Determine the mean and standard deviation of the variable X in each of the following binomial distributions: a. n = 4 and = 0.10 b. n = 4 and = 0.40 c. n = 5 and = 0.80 d. n = 3 and = 0.50

The probability that all of the offices in the environmental club are filled by members of the debate team is approximately 0.021 or 2.1%.

To find the probability that all of the offices in the environmental club are filled by members of the debate team, we need to use the concept of combinations.

First, we need to find the total number of ways to fill all four offices from a pool of 13 candidates. This can be done using the formula for combinations:

[tex]C(13,4) = \frac{13!}{4!(13-4)!} = \frac{13\times12\times11\times10}{4\times3\times2\times1} = 715[/tex]

So there are 715 different ways to fill the four offices.

Next, we need to find a number of ways to fill all four offices with members of the debate team. There are 6 members of the debate team, so we need to choose all four of them:

[tex]C(6,4) = \frac{6!}{4!(6-4)!} = \frac{6\times5\times4\times3}{4\times3\times2\times1} = 15[/tex]

So there are 15 different ways to fill all four offices with members of the debate team.

Finally, we can find the probability by dividing the number of ways to fill all four offices with members of the debate team by the total number of ways to fill the four offices:

P(all offices filled by debate team) = 15/715 ≈ 0.021

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To determine the angle from the vernal equinox to the station at the time of measurement, we need to use the following formula:

Angle = (Sidereal Time at Greenwich + Longitude of the Station - Hour Angle of the Object) * 15 degrees/hour

First, we need to determine the Hour Angle of the Object, which is the amount of time since the object (in this case, the radar measurement) passed over the Greenwich meridian. We know that the radar measurement occurred 2.8 hours after noon on January 1, so the Hour Angle of the Object is:

Hour Angle = 2.8 hours * 15 degrees/hour = 42 degrees

Next, we can plug in the values we know into the formula:

Angle = (100 degrees + (-4 degrees) - 42 degrees) * 15 degrees/hour
Angle = 54 degrees * 15 degrees/hour
Angle = 810 degrees/hour

Therefore, the angle from the vernal equinox to the station at the time of the radar measurement is 810 degrees/hour.

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In order to determine if the estimated betas are significant, we can use a t-test. The t-test assesses the statistical significance of the relationship between the independent variable(s) and the dependent variable.

In this context, the betas represent the estimated coefficients for each independent variable.

If the t-test yields a p-value less than the predetermined significance level (usually 0.05), it indicates that the betas are significant. This means that there is a statistically significant relationship between the independent variables and the dependent variable. On the other hand, if the p-value is greater than the significance level, the betas are not significant, and we cannot conclude that there is a relationship between the variables.

When it comes to interpreting the estimated coefficient for the Fitness Center, we should consider the magnitude and direction of the beta value. A positive beta value indicates a positive relationship between the Fitness Center variable and the dependent variable, meaning that as the value of the Fitness Center variable increases, so does the dependent variable. Conversely, a negative beta value implies a negative relationship, with an increase in the Fitness Center variable leading to a decrease in the dependent variable.

The magnitude of the coefficient for the Fitness Center reflects the strength of the relationship. A larger absolute value indicates a stronger relationship between the variables, while a smaller absolute value suggests a weaker relationship. It's important to remember that correlation does not imply causation, so we can only draw conclusions about the relationship between the variables, not a cause-and-effect relationship.

In summary, to determine the significance of the estimated betas, we can use a t-test. The direction and magnitude of the estimated coefficient for the Fitness Center can help us understand the relationship between the variables. However, it is essential to keep in mind that correlation does not imply causation.

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The two way frequency table is discussed below. The table to show the relative frequencies for each grade category is discussed below. According to the relative frequency table, 8th grade had the greatest number of students who preferred one of the toppings.

The completed two-way frequency table is shown below

               Cheese         Pepperoni           Veggie           Total

7                20                      12                      8                    40

8                18                       16                      14                   48

Total          38                      28                     22                  88

To find the relative frequency for each grade category, we need to divide each frequency by the total number of students

                Cheese         Pepperoni           Veggie            Total

7                0.227             0.136                  0.090              0.453

8                0.204             0.181                   0.159               0.544

Total           0.431              0.317                  0.249               0.997

According to the relative frequency table, 8th grade had the greatest number of students who preferred one of the toppings, with a relative frequency of 0.544.

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The conditions at the bottom of the Mariana Trench are vastly different from those in a typical bathtub. The water pressure at that depth is extreme, with over 8 tons of pressure per square inch. In contrast, the water pressure in a bathtub is negligible. Additionally, the water in the Mariana Trench is near freezing, while the water in a bathtub is typically warm or hot. Overall, the conditions in the Mariana Trench are incredibly harsh and inhospitable, making it one of the most extreme environments on Earth.
The Mariana Trench is the deepest part of the ocean at 39,069 feet. The conditions there differ significantly from those in your bathtub. In the Mariana Trench, the water pressure is incredibly high, reaching over 1,000 atmospheres. The temperature is near freezing, ranging from 34-39°F (1-4°C). In contrast, the conditions in your bathtub usually involve much shallower water, lower pressure, and warmer temperatures for a comfortable bathing experience.

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The fraction of washers with thicknesses greater than 2.4 millimeters. We need to understand the normal distribution of washer thicknesses. In a normal distribution, data is centered around the mean value, and the standard deviation (SD) determines the spread.

For this problem, we need the mean thickness and SD of the washers being produced.

Once we have the mean and SD, we can calculate the z-score, which represents the number of standard deviations a data point is from the mean. The formula for the z-score is:

Z = (X - mean) / SD

Where X is the specified thickness (2.4 millimeters in this case). After calculating the z-score, we can use a standard normal distribution table (also known as a z-table) to find the corresponding area to the right of the z-score. This area represents the fraction of washers that are expected to be greater than 2.4 millimeters thick.

Unfortunately, without the mean and standard deviation values, we cannot provide a specific answer to your question. However, once you have those values, you can follow the steps above to find the fraction of washers with thicknesses greater than 2.4 millimeters.

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The length of the missing side for the triangle is equal to 5.96 to the nearest tenth hundredth using the sine rule.

The sine rule is a relationship between the size of an angle in a triangle and the opposing side.

First, we find the angle opposite the side length 5 as follows;

180 - (34 + 118) = 28 {sum of interior angles of a triangle}

Using the sine rule;

5/sin28° = ?/sin34°

? = (5 × sin34°)/sin28° {cross multiplication}

? = 5.9556

Therefore, the length of the missing side for the triangle is equal to 5.96 to the nearest tenth hundredth using the sine rule.

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The exponential function graphed in this problem is defined as follows:

y = 2(0.5)^x.

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

The graph crosses the y-axis at y = 2, hence the parameter a is given as follows:

a = 2.

When x increases by one, y is divided by two, hence the parameter b is given as follows:

b = 0.5.

Thus the function is:

y = 2(0.5)^x.

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The mean is 172, the variance is 34.4, and the standard deviation is 5.86.

The United States has a system of bicameralism, which means that each state has two chambers in its legislature: a lower chamber (such as the Assembly or House of Representatives) and an upper chamber (such as the Senate).

The number of constituents per district in each chamber varies from state to state, and it is usually determined by the state's constitution or by a state redistricting commission.

As of the 2010 census, Texas had about 811,147 constituents per state senate district.

However, this is not the highest number of constituents per senator among all the states.

In fact, the state with the highest number of constituents per senator is California.

According to the U.S. Census Bureau, as of the 2010 census, California had a population of approximately 37.3 million people.

The state's constitution provides for 40 state senators, which means that each senator represents approximately 933,000 constituents.

This is significantly higher than the number of constituents per senator in Texas.

The high number of constituents per senator in California can be attributed to the state's large population and the fact that the number of state senators has not kept up with population growth.

The last time the number of state senators in California was increased was in 1973, when the state's population was around 20 million people.

In conclusion, while Texas has a high number of constituents per state senate district, it is not the only state with a high number of constituents per senator.

California has a significantly higher number of constituents per senator, due to its large population and the fact that the number of state senators has not kept up with population growth.

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The value of given expression 1/5/14/3 of 10/7×14/5 is 6/35 with the help of PEMDAS rule.

PEMDAS is a commonly used acronym in mathematics that stands for "Brackets, Orders, Division, Multiplication, Addition, Subtraction." It is a rule that helps you remember the order of operations to solve mathematical expressions.

Use PEMDAS rule to solve the given expression

1/5/14/3 of 10/7 × 14/5

= 1/5/14/3 × 10/7 ×14/5

= 1/5 × 3/14 × 10/7 × 14/5

Cancelling the same terms and factors

= 1/5 × 3/1 × 10/7 × 1/5

= 1/5 × 3/1 × 2/7

= 6/35

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If the significance level that you obtain for Levene's Test for Equality of Variances equals .013, it means that there is a statistically significant difference between the variances of the groups being compared. In this case, the assumption of homogeneity of variance is violated.

To address this issue, you have a few options. One approach is to use a modified version of the t-test called the Welch's t-test, which does not assume equal variances. Another option is to use a non-parametric test such as the Mann-Whitney U test or the Kruskal-Wallis test, which do not require the assumption of equal variances.

It is important to choose an appropriate statistical test based on the specific research question and the data being analyzed. While violating the assumption of equal variances can complicate statistical analysis, there are alternative methods available to ensure accurate and valid results.

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Tony sent 4 times as many messages as Kira. Reuben sent 17 messages, Kira sent 24 messages, and Tony sent 96 messages.

Let's start by assigning variables to represent the number of messages each person sent.
Let's say that Reuben sent x messages.
Then we know that Kira sent 7 more messages than Reuben, so Kira sent x+7 messages.
We also know that Tony sent 4 times as many messages as Kira, so Tony sent 4(x+7) messages.
We're told that the total number of messages sent was 137, so we can set up an equation:
x + (x+7) + 4(x+7) = 137
Simplifying this equation:
6x + 35 = 137
Subtracting 35 from both sides:
6x = 102
Dividing both sides by 6:
x = 17
So Reuben sent 17 messages, Kira sent 7 more than Reuben which is 17+7=24 messages, and Tony sent 4 times as many messages as Kira which is 4(24)=96 messages.

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If we leave off the error term from the population linear model, the left-hand side of the equation is now the expected value of Y for a given x value. false

The error term in a linear regression model captures the unobserved factors that affect the dependent variable Y. If we remove the error term, we would end up with a model that only explains the relationship between the dependent variable and the independent variable(s).

The left-hand side of the equation represents the actual value of the dependent variable Y, whereas the right-hand side represents the predicted or expected value of Y given the values of the independent variables.

In a population linear model, if we remove the error term, the left-hand side would still represent the actual values of Y in the population, and the right-hand side would represent the expected value of Y given the values of the independent variables.

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The probability that a random sample of 4 of the articles will contain a defective article is approximately 0.2916, or about 29.16%.

To find the probability that a random sample of 4 articles will contain a certain number of defective articles, we can use the binomial probability formula:

P(X = k) = (nCk) * (p^k) * (1-p)^(n-k)

where:
- n is the total number of articles in the sample (4 in this case)
- k is the number of defective articles we want to find the probability for
- p is the probability of an article being defective (1/10)
- 1-p is the probability of an article not being defective (9/10)
- nCk represents the number of combinations of n items taken k at a time

It appears that you haven't mentioned the specific number of defective articles you want in the sample of 4. However, you can use the formula above and plug in the values for k (0, 1, 2, 3, or 4) to find the probability for any desired number of defective articles in the sample.

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The researcher most likely used the mean as the measure of central tendency to describe,

the hospital admission rates for coronary heart disease at the 10 local hospitals. The mean is calculated by adding up all of the hospital admission rates and dividing by the total number of hospitals.

By identifying the two hospitals with the highest overall rates of hospital admissions, the researcher likely calculated the mean of all the hospital admission rates and compared each hospital's rate to this value.

This helps to identify which hospitals had rates that were higher or lower than average.

However, without more information on the data distribution, it is possible that the researcher could have also used the median or mode as the measure of central tendency.

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Answer:

8 10's were multiplied

Step-by-step explanation:

10 - 1 = 9

100 - 1 = 99

1,000 - 1 = 999

10^8 - 1 = 100,000,000 - 1 = 99,999,999

9 × 8 = 72

When employees have different responsibilities, those relationships can be modeled with multiple associations between the employee class and the linked class.

In object-oriented programming, a class is a blueprint for creating objects that have similar properties and behaviors. One of the key concepts in class design is associations, which represent relationships between classes. Associations are used to define how objects of one class are connected to objects of another class.

When employees have different responsibilities, it means that there are multiple ways in which they can be associated with other classes. For example, a software company may have a class of employees who are responsible for developing software, and another class of employees who are responsible for testing the software. Each of these classes has a different set of responsibilities and requires different skills and knowledge.

To model these relationships, we can create multiple associations between the employee class and the linked class. For example, we could create one association between the employee class and the software development class, and another association between the employee class and the software testing class. Each of these associations would have different attributes, such as the employee's role, responsibilities, and qualifications.

By modeling these relationships with multiple associations, we can create more accurate and flexible class designs that reflect the real-world relationships between employees and their responsibilities. This approach also allows us to easily modify or extend the class design as the requirements change, without having to make major changes to the existing code. Overall, multiple associations provide a powerful tool for designing robust and adaptable class structures.

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If you rolled two dice, recorded the face values and summed them up, you would be collecting quantitative data. This is because quantitative data is numerical in nature and involves counting, measuring or quantifying something.

In this case, the numbers on the faces of the dice would be counted and added together to obtain a total sum. This data can be further classified as discrete since the possible outcomes of rolling dice are limited to a set of discrete values.

Therefore, this data can be easily analyzed using statistical methods to determine the probability of certain outcomes occurring. Collecting quantitative data is essential in many fields such as science, economics, and finance, as it provides valuable insights into the behavior and trends of various phenomena.

In this situation, the face values on the dice represent numbers, and the sum of these values is also a number. The data you collect can be analyzed using statistical methods and can provide meaningful insights.

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The number of solutions that a homogeneous system of equations with 13 variables and 8 equations will have depends on the rank of the coefficient matrix.

If the rank of the coefficient matrix is less than the number of variables (13), then the system will have infinitely many solutions.

If the rank is equal to the number of variables, then the system will have a unique solution. If the rank is less than the number of variables but greater than the number of equations (8), then the system will have a nontrivial solution.

It is not possible to determine the rank of the coefficient matrix or the number of solutions without actually solving the system or knowing more information about the specific equations involved.

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Considering the random sample of 500 people from the 2000 U.S. Census with a mean commute time of 28.4 minutes and a standard deviation of 18.9 minutes, we cannot definitively conclude that the mean commute time in the U.S. is less than half an hour.

Based on the information provided, we can't definitively conclude that the mean commute time in the U.S. is less than half an hour. While the sample mean of 28.4 minutes is less than half an hour, the standard deviation of 18.9 minutes is quite large. This suggests that there is a lot of variability in the commute times reported in the sample, and it's possible that there are many people with much longer commutes that are driving up the overall mean. Additionally, the fact that commute times in the U.S. are heavily skewed to the right means that the distribution is not symmetrical and may not be well-represented by the mean alone.

To make a more definitive conclusion, we would need to perform a hypothesis test with a null hypothesis that the mean commute time in the U.S. is half an hour or more and a significance level of our choice.

While the sample mean is close to 30 minutes, the data is heavily skewed to the right, which means that the true population mean might be different. A larger sample size or more representative data would be needed to make a stronger conclusion.

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Significant correlations are useful statistical tools for identifying relationships between variables, but they are not able to indicate causality.

While they can demonstrate the strength of the effect through the correlation coefficient, the size of the effect by examining the magnitude of the relationship, and the probability level by evaluating the likelihood that the observed relationship occurred by chance, they cannot prove that one variable directly causes changes in another variable.

Correlations can only show that two variables are related, but they do not provide information about the nature of that relationship. It is important to remember that correlation does not imply causation. There might be other factors, known as confounding variables, that affect both variables and create the appearance of a relationship where none truly exists.

To determine causality, researchers must conduct controlled experiments where they manipulate the independent variable and observe the effect on the dependent variable, while holding all other factors constant. This allows them to isolate the cause-and-effect relationship between the two variables and draw more accurate conclusions.

In summary, while significant correlations can provide valuable information about the strength, size, and probability level of the relationship between variables, they cannot establish causality. To determine if one variable truly causes changes in another, controlled experiments must be conducted.

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The F-ratio is a statistic used in the analysis of variance (ANOVA) test to compare the means of two or more groups. The F-ratio is calculated as the ratio of the between-group variance to the within-group variance. A negative F-ratio is not possible, so it is likely that there was an error in the calculation or reporting of the statistic.

Assuming that the F-ratio was calculated correctly and reported accurately, a negative F-ratio implies that the between-group variance is smaller than the within-group variance. This is unusual and could indicate that there are issues with the data, such as outliers or a violation of the assumption of homogeneity of variances.

In general, a significant F-ratio (i.e., one that is large enough to reject the null hypothesis) indicates that there are differences between the means of the groups being compared.

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To use the trapezoidal rule to estimate the definite integral of the function f(x) = 1/2x^3+10 on the interval [1,3], we need to divide the interval into n subintervals of equal width h, where h = (b-a)/n = (3-1)/4 = 1/2.

Then, we can use the following formula to approximate the definite integral:

∫1^3 (1/2x^3+10) dx ≈ h/2 * [f(a) + 2∑f(xi) + f(b)]

where xi = a + ih for i = 1, 2, ..., n-1.

Applying this formula with n = 4, we get:

∫1^3 (1/2x^3+10) dx ≈ 1/4 * [f(1) + 2f(5/2) + 2f(2) + 2f(7/2) + f(3)]

where f(x) = 1/2x^3+10.

Evaluating f at the endpoints and midpoints of the subintervals, we obtain:

f(1) = 1/2(1)^3+10 = 10.5

f(5/2) = 1/2(5/2)^3+10 = 27.125

f(2) = 1/2(2)^3+10 = 11

f(7/2) = 1/2(7/2)^3+10 = 35.875

f(3) = 1/2(3)^3+10 = 19.5

Plugging these values into the formula, we get:

∫1^3 (1/2x^3+10) dx ≈ 1/4 * [10.5 + 2(27.125) + 2(11) + 2(35.875) + 19.5]

≈ 27.25

To calculate the absolute error, we need to find the exact value of the definite integral:

∫1^3 (1/2x^3+10) dx = [1/8x^4+10x]1^3 = 99/8

The absolute error is then given by:

|∫1^3 (1/2x^3+10) dx - 27.25| = |99/8 - 27.25| = 219/8

Therefore, the exact value of the absolute error is 219/8.

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the probability of blindly drawing at least one blue marble in two attempts from the given bag of marbles is 1/2 or 50%.

To calculate the probability of drawing at least one blue marble in two attempts from a bag containing one blue, one green, one orange, and one yellow marble, we need to consider the possible outcomes.

In the first attempt, there are four marbles in the bag, and one of them is blue. So, the probability of drawing a blue marble on the first attempt is 1/4.

In the second attempt, if a blue marble was not drawn in the first attempt, there will be three marbles left in the bag, and one of them is blue. The probability of drawing a blue marble on the second attempt, given that a blue marble was not drawn in the first attempt, is 1/3.

To find the probability of drawing at least one blue marble, we can calculate the probability of the complement event (not drawing a blue marble in both attempts) and subtract it from 1:

Probability of drawing at least one blue marble = 1 - Probability of not drawing a blue marble in both attempts

Probability of not drawing a blue marble in both attempts = (3/4) * (2/3) = 1/2

Probability of drawing at least one blue marble = 1/2 or 50%.

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The natural values of n for which the difference (2-2n) - (5n-27) is positive are 1, 2, 3, and 4.

To find the natural values of n for which the difference (2-2n) - (5n-27) is positive, we need to simplify the expression and then solve for n.

(2-2n) - (5n-27) = 2 - 2n - 5n + 27

= -7n + 29

So, we need to find the natural numbers n for which -7n + 29 > 0.

To do this, we can solve for n as follows

-7n + 29 > 0

-7n > -29

n < 29/7

Since n is a natural number, it must be an integer greater than or equal to 1. Therefore, the natural values of n for which the difference (2-2n) - (5n-27) is positive are 1, 2, 3, and 4.

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A relationship between a causal variable and a dependent variable within one value of another causal variable is known as a conditional relationship.

A relationship between a causal variable and a dependent variable within one value of another causal variable is known as a conditional relationship or a moderated relationship. In this type of relationship, the relationship between the causal variable and the dependent variable is not fixed, but instead depends on the level or value of the moderating variable.

For example, let's say we want to investigate the relationship between exercise and weight loss, and we suspect that age may moderate this relationship. In other words, we think that the relationship between exercise and weight loss may be different for different age groups. We might find that for younger people, exercise is a strong predictor of weight loss, while for older people, exercise has little to no effect on weight loss. In this case, age is the moderating variable that affects the relationship between exercise and weight loss.

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The explicit rule for this situation is f(n) = 9 - n and there will be 4 cans in the 5th row

Given thay

This means that the explicit rule is 1 removed from the previous row to get the current number of cans

So, we have

f(n) = 9 - n

Where n is the nth row

In the 5th row, we have

n =5

So, we have

f(5) = 9 - 5

Evaluate

f(5) = 4

Hence, there will be 4 cans in the 5th row

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Answer:

Step-by-step explanation:

Given, 12 / (-4) * 3 + 5

Here we can use the BODMAS rule and solve this problem.

B ⇒ Brackets

O ⇒ Of

D ⇒ Division

M ⇒ Multiplication

A ⇒ Addition

S ⇒ Subtraction

Now, let’s solve this by applying the BODMAS rule.

In the given sum we can find the Brackets in (-4).

12 / -4 * 3 + 5

There is no Of in this sum.

Let’s gust ignore it.

12 / -4 * 3 + 5

In this sum we can Divide 12 and -4.

-3 * 3 + 5

In this sum we can Multiply -3 and 3.

-9 + 5

In this sum we can Add -9 and 5.

-4

The missing angle in the triangle is as follows:

m∠ABC = 54 degrees

When lines segment intersect, angle relationships are formed such as vertically opposite angles,  adjacent angles etc.

Therefore, let's find m∠ABC.

Hence,

9x - 9 + 3x + 9 = 180 (sum of angles on a straight line)

12x  = 180

divide both sides of the equation by 12

x = 180 / 12

x = 15

Therefore,

m∠ABC = 3x + 9(Vertically opposite angles)

m∠ABC = 3(15) + 9

m∠ABC = 45 + 9

m∠ABC = 54 degrees

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