(Find the HCF of):
p^2+4pq+4q^2, p^4 + 8pq^3 and 3p^4 - 10p^2q^2+ p^3q​

The Chi-square test is a statistical test used to determine if there is a significant difference between observed and expected frequencies in categorical data. In this example, the test is used to assess whether there is a significant difference in the mean breaking strengths of two types of cables.

The Chi-square test of significance is employed when dealing with categorical or nominal data. It compares the observed frequencies with the frequencies that would be expected if the variables were independent. In this case, the breaking strengths of the two cables are the variables of interest.

To perform the test, the first step is to define the null hypothesis (H0) and the alternative hypothesis (Ha). In this example, H0 assumes that there is no difference in the mean breaking strengths of the two cables, while Ha suggests that there is a difference.

Next, the test statistic, denoted by X2 (chi-square), is calculated using the formula X2 = Σ[(O - E)²/E], where O represents the observed frequencies and E represents the expected frequencies under the assumption of independence.

To determine the expected frequencies, we need to estimate the means and variances of the breaking strengths. Here, x = 1925 and sigma = 40 for the first cable, and x = 1905 and sigma = 30 for the second cable.

Once the test statistic is calculated, it is compared to a critical value from the Chi-square distribution with degrees of freedom equal to (r - 1)(c - 1), where r is the number of rows and c is the number of columns in the contingency table. The significance level of 0.01 determines the critical value.

If the calculated X2 value is greater than the critical value, we reject the null hypothesis and conclude that there is sufficient evidence to indicate a difference in the mean breaking strengths of the two cables. Conversely, if the calculated X2 value is less than or equal to the critical value, we fail to reject the null hypothesis and conclude that there is no significant difference.

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m = (y2-y1)/(x2-x1)

m = (1-0)/(-3-5)

m = 1/-8

The conditions that must hold for inferential procedures to be valid for this scenario are:

(b) the two sample groups must be independent of each other, (c) the data distribution for both men's and women's hemoglobin levels must be normally distributed or each sample size must be larger than 30, and (d) the observations within each sample must be independent.

(b) The two sample groups must be independent of each other because the samples should not be related in any way that could influence the results.

(c) The data distribution for both men's and women's hemoglobin levels must be normally distributed or each sample size must be larger than 30. If the data is not normally distributed, then the Central Limit Theorem can be applied if the sample size is greater than 30.

(d) The observations within each sample must be independent to avoid bias in the results. This means that each observation should not be influenced by any other observation.

(a) The expected count for each level of the categorical variable must be at least 5. This condition is relevant for Chi-square tests of independence, which are not being used in this scenario.

(e) There must be 10 successes and 10 failures in each sample. This condition is relevant for tests of proportions, which are not being used in this scenario.

So b,c and d are correct options.

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The hypothesis is that more people will complete the survey if they are paid, potentially leading to a larger and more representative sample of the population.

When conducting a survey, it is important to ensure that the sample is representative of the population being studied in order to obtain accurate information. However, if only a small percentage of the sample actually returns the survey, the information collected may be biased and not truly representative of the population. This is where the concept of incentives comes into play. Providing an incentive, such as payment, may encourage more people to complete the survey and increase the response rate.

In the study examining the relationship between monetary incentive and survey completion rates, the researchers found that offering payment did in fact increase the percentage of the sample who completed the survey. This suggests that monetary incentives may be an effective way to improve response rates and obtain more representative data.

However, it is important to note that the amount of payment offered may also affect the response rate and the quality of the data collected. Overall, while incentives may improve response rates, it is crucial to carefully consider the potential biases and limitations of survey data, and to design and implement surveys in a way that minimizes these issues.

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Answer: 81,000

Step-by-step explanation:

We can solve this by using the formula given.

If f(1)=1000x3^1, then 1,000x3=3,000

If f(2)=1000x3^2, then 3^2=9 and 1000x9=9000,

and so on,

Now, f(4) will equal 1000x3^4, and 3^4 is 3x3x3x3, which is 9x9 or 9^2, which would be equal to 81, and 81x1000=81,000

To complete the table of values for the exponential function f(x) = 1000*3^x, we can evaluate the function for x = 0, 1, 2, 3, and 4, since we are interested in the number of bacteria on the phone after 4 hours.

x f(x)

0 1000

1 3000

2 9000

3 27,000

4 81,000

Therefore, after 4 hours, there will be 81,000 bacteria on the surface of the phone, assuming the number of bacteria triples every hour and can be described by the exponential function f(x) = 1000*3^x.

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Answer:

0

Step-by-step explanation:

3996 is closer to 0 than 10,000

Answer:

4.47, 121/25, 4 17/20, 4.859

More details: U could just change them into decimals bc it’s easier that way but people have different ways so it’s ok that’s just my opinion.

Answer:

100

Step-by-step explanation:

\((100 \times 3) - (100 \times 2) = 100 \)

Answer:

rent for another $2.00 an hour. Lessons are $33.80 an hour. And he needs a lesson! He decides to snow board for 5 hours and, in that time, get a 1-hour

Step-by-step explanation:

It is simpler to compute the likelihood of the complement event when calculating probabilities since you can then just subtract it from 1 to determine the probability.

the variety of strategies for success. all events that could possibly occur.

Since 13% of people are lefties and 87% are righties, we'll assume that everyone is either a righty or a lefty, thus the decimal percentage of 0.87 divided by the total number of participants, 12, is the mean.

P(Right handed) = 1 - 0.13 = 0.87 where P(Left handed) = 0.13 and P(Right handed) = 0.13 12 people make up the nth number. The binomial probability distribution will be used in this case, and it can be computed using the formula P(X = n|N,p) = NCn*(pn)*(1-p) (N-n).

where p is the chance of success and n is the sample size, or 12, in this case. Additionally, q represents the 0.13 failure chance.

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P(Right handed) = 1 - 0.13 = 0.87 where P(Left handed) = 0.13 and P(Right handed) = 0.13 12 people make up the nth number. It is simpler to compute the likelihood of the complement event when calculating probabilities.

the variety of strategies for success. all events that could possibly occur.

Since 13% of people are lefties and 87% are righties, we'll assume that everyone is either a righty or a lefty, thus the decimal percentage of 0.87 divided by the total number of participants, 12, is the mean.

P(Right handed) = 1 - 0.13 = 0.87 where P(Left handed) = 0.13 and P(Right handed) = 0.13 12 people make up the nth number. The binomial probability distribution will be used in this case, and it can be computed using the formula P(X = n|N,p) = NCn*(pn)*(1-p) (N-n).

where p is the chance of success and n is the sample size, or 12, in this case. Additionally, q represents the 0.13 failure chance.

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The value of side length w is 13.75 .

Given right angled triangle,

Perpendicular = w

Hypotenuse = 17

Angle of triangle = 54°

So,

According to the trigonometric ratios,

tanФ = p/b

cosФ = b/h

sinФ = p/h

By using sinФ,

sinФ = p/h

sin 54° =  w/ 17

0.809 = w/17

w = 13.75 .

Thus after correction w will be 13.75

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⠀⠀ ⠀ ⠀⠀ \(\huge{\tt{\red{❥}\green{A}\purple{N}\pink{S}\blue{W}\orange{E}\red{R}}}\)\(\longmapsto- 1 = 7 - 6\)

Answer:

hello again haha

-2, -1, 0, 1

Answer:

157

Step-by-step explanation:

Formula: C= 2r3.14, so multiply them together to get 157.

or to make it easy do C= D3.14

D being diameter and r being radius.

10m3n2 and 15mn4 could have a greatest common factor  of 5m2n2.

Two terms that could have a greatest common factor of 5m2n2 are 10m3n2 and 15mn4.

To see why, we can factor each term into its prime factors and then identify the factors that are common to both terms.

First, let's factor 10m3n2:
10m3n2 = 2 × 5 × m × m × m × n × n

Next, let's factor 15mn4:
15mn4 = 3 × 5 × m × n × n × n × n

Now, we can identify the factors that are common to both terms:
- 5
- m
- n
- n

These common factors can be combined to give the greatest common factor of the two terms:
5m2n2

Therefore, 10m3n2 and 15mn4 could have a greatest common factor of 5m2n2.

It's worth noting that there could be other pairs of terms that also have a greatest common factor of 5m2n2, but this is just one example. To find other pairs, we would need to factor the terms and look for common factors.

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Answer:

True

Right angles measure 90° . So each vertical angle = 90° and hence they are equal

Step-by-step explanation:

Table B correctly represents the ratio of students to adult

Ratio is an ordered pair of numbers x and y, which can written in form x/ y where y is not 0.

For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is 8 :6 Similarly, the ratio of lemons to oranges is 6:8

ratio 48:6= 48/6

= 8

this means that 8 student to 1 adult

in table B all ratio of student to adult is 8:1

therefore only table 2 obeys this ratio

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In linear equation, 24.9  tall is the tree .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

We can set up a proportion comparing the height of each object to the length of the shadow.

     h/15 = 21.1/12.7

     h = 1.66 * 15  

   h   = 24.9

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To test the hypothesis that the mean weight of two sheets is equal (μ1 - μ2) against the alternative that it is not, and assuming equal variances, we can use a two-sample t-test. The t-statistic can be calculated using the following formula:

t = (x1 - x2) / (s_p * sqrt(1/n1 + 1/n2))

where:

x1 and x2 are the sample means of the two sheets,

s_p is the pooled standard deviation,

n1 and n2 are the sample sizes.

The pooled standard deviation (s_p) can be calculated using the following formula:

s_p = sqrt(((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2))

where:

s1 and s2 are the sample standard deviations.

To calculate the t-statistic, we need the sample means, sample standard deviations, and sample sizes.

Once you provide the specific values for these variables, I can assist you in calculating the t-statistic to 3 decimal places.

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To test the hypothesis that the mean weight of the two sheets is equal (μ1 - μ2) against the alternative that it is not, we can use a paired t-test assuming equal variances. The paired t-test is used when we have paired data or measurements on the same subjects or objects.

The t-statistic for a paired t-test is calculated as follows:

t = (X1 - X2) / (s / √n)

where X1 and X2 are the sample means of the two samples, s is the pooled standard deviation, and n is the number of pairs.

Please provide the sample means, standard deviation, and sample size for each sheet so that we can calculate the t-statistic to 3 decimal places.

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Answer:

Yes, they do make sense because the amount of square feet is equal to the amount of money needed to make the purchase in the mathematical abbreviations.

Step-by-step explanation:

Answer:

y = 7

Step-by-step explanation:

The equation: 2y+5=3y-2

-

Solving the equation:

1) We have to move 2y to the other side while also moving the -2 to the other side.

The equation will now be 5+2=3y-2y

2) Now we can add and subtract the values.

So, it'll  be 7 = y.

Therefore, Y is equal to 7.

To represent the world population in billions t years after 2000, an exponential growth equation can be used.

Explanation:

Let y be the world population in billions t years after 2000. Let t be the time elapsed in years since 2000. Let y0 be the world population in billions in the year 2000. Let r be the annual growth rate of the world population as a decimal.

Using the exponential growth equation, we can write:

y = y0 * (1 + r)^t

To find the value of r, we can use the population data from 2000 and 2005. The population growth from 2000 to 2005 can be calculated as:

(6.515 - 6.124) / 6.124 = 0.0638

This means that the world population grew at an annual rate of 0.0638 or 6.38% per year. Therefore, the exponential growth equation for the world population in billions t years after 2000 is:

y = 6.124 * (1 + 0.0638)^t

This equation can be used to estimate the world population in any year t after 2000.

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The amount he gets for lunch is an illustration of mean and averages.

He gets for lunch is $240 daily

Represent the amount he gets for lunch each day be x.

So, the amount saved each day is x/2

From Monday to Friday, the total savings would be 5x/2

So, we have:

\(\mathbf{\frac{5x}{2} = \$600}\)

Multiply both sides by 2

\(\mathbf{5x = \$1200}\)

Divide both sides by 5

\(\mathbf{x = \$240}\)

Hence, the amount he gets for lunch is $240 daily

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Answer:

Hi there!

Recall that slope-intercept form is:

y = mx + b

Where m = slope

In this instance, we are given a slope of 4,

therefore:

y = 4x + b

Substitute in the x and y coordinates of the point given:

0 = 4(3) + b

0 = 12 + b

Substract 12 from both side:

-12 = b

Therefore, the equation would be:

y = 4x - 12

Graph the equation by finding x and y values or using a calculator:

x = 0, y = 4(0) - 12 = 12 (0, 12)

x = 1, y = 4(1) - 12 = - 8 (1, -8)

x = 2, y = 4(2) - 12 = - 4 (2, -4)

x = 3, y = 4(3) - 12 = 0 (3, 0)

And so forth:

Thanks<8

30 players

Question 1:

To determine the number of players expected to get between 42 and 72 seconds, we need to calculate the proportion of the circle corresponding to this range. The range covers 72 - 42 = 30 units on the circle. Since the circle is marked evenly from 0 to 100, each unit corresponds to 100/100 = 1% of the circle. Therefore, the proportion of the circle representing the range is 30%.

If 100 players are selected randomly, we can expect approximately 30% of them to get between 42 and 72 seconds to solve the puzzle. Therefore, the expected number of players in this range is 0.3 * 100 = 30 players.

Question 2:

To calculate the probability that the number of players who will get between 42 and 72 seconds is within two standard deviations of the expected number, we need to consider the distribution of the number of players in this range.

Assuming that the number of players in the range follows a binomial distribution with n = 100 (the number of trials) and p = 0.3 (the probability of success), the mean of the distribution is given by μ = n * p = 100 * 0.3 = 30 players.

The standard deviation of a binomial distribution is given by σ = sqrt(n * p * (1 - p)) = sqrt(100 * 0.3 * 0.7) ≈ 4.58 players.

Within two standard deviations of the mean, we have a range of 2 * σ = 2 * 4.58 = 9.16 players.

To calculate the probability that the number of players falls within this range, we need to find the probability of the range 30 ± 9.16 in the binomial distribution. This can be calculated using the cumulative distribution function (CDF) of the binomial distribution.

Unfortunately, the specific probability cannot be determined without further information about the shape of the distribution or additional assumptions.

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We are given two rational expressions: one with (y² - 13y + 36) in the numerator and (y² + 2y – 3) in the denominator, and the other with (y² - y – 12) in the numerator and (y² - 2y + 1) in the denominator. We need to simplify these rational expressions.

Simplifying the first rational expression:
The numerator of the first expression, y² - 13y + 36, can be factored as (y – 4)(y – 9).
The denominator, y² + 2y – 3, can be factored as (y + 3)(y – 1).
Therefore, the first rational expression simplifies to (y – 4)(y – 9) / (y + 3)(y – 1).

Simplifying the second rational expression:
The numerator of the second expression, y² - y – 12, can be factored as (y – 4)(y + 3).
The denominator, y² - 2y + 1, can be factored as (y – 1)(y – 1) or (y – 1)².
Therefore, the second rational expression simplifies to (y – 4)(y + 3) / (y – 1)².

By factoring the numerator and denominator of each rational expression, we obtain the simplified forms:

First rational expression: (y – 4)(y – 9) / (y + 3)(y – 1)
Second rational expression: (y – 4)(y + 3) / (y – 1)²

These simplified expressions are in their simplest form, with no common factors in the numerator and denominator that can be further canceled.


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The required coordinate of b is given as (-7, 4 ).

Given that,

To determine the coordinate of b  if M is the midpoint of AB. A(1, -4) and M(-3 ,0).

The midpoint is that point the line whose distance from both the ends of the line is equal.

Here,

We have given two coordinates one of the endpoints of AB and the other is midpoint M i.e. A(1, -4) and M(-3, 0).

Definition of midpoint says,

x = [x₁ +  x₂] / 2 ; y = [y₁ + y₂] / 2

x₁ = 1, x = -3 , y₁ = -4, y = 0

now,

-3 = [1 + x₂] / 2 ; 0 = [-4 + y₂] / 2

x₂ = -6 - 1 ; y₂ = 0 + 4

x₂ = -7 : y₂ = 4

Thus, the required coordinate of b is given as (-7, 4 ).

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