observations. If the means are same, it means that the test is successful.

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The percentage error in selecting the random box is 2.285 %

Let the total amount of bag of cereal be = 350 grams

The box selected at random had a weight of = 342 grams

We know the formula of percentage error.

The percentage error is calculated by the formula

Percentage Error =

( ( Original Value - Observed Value ) / Original Value ) x 100

Plug the values in above formula:

Percentage Error = ( ( 350 - 342 ) / 350 ) x 100

                             = ( 8 / 350 ) x 100

                              = 0.02285 x 100

                              = 2.285 %

Hence , The percentage error in selecting the random box is 2.285 %

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The required closest approximation of city A's population is 1.185 million.

Percentages  are basically divisions where the denominator is 100. To show that a number is a percent, we utilize the percent image (%) close to the number. For instance, on the off chance that you got 75 inquiries right out of 100 on a test (75/100), you would have scored 75%.

We have, city A is 23.5% of city B

A/B = 235/1000 = 47/200 = (B)47/200-----------(1)

and, city B is 51% of city C.

B/C = 51/100

B = (51/100)×9.89 = 5.0439 million

As C = 9.89 million

Put the value of c in equation (1)

A =  (5.0439)47/200 = 1.185 million

Thus, required population of city A is 1.185 million.

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The antiderivative of a function f will be the integral of differentiated  value of the function i.e. the function itself.

What is Antiderivative of a function?

A function is said to be antiderivative if its derivative equals the original function. The antiderivative function is the same as an indefinite integral. The limit of a sum of terms f (x) x in the limit that approaches zero, where is the integrand function, is known as a definite integral.

Considering a function f(x) = Sin x

                                  dy/dx = Cos x

 Now, the integral of Cos x would be known as Anti derivative.

here, ∫ Cos x = Sin x

thus, Anti derivative of Cos x is equal to the function itself.

hence, proved.

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Answer: I dunno

Step-by-step explanation:

Answer: 13

Step-by-step explanation: Solve this problem by. using the Pythagorean Theorem

[tex]12^{2} + 5^{2} = \sqrt[2]{C}[/tex]

144 + 25 = 169

[tex]\sqrt[2]{169}[/tex] = 13

THe Hypotenuse or distance between the triangle diagonals is 13.