What number should be added to both sides of the equation to complete the square? x2 + 3x = 6
a. (StartFraction 3 Over 2 EndFraction)
b. squared 3/2
c. 3
d. 6^2

To order the sides of ΔABC from shortest to largest, we need to measure each side and compare them. The shortest side of the triangle will be the one with the smallest length, while the largest side will be the one with the greatest length. The middle side will be the one that is neither the shortest nor the largest.

To measure the sides of ΔABC, we can use a ruler or a measuring tape. Once we have measured each side, we can compare them to determine which is the shortest, which is the middle, and which is the largest.

For example, if the lengths of the sides of ΔABC are 3 cm, 4 cm, and 5 cm, then the shortest side is 3 cm, the middle side is 4 cm, and the largest side is 5 cm.

In summary, to order the sides of ΔABC from shortest to largest, we need to measure each side and compare them. The side with the smallest length will be the shortest side, the side with the greatest length will be the largest side, and the remaining side will be the middle side.

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The eigenvalues of the coefficient matrix A is λ = 5 ± 6i

An eigenvector corresponding to the eigenvalue with a positive imaginary part is v = k(3 + 2i, 1)

The general solution can be expressed as

X(t) = e^(5t) × (C1 × cos(6t) + C2 × sin(6t)) × (3 + 2i, 1)

Given,  dx/dt = 7x + 13y and dy/dt = -2x + 9y.

Eigenvalues of the coefficient matrix A:

The coefficient matrix A is:

[tex]A = \left[\begin{array}{cc}7&13\\-2&9\end{array}\right][/tex]

To get the eigenvalues, we have to solve the characteristic equation.

| (7 - λ) (9 - λ) - (-2)(13) | = 0

63 - 7λ - 9λ +λ² + 26 =0

λ² - 16λ + 89 =0

Solving this equation, we get the eigenvalues λ = 5 ± 6i.

The positive imaginary part eigenvalue λ = 5 + 6i. Let v be the eigenvector now we have to solve the system (A - λI)v = 0.

| (2 - 6i)  13     | |x| = |0|

|  -2      (4 - 6i)| |y| = |0|

After solving this system, we get an eigenvector v = k(3 + 2i, 1), where k is a constant.

The general solution of the given system:

The general solution can be expressed as

X(t) = e^(5t) × (C1 × cos(6t) + C2 × sin(6t)) × (3 + 2i, 1)

Where C1 and C2 are constants.

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Secular drift would be most likely to name as the problem of internal invalidity. Therefore option D is correct.

Secular drift is a type of internal invalidity that occurs when external factors unrelated to the study cause changes in the study outcomes. In this case, the major recession in the economy could have affected the job market and reduced the effectiveness of the job training program. This external factor could be a threat to the internal validity of the study because it undermines the ability to attribute changes in the outcome variable to the treatment. Therefore, the experiment's designers would be most likely to name secular drift as the problem.

Instrumentation refers to changes in the measurement instrument or procedures that affect the results. Contamination refers to the spread of treatment effects to the control group or vice versa. Selection bias occurs when participants are not randomly assigned to treatment groups, resulting in groups that differ in important ways. Regression occurs when participants are selected based on extreme scores, and their scores tend to regress to the mean on subsequent measurements.

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The upper bound of the 95% confidence interval for the difference in population mean heights between eighth-grade students and fifth-grade students is given as follows:

48.29 cm.

The difference of the means is given as follows:

160 - 130 = 30 cm.

The standard error of the difference of the means is given as follows:

s = sqrt((35/sqrt(25))² + (32/sqrt(30))²)

s = 9.12.

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 30 + 25 - 2 = 53 df, is t = 2.0057.

The upper bound of the interval is then given as follows:

30 + 2.0057 x 9.12 = 48.29 cm.

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Answer:

The answer is Sometimes.

The solution of the system of equations is given by the ordered pair (2, 2).

In order to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

y = -x + 4    ......equation 1.

y = 1/2(x) + 1 ......equation 2.

Based on the graph shown in the image attached above, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant I, and it is given by the ordered pairs (2, 2).

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The system has a unique solution, and therefore, there is only one solution to the system of equations.

Given the system of equation in the question:

x + y = 7

2x - 3y = -21

First, solve one of the equations for one of the variables and substitute it into the other equation.

From equation (1), we can solve for y in terms of x as follows:

x + y = 7

y = 7 - x --- equation (3)

Now we can substitute equation (3) into equation (2) and solve for x:

2x - 3y = -21

Plug in y = 7 - x

2x - 3(7 - x) = -21

Simplifying the above equation, we get:

2x - 21 + 3x = -21

5x - 21 = -21

5x = 0

x = 0

Now we can substitute x = 0 into equation (1) to find y:

x + y = 7

Plug in x = 0

0 + y = 7

y = 7

Therefore, the solution to the system of equations is x = 0, y = 7.

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A male at the 70th percentile has a body temperature of 98.26°F.

The body temperature of a male at the 70th percentile, we need to use the cumulative distribution function (CDF) of the normal distribution.

The CDF gives the probability that a random variable (in this case, body temperature) is less than or equal to a certain value.

A standard normal distribution table or a calculator to find the corresponding z-score for the 70th percentile, and then use the formula:

z = [tex](x - \mu) / \sigma[/tex]

x is the body temperature we want to find, mu is the mean, sigma is the standard deviation, and z is the z-score corresponding to the 70th percentile.

Using a standard normal distribution table, we find that the z-score for the 70th percentile is approximately 0.52.

Plugging in the values we have:

0.52 = (x - 98.1) / 0.30

Solving for x, we get:

x = 98.1 + 0.30 × 0.52

x = 98.26°F

To draw a well-labeled sketch to support the answer, we can start by drawing a normal distribution curve with the mean of 98.1°F and a standard deviation of 0.30°F.

The point on the x-axis corresponding to the body temperature of a male at the 70th percentile, which is 98.26°F.

The area under the curve to the left of this point, which represents the probability that a male has a body temperature less than or equal to 98.26°F.

The resulting sketch would look like this:

Normal Distribution Curve with 70th Percentile

The shaded area under the curve represents the probability that a male has a body temperature less than or equal to 98.26°F, is approximately 0.70 or 70%.

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There is an inverse relationship between the EBP and the required sample size. As the EBP increases, the required sample size decreases, and vice versa.

As the error bound of the proportion (EBP) increases, the required sample size decreases.

The EBP is a measure of the maximum error that is allowed in estimating a population proportion using a sample proportion. It is calculated as the difference between the sample proportion and the true population proportion, divided by the sample proportion. For example, an EBP of 0.02 means that the estimated proportion could differ from the true population proportion by up to 2%.

When the EBP is large, it means that the allowable margin of error is also large, so we do not need as large a sample size to achieve the desired level of precision in our estimate. In other words, if we are willing to tolerate a larger error in our estimate, we can use a smaller sample size to achieve the same level of accuracy.

Conversely, when the EBP is small, it means that the allowable margin of error is also small, so we need a larger sample size to achieve the desired level of precision in our estimate. This is because a smaller margin of error requires a more precise estimate, which in turn requires a larger sample size to reduce the effect of random sampling variability.

Therefore, there is an inverse relationship between the EBP and the required sample size. As the EBP increases, the required sample size decreases, and vice versa.

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to answer the question, we would need to perform a statistical analysis and report the correlation coefficient between log(income) and prppov as well as the two-sided p-values for each variable. If the p-value for each variable is less than 0.05, we can conclude that each variable is statistically significant in some way.

To determine the correlation between log(income) and prppov, we can use a statistical analysis tool such as a Pearson's correlation coefficient. The resulting correlation coefficient will be between -1 and 1, with a value of 0 indicating no correlation, a value of -1 indicating a negative correlation, and a value of 1 indicating a positive correlation.

To determine if each variable is statistically significant, we can calculate the two-sided p-values. A p-value is a measure of the probability of obtaining a result as extreme as the one observed, assuming that there is no true association between the variables. A p-value less than 0.05 is typically considered statistically significant, meaning that the probability of obtaining the observed result if there is no true association is less than 5%.

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The constant of proportionality is 2.5.

We can start by using the formula for a proportional relationship, which is:

y = kx

where y is the cost in dollars, x is the length of track in inches, and k is the constant of proportionality.

We know that when x = 6.4, y = 16. So we can substitute these values into the formula and solve for k:

16 = k * 6.4

Dividing both sides by 6.4, we get:

k = 16 / 6.4

Simplifying this fraction, we get:

k = 2.5

Hence, 2.5 is the constant of proportionality.

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Answer:

2.5

Step-by-step explanation:

Answer:

We can use the Pythagorean theorem to calculate the distance diagonally from Jenny's home to the softball field.

The distance she walks north is 10 blocks, and the distance she walks west is 4 blocks. Using the Pythagorean theorem, the diagonal distance is:

√(10² + 4²) = √116 ≈ 10.77 blocks

To find the total distance she walks to practice and back home, we need to double the diagonal distance:

2 × 10.77 ≈ 21.54 blocks

Therefore, if Jenny takes the diagonal path home, she will walk approximately 21.54 blocks in total to practice and back home.

Step-by-step explanation:

The mean and median on a density curve may be very close or even the same, especially for symmetric distributions.

For skewed distributions, the mean and median may be quite different.

On a density curve, the mean and median can be marked as follows:

Mean:

The mean of a density curve represents the average value of the data.

It is also known as the expected value.

The mean is the point at which the density curve would balance if it were made of a solid material.

To mark the mean on a density curve, locate the point where the curve is cut in half by its own weight.

This point is the mean of the distribution.

It can be represented by a vertical line drawn through this point on the x-axis.

Median:

The median of a density curve is the point that divides the area under the curve in half.

It is the point that separates the lower 50% of the data from the upper 50%.

To mark the median on a density curve, locate the point where the curve intersects the horizontal line at the midpoint of the area under the curve.

This point is the median of the distribution.

It can be represented by a vertical line drawn through this point on the x-axis.

In general, the mean is more sensitive to outliers than the median, which makes the median a better measure of central tendency for distributions with extreme values.

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If Quadrilateral ABED is inscribed in a circle with AE is a diameter, the measure of angle DEB is 2 degrees.

Since AE is a diameter of the circle, angle AEB is a right angle (90°).

Using the fact that the opposite angles of an inscribed quadrilateral are supplementary, we can find the measure of arc DE:

m(arc DE) = 180° - m(∠ABE) - m(∠AED)

m(arc DE) = 180° - (90° + 86°)

m(arc DE) = 4°

Since arc DE is a central angle, it is twice the measure of angle DEB:

m(arc DE) = 2m(∠DEB)

4° = 2m(∠DEB)

m(∠DEB) = 2°

In conclusion, using the properties of inscribed quadrilaterals and central angles in circles, we can determine that the measure of angle DEB in quadrilateral ABED is 2 degrees.

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The heavy marble using a two-pan balance, the minimum number of weighings required is two.

Here's how you can do it:

Divide the eight marbles into two groups of four.

Weigh the two groups against each other.

If the two groups weigh the same, the heavy marble is one of the remaining four marbles. Proceed to step 3.

If one group weighs more, the heavy marble is in that group. Proceed to step 3.

Divide the four marbles from the heavier group into two groups of two.

Weigh the two groups of two against each other.

If the two groups weigh the same, the heavy marble is one of the remaining two marbles. Proceed to step 5.

If one group weighs more, the heavy marble is in that group. Proceed to step 5.

Weigh the remaining two marbles against each other.

The heavier marble is the heavy marble.

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Required critical value is 0.001.

For the two-tailed test with α = 0.002, you

need to find the positive critical value zα/2. To do this, use the invNorm function in your calculator:

1. Divide the alpha level by 2: 0.002 / 2 = 0.001

2. Find the corresponding z-score using invNorm: invNorm(1 - 0.001) = invNorm(0.999)

3. Round the z-score to three decimal places.

For the left-tailed test with α = 0.01, you need to find the critical value zα. To do this, use the invNorm function in your calculator:

1. Find the corresponding z-score using invNorm: invNorm(0.01)

2. Round the z-score to three decimal places.

After calculating the z-scores, your answer should look like this:

For the two-tailed test with α = 0.002, the positive critical value zα/2 is approximately 0.001 (replace with your calculated value). For the left-tailed test with α = 0.01,

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Answer:

(1,1,36), (1,3,12), (1,2,18), (1,6,6), (1,4,9), (2,3,6), (2,2,9), (3,3,4)

Step-by-step explanation:

, = multiply

The set of polynomials P does not form a basis for P₃, as it is not linearly independent.

What is a polynomial?

In mathematics, a polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables

To determine if the set of polynomials P = {P₁(t) = 3 + 7t, P₂(t) = 6 + t - 4t³, P₃(t) = 2t - 2t², P₄(t) = 6 + 33t - 6t² + 4t³} forms a basis for P₃, we need to check if the set is linearly independent and spans P₃.

To check for linear independence, we set up the following linear combination:

c₁P₁(t) + c₂P₂(t) + c₃P₃(t) + c₄P₄(t) = 0

where c₁, c₂, c₃, and c₄ are constants, and the zero on the right side indicates the zero polynomial. We want to show that c₁ = c₂ = c₃ = c₄ = 0 is the only solution.

Substituting the polynomials into the equation, we get:

c₁(3 + 7t) + c₂(6 + t - 4t³) + c₃(2t - 2t²) + c₄(6 + 33t - 6t² + 4t³) = 0

Simplifying and collecting like terms, we get:

(4c₄ - 4c₃)t³ + (-6c₄ - 6c₃)t² + (7c₁ + c₂ - 2c₃)t + (3c₁ + 6c₂ + 6c₄) = 0

For this equation to hold for all t, each coefficient must be zero. Therefore, we have the following system of equations:

4c₄ - 4c₃ = 0

-6c₄ - 6c₃ = 0

7c₁ + c₂ - 2c₃ = 0

3c₁ + 6c₂ + 6c₄ = 0

Solving this system of equations, we obtain c₁ = -2c₂, c₃ = -c₄, and we can choose c₂ and c₄ freely. This means that the set of polynomials P is not linearly independent, as there are non-trivial solutions to the equation c₁P₁(t) + c₂P₂(t) + c₃P₃(t) + c₄P₄(t) = 0.

Therefore, the set of polynomials P does not form a basis for P₃, as it is not linearly independent.

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The exact values of sin(alpha + beta), cos(alpha - beta), and tan(alpha - beta) are 504/725, 567/725, and -12/5, respectively.

sin(alpha + beta) = sin(alpha)cos(beta) + cos(alpha)sin(beta)

= (24/25)(20/29) + (7/25)(21/29)

= 504/725

cos(alpha - beta) = cos(alpha)cos(beta) + sin(alpha)sin(beta)

= (7/25)(20/29) + (24/25)(21/29)

= 567/725

tan(alpha - beta) = (sin(alpha)cos(beta) - cos(alpha)sin(beta))/(cos(alpha)cos(beta) + sin(alpha)sin(beta))

= (24/25)(20/29) - (7/25)(21/29))/((7/25)(20/29) + (24/25)(21/29))

= -12/5

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The polynomial representing the shaded area between two squares with given dimensions is 3x² + x - 6. Solving for x using the given area of 24 square units, x equals 3.

To find the polynomial that represents the area of the shaded region, we need to subtract the area of the inner square from the area of the outer square.

The area of the outer square is (3x-2) * (x+3) = 3x² + 7x - 6.

The area of the inner square is 6 * x = 6x.

So, the area of the shaded region is (3x² + 7x - 6) - 6x = 3x² + x - 6.

To solve for x given that the area of the shaded region is 24 square units, we can set the polynomial equal to 24 and solve for x

3x² + x - 6 = 24

3x² + x - 30 = 0

Using the quadratic formula, we get

x = (-1 ± √(1 - 4(3)(-30))) / (2(3))

x = (-1 ± 19) / 6

x = 3 or x = -10/3

Since x must be a positive value in this context, we choose x = 3.

Therefore, the polynomial that represents the area of the shaded region is 3x² + x - 6, and x = 3 satisfies the condition that the area of the shaded region is 24 square units.

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--The given question is incomplete, the complete question is given

" Write a polynomial to represent the area of the shaded region. Then solve for x given that the area of the shaded region is 24 square units.

3x2 + x - 6; x = 3

3x2 + 7x - 6; x = 2

3x2 + 7x - 6; x = 5

WILL GIVE BRAINLIEST WITH EXPLANATION"--

The answer is (b) getting 50 twos after 600 separate rolls of a single die. The law of large numbers states that as the sample size increases, the sample mean approaches the population mean.

In other words, the more times you roll the die, the closer you should get to the expected value of each number on the die (which is 1/6 for a fair die). Option (a) of getting 200 threes and option (c) of getting 100 sixes are both too far away from the expected value to be consistent with the law of large numbers. Option (b) of getting 50 twos is closer to the expected value and thus consistent with the law of large numbers.

Therefore, the  law of large numbers predicts that over a large number of trials, the frequency of an event should approach its probability of occurrence. In this case, the probability of rolling a two on a fair die is 1/6, so getting 50 twos after 600 rolls is consistent with the law of large numbers.

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The common ratio (r) is 0.2, the series is convergent, and its sum is 2.5.

Given the series: 2 + 0.4 + 0.08 + 0.016 + ...

To find the common ratio (r), we can divide any term by its preceding term. For example:

r = 0.4 / 2 = 0.2

Now that we have the common ratio, we can determine if the series is convergent or divergent. A geometric series is convergent if the absolute value of the common ratio is less than 1 (|r| < 1), and divergent otherwise. Since |0.2| < 1, the series is convergent.

For a convergent geometric series, we can find its sum using the formula:

Sum = a / (1 - r)

where 'a' is the first term of the series. In this case, a = 2, and r = 0.2. So, the sum is:

Sum = 2 / (1 - 0.2) = 2 / 0.8 = 2.5

Therefore, the common ratio (r) is 0.2, the series is convergent, and its sum is 2.5.

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The expression for the cost of 5 large Italian ices in terms of the cost of a medium Italian ice is "5d + 10" dollars.

To find the cost of 5 large Italian ices, we need to multiply the cost of one large Italian ice by 5. So, the expression for the cost of 5 large Italian ices is:

5 × (d + 2)

We can simplify this expression by using the distributive property of multiplication. This means that we can multiply the number outside the parentheses (5) by each term inside the parentheses (d and 2):

5 × (d + 2) = 5 × d + 5 × 2

Simplifying further, we get:

5d + 10

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The age of Layla who youngest of four siblings is 18 years old

The age of 4 sibling are in consecutive even integers

Age of 1st sibling = x

Age of 2nd sibling = x + 2

Age of 3rd sibling = x + 4

Age of 4th sibling = x + 6

Sum of the sibling age = 84

x + x + 2 + x + 4 + x + 6 =84

4x + 12 = 84

4x = 84 -12

4x = 72

x = 18

Layla is youngest  sibling hence her age will be 18 years

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The question is incorrect the correct question is :

Layla is the youngest of four siblings whose ages are consecutive even integers. If the sum of their ages is 84, find Layla's age

When talking about a scale drawing or model, the scale factor is determined by the ratio of a given length on the drawing or model to its corresponding length on the actual object.

This can be written as a fraction, with the length on the drawing or model as the numerator and the corresponding length on the actual object as the denominator. For example, if a drawing of a building has a scale factor of 1:100 and the length of a wall on the drawing is 5 cm, the corresponding length on the actual building would be 500 cm (5 cm x 100). Therefore, the scale factor can be written as 5/500 or simplified to 1/100.

When talking about a scale drawing or model, the term you're looking for is "scale factor." It is determined by the ratio of a given length on the drawing or model to its corresponding length on the actual object. To write this as a fraction, you would place the length on the drawing or model as the numerator and the corresponding length on the actual object as the denominator. For example, if the scale factor is 1:10, you would write it as 1/10.

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The researcher may consider following up with non-respondents to encourage their participation and ensure the sample is as representative as possible.

The population of interest in this study is the students who graduated from the manicurist class in 2018 from WBI. The data collection process involves asking the question "Are you have a California State Board manicurist License yes or not?" to a sample of these students.

The potential source of bias in this study is sampling bias, as the technique used to obtain the sample may favor one part of the population over another. For example, if the researcher only selects students who were successful in the program, this may not be representative of the entire population of students who graduated from the program.

Non-response bias may also be a concern if some students do not respond to the survey, as their characteristics may differ from those who do respond. For example, if students who did not pass the licensing exam are less likely to respond to the survey, this may affect the accuracy of the results.

Response bias may also be a concern if students provide inaccurate or incomplete information in their responses. For example, if students who did not pass the licensing exam feel embarrassed or ashamed and are more likely to falsely claim that they have a license, this may affect the accuracy of the results.

To minimize these biases, the researcher should aim to obtain a random and representative sample of students who graduated from the program, and ensure that the survey questions are clear and unbiased. Additionally, the researcher may consider following up with non-respondents to encourage their participation and ensure the sample is as representative as possible.

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Answer:

20,908

Step-by-step explanation:

We can represent the amount of people after each year as 103% of the amount from the previous year. Using this logic, we can multiply the town's original population (its principal value) by 103% 7 times, because the increase happens every year. We can represent this in the equation:

P = (og. population) × 103%⁷

We can use an exponent of 7 to indicate repeated multiplication, and when plugging a percentage into a calculator, we have to represent it as a decimal (103% => 1.03).

P = 17,000 × 1.03⁷

P ≈ 20,907.86

P ≈ 20,908

Note that we rounded the population to the nearest whole number as instructed instead of performing a more realistic truncation of the partial person.

The probability of return was the least for the Dining hall method and greatest for the Class delivery method. Therefore, E is the correct answer here.

There cannot be a positive or negative association between a categorical and a numerical variable. here the delivery method is a categorical variable.

We cannot determine what the total number for any of the delivery methods was as we are only given the conditional probability of whether they were returned or not.

We can clearly see that the probability of return was the least for the Dining hall method and greatest for the Class delivery method. Therefore, E is the correct answer here.

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The appropriate test to compare the satisfaction scores before and after the introduction of the new service is a paired t-test or a dependent t-test.

This is because the same group of customers is being surveyed before and after the introduction of the new service. The two samples are not independent of each other, but are related or dependent because they are measuring the same thing in the same individuals at different points in time.

A paired t-test compares the means of two related samples and determines whether the difference between them is statistically significant or simply due to chance. In this case, the null hypothesis would be that there is no significant difference in customer satisfaction before and after the introduction of the new service, and the alternative hypothesis would be that there is a significant difference.

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The derivative of the given integral with respect to x is 2x * sin(x⁶) - 1.

What is integration?

Integration is a mathematical operation that is the reverse of differentiation. Integration involves finding an antiderivative or indefinite integral of a function.

To solve this problem, we need to use the fundamental theorem of calculus and the chain rule.

Let's start by applying the fundamental theorem of calculus, which states that if F(x) is the antiderivative of f(x), then the integral of f(x) from a to x is equal to F(x) - F(a). In other words:

∫[a,x] f(t) dt = F(x) - F(a)

In this case, we have:

F(x) = ∫[0,x²] sin(t³) dt

So, applying the fundamental theorem of calculus, we get:

d/dx [∫[0,x²] sin(t³) dt] = d/dx [F(x) - F(0)]

Now, we need to apply the chain rule to find d/dx [F(x)]. Let's define a new function g(u) = ∫[0,u] sin(t³) dt. Then, we have:

F(x) = g(x²)

Using the chain rule, we get:

d/dx [F(x)] = d/dx [g(x²)] = g'(x²) * d/dx [x²] = 2x * g'(x²)

Substituting this back into the previous equation, we get:

d/dx [∫[0,x²] sin(t³) dt] = 2x * g'(x²) - F'(0)

To find g'(u), we can use the fundamental theorem of calculus again:

g'(u) = d/du [∫[0,u] sin(t³) dt] = sin(u³)

Substituting this back into the previous equation, we get:

d/dx [∫[0,x²] sin(t³) dt] = 2x * sin(x⁶) - cos(0) = 2x * sin(x⁶) - 1

Therefore, the derivative of the given integral with respect to x is 2x * sin(x⁶) - 1.

To learn more about integration from the given link:

brainly.com/question/18125359

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