Use the right triangle below to answer the following question. What is the value of x? Enter the answer in the box. degrees​

By using LCM, we find that the three planets  x, y and z will be in the exact same locations again after $5400$ days.

To find the minimum positive number of days before the planets are all in the exact same locations again, we need to find the least common multiple (LCM) of the three given periods of rotation.

The prime factorization of each of the given periods of rotation is as follows

$360 =[tex]2^3 \cdot 3^2 \cdot 5$[/tex]

$450 =[tex]2 \cdot 3^2 \cdot 5^2$[/tex]

$540 =[tex]2^2 \cdot 3^3 \cdot 5$[/tex]

To find the LCM, we need to take the highest power of each prime factor that appears in any of the three factorizations. So the LCM is:

[tex]$LCM = 2^3 \cdot 3^3 \cdot 5^2 = 2^3 \cdot 27 \cdot 25 = 5400$[/tex]

Therefore, the three planets will be in the exact same locations again after $5400$ days.

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This equation fits the given data: Oy = -2x + 10. The equation creates a linear relationship between the x and y values, with each x value increasing by 1 resulting in a decrease in the y value by 2.

Linear refers to a type of relationship between two or more variables. It is a straight line relationship where the output is directly proportional to the input. Linear relationships can be observed in the natural world such as in the relationship between distance and time. They can also be observed in mathematical equations and models, where the output is directly related to the input. Linear relationships are also used to represent real-world problems in the form of linear equations and models.

The equation satisfies the data points, as plugging in each x value will result in the corresponding y value. For example, when x = 0, the equation produces y = 10, which is the given data point. Similarly, when x = 2, the equation produces y = 6, which is also the given data point.

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This equation fits the given data: y = 1/3x + 2. The equation creates a linear relationship between the x and y values. Hence the correct option is b.

Linear refers to a type of relationship between two or more variables. It is a straight line relationship where the output is directly proportional to the input. Linear relationships can be observed in the natural world such as in the relationship between distance and time. They can also be observed in mathematical equations and models, where the output is directly related to the input. Linear relationships are also used to represent real-world problems in the form of linear equations and models.

The equation satisfies the data points, as plugging in each x value will result in the corresponding y value. For example, when x = 0, the equation produces y = 10, which is the given data point. Similarly, when x = 2, the equation produces y = 6, which is also the given data point.

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Answer:

The answer to our problem is, $17.75

Step-by-step explanation:

First we need to find out what is 25% of 71

25% of 71 is 17.75. Or [tex]17\frac{3}{4}[/tex] We would need to stick to the term in decimals because of we are using money. Have you ever heard of a fraction in money my guess is no. So let’s stay with decimals. 17.75

How I got it:

25 percent * 71

= (25:100)* 71

= (25* 71):100

= 1775:100

= 17.75

Percentage solution with steps:

71 = 100% (1)

X = 25% (2)

Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of bothequations have the same unit (%); we have

[tex]\frac{71}{x} = \frac{25}{100}[/tex]

X = 17.75

Thus the answer to your problem is, $17.75

The number of driving lessons you need to take with a professional instructor before your parents can teach you varies depending on the regulations in your area. In some regions, a specific number of driving lessons is required by law before you can apply for your driver's license. As a result, you should check with your local Department of Motor Vehicles (DMV) or other regulatory agency to learn more about the specific requirements in your area.

In general, however, it is usually beneficial to take as many driving lessons as possible with a professional instructor. Professional driving instructors have been educated in how to teach driving skills safely and effectively. They have also assisted many other people in learning how to drive, and as a result, they have a wealth of knowledge and expertise to draw on.

The more driving lessons you take with a professional instructor, the more chances you'll have to learn and improve your driving abilities. You may be able to practice with your parents after only a few lessons, but it's generally a good idea to take as many as possible with an instructor before doing so. This will give you the best chance of success while you learn to drive safely and confidently.

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Answer: y = 17x + 114

Step-by-step explanation:

The equation for the slope-intercept form is y = mx + b.

Arrange the equation so that it resembles y = mx + b.

You will do this by multiplying and subtracting so y is on the left side of the equation and mx + b is on the right side of the equation.

y + 5 = 17(x + 7)

y + 5 = 17x + 119

y + 5 - 5 = 17x + 119 - 5

y = 17x + 114

Answer:

Y = 17x + 114

Step-by-step explanation:

1. Y + 5 = 17 (x+7)

2. Y + 5 = 17x + 119   [Multiply the numbers in parenthesis by 17.]

3. Y = 17x + 114.     [To keep the balance and move the 5 over, subtract it from 119.]

The expression 3x-(4-x) is equivalent to 4x-4

The distributive property is a mathematical property that describes the relationship between multiplication and addition or subtraction. It states that when a number is multiplied by a sum or difference of two or more numbers, the result is the same as if we multiplied the number by each of the individual terms inside the parentheses and then added or subtracted the products.

To simplify the expression 3x-(4-x), we can distribute the negative sign to the second term inside the parentheses, which gives:

3x - (4 - x) = 3x - 4 + x

Now we can combine the like terms (3x and x) to get:

3x - 4 + x = 4x - 4

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The given question is incomplete, the complete question is:

Which expression is equivalent to 3x-(4-x)?

The solution of the system of equations is (2, 1).

Here we have the system of equations:

y = 2x - 3

y = -x + 3

To solve the system of equations graphically, we need to graph both of these lines in the same coordinate axis and then find the point where the lines intersect.

That point will be the solution of the system.

On the image at the end you can see the graph of the system of equations, there we can see that the solution is (2, 1).

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Answer:

Data Visualization Tools

Step-by-step explanation:

Yes, the number of linearly independent columns in a matrix A is equal to the number of linearly independent rows in A.

This is because the definition of linear independence states that no linear combination of a set of vectors can equal the zero vector, so if one set of vectors is linearly independent, the other set of vectors must also be linearly independent.

To explain further, the number of linearly independent vectors in a matrix A is determined by the rank of the matrix. The rank of a matrix is the number of linearly independent rows and columns in the matrix.

So if the rank of A is n, then the number of linearly independent columns and rows of A must be n. This is because if there are n linearly independent columns in the matrix, the number of linearly independent rows must also be n.

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Answer: slope=4

Step-by-step explanation:

[tex]Slope=\frac{y2-y1}{x2-x1}[/tex]

[tex]Slope=\frac{4- - 4}{3-2}[/tex]

[tex]Slope=\frac{4+4}{3-2}[/tex]

[tex]Slope=4[/tex]

Therefore, the amount of heat produced when 52.40 g of methane, CH4, burns in an excess of air is -39568.2 kJ

The amount of heat produced when 52.40 g of methane, CH4, burns in an excess of air can be calculated using the following equation:

[tex]Q = mcΔT[/tex]

Where Q is the amount of heat produced (in kJ), m is the mass of the methane (in g), and ΔT is the change in temperature (in K).

Using the equation, the amount of heat produced can be calculated as follows:

Q = [tex](52.40 g)(-753.15 K) = -39568.2 kJ[/tex]
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Answer:

Step-by-step explanation:

First, we need to calculate the annual interest rate from the given APR.

APR = 2.25%

Daily interest rate = 2.25% / 365 = 0.00616438

Now, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the final amount

P = the principal (initial amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = time in years

In this case, P = $2,000, r = 0.00616438, n = 365 (daily compounding), and t = 4.

A = 2000(1 + 0.00616438/365)^(365*4)

A = 2000(1.00616438)^1460

A = $2,388.34 (rounded to the nearest cent)

Therefore, the answer is option D) $2,388.34.

The equation of the line that contains the point (-6, 5) and is parallel to x + 2y = 14 in slope-intercept form is y = (-1/2)x + 2.

Due to their similar slopes, parallel lines move in the x direction with the same rate of change. If we know the slope of a line, we can use that slope to determine the slope of any line that is parallel to it. The point-slope form of a line can be used to get the equation of a line that is parallel to a given line and passes through a specified point.

The given equation of the line is:

x + 2y = 14

Rewriting the equation in standard form we have:

y = (-1/2)x + 7

where, -1/2 is the slope of the line.

The slope of two parallel lines are equal. Thus the slope of new line is m = -1/2.

Now, using the point slope form:

y - y1 = m(x - x1)

Substitute the values:

y - 5 = (-1/2)(x - (-6))

y - 5 = (-1/2)x - 3

y = (-1/2)x + 2

Hence, the equation of the line that contains the point (-6, 5) and is parallel to x + 2y = 14 in slope-intercept form is y = (-1/2)x + 2.

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By using the formula for the confidence interval and the standard error, we were able to calculate the lower limit of the interval as 7.59.

To construct a 95% CI for the population mean of a normal distribution, we can use the formula:

CI = sample mean ± z* (standard error)

Where z* is the critical value from the standard normal distribution that corresponds to a 95% confidence level (i.e., 1.96), and the standard error is calculated as:

standard error = population standard deviation / √sample size

In this case, we are given that the population variance is 30, so the population standard deviation is √30 = 5.48 (rounded to two decimal places). The sample size is 20, so the standard error is:

standard error = 5.48 / √20 = 1.226

Now, we can use the formula for the CI:

CI = 10 ± 1.96 x 1.22

Simplifying this expression gives us:

CI = (7.59, 12.41)

This means that we are 95% confident that the true population mean lies within the interval from 7.59 to 12.41. The lower limit of the CI is 7.59, rounded to one decimal place.

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2x + y = -7

y= -7-2x

put this value in 2nd equation

3x=6+4(-7-2x)

3x=6-28-8x

11x= -22

x= -2

y= -7-2(-2)

y= -7+4

y= -3

The number of ways to arrange N people with A and B separated is given by expression   N! - 2*(N-1)! .

What exactly are expressions?

In mathematics, an expression is a combination of numbers, variables, operators, and functions that are grouped together in a meaningful way. Expressions can be as simple as a single number or variable, or they can be complex and include many different elements. They are used to represent mathematical relationships and operations, and can be evaluated or simplified using mathematical rules and techniques. Examples of expressions include:

Now,

Let the two particular people be A and B.

If we place A in a spot, there are N-1 spots left for B to be placed. Once A and B are placed, there are (N-2)! ways to place the remaining people. Therefore, the number of ways to arrange N people with A and B separated is:

(N-1) * (N-2)!

Alternatively, we can find the total number of ways to arrange N people in a line (N!) and subtract the number of ways to arrange them with A and B together.

To find the number of ways to arrange N people with A and B together, we can treat A and B as a single entity, so there are (N-1)! ways to arrange the remaining people with AB together. However, A and B can be arranged in two ways (AB or BA), so we need to multiply (N-1)! by 2.

Therefore, the number of ways to arrange N people with A and B separated is:

N! - 2*(N-1)!

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Answer:

a. Since taxes owed ($4,576) are greater than the amount withheld ($4,323), the person would owe an additional amount.

b. The additional amount owed can be calculated by subtracting the amount withheld from the taxes owed:

Additional amount owed = Taxes owed - Amount withheld

= $4,576 - $4,323

= $253

Therefore, the person would owe an additional $253.

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Answer:

A circle has 360 degrees, so 5/6 of the circle can be found by multiplying 360 by 5/6:

5/6 of 360 = (5/6) × 360 = 300

Therefore, the angle measures of 5/6 of the circle is 300 degrees.

354 Valencia student tickets and 133 non-student tickets were sold.

Let's use algebra to solve the problem. Let

x be the number of Valencia student tickets sold

y be the number of non-student tickets sold

We know that

x + y = 487 (the total number of tickets sold is 487)

14x + 25y = 8391 (the total receipts from ticket sales is $8391)

We can use the first equation to express one of the variables in terms of the other. For example, we can solve for y

y = 487 - x

Here we have to use the substitution method, we can then substitute this expression for y into the second equation

14x + 25(487 - x) = 8391

Simplifying and solving for x

14x + 12275 - 25x = 8391

-11x = -3884

x = 354

So, 354 Valencia student tickets were sold. We can use the first equation to find y

x + y = 487

354 + y = 487

y = 133

So, 133 non-student tickets were sold.

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There is a probability of around 60% that during a week picked randomly, the combined sum of their earnings will be below $0.2533.

The given probability is a measure of the chances that the occurrence of an event will happen. In the context of the question, we want to calculate the combined total of earnings that are less than a certain amount. We know that the probability is approximately 0.6. Therefore, the answer is given by the value that satisfies this condition.

That is, P(X < a) = 0.6where X represents the combined total earnings of a randomly selected week, and a is the required amount.

To solve for a, we can use the cumulative distribution function (CDF) of X. The CDF gives the probability that X is less than or equal to a. Therefore, CDF(a) = P(X ≤ a)

The complement of this probability isP(X > a) = 1 - CDF(a)

We know that P(X < a) = 0.6, which is equivalent to (X ≤ a) = P(X < a) + P(X = a) = 0.6 + 0 = 0.6

Therefore, P(X > a) = 1 - CDF(a) = 1 - P(X ≤ a) = 1 - 0.6 = 0.4

Now we can use a calculator to find the value of a that corresponds to P(X > a) = 0.4.

For example, if we use a calculator, we get a value of a = 0.2533 (rounded to four decimal places).

Therefore, the probability is approximately 0.6 that in a randomly selected week, they will make a combined total of less than $0.2533.


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The population of foxes in the region in 2020 is predicted to be 40,174.

The population of foxes in the region in 2020 can be calculated using the formula [tex]P = P0 (1+r)^n[/tex], where P is the population at the end of n years, P0 is the initial population, and r is the annual growth rate. The fox population iun a certain region has an annual growth rate of 9% per year. in the year 2012 there were 23900 fox counted in the area.In this case, P0 = 23900 and r = 0.09. Since the starting year is 2012, the number of years since then is n = 8. Plugging these values into the formula, P = 23900 (1.09)^8 = 40,174. Therefore, the population of foxes in the region in 2020 is predicted to be 40,174.

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If 10 friends are going to occupy 10 seats in a shuttle on the way to the airport, then they can arrange themselves in the shuttle in 10! or 3,628,800 ways.

Step-by-step explanation: There are 10 friends and 10 seats to be occupied in a shuttle.

Therefore, the number of ways to arrange the 10 friends in 10 seats is given by 10! (10 factorial), which is calculated as follows: 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1= 3,628,800

Therefore, 10 friends can arrange themselves in the shuttle in 3,628,800 ways.

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Each slice has an exterior edge that measurement roughly 0.6981 feet in length. Hence, the price per slice is around $11.11.

What does measurement and example mean?

Comparison of a parameter with a predetermined reference value is the process called measurement. For instance, when a measurement is represented as 10 kg, kg is the accepted unit of mass and 10 represents the physical quantity's size. Make correction suggestions.

The formula for calculating the arc length of the a sector, which is as follows, may be used to get the measurement of each slice's outer edge:

arc length is equal to (angle/360) x 2r.

when r is the pizza's radius, which is equal to its diameter. When we replace r with 2 feet & angle with 40 degrees, i get:

arc length is (40/360) x 2 x 2 feet, which is rounded to 0.6981 feet with 4 decimal places.

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The answer to the expression 547 + 233 × 5 - 142 is 1752. To solve the expression, we must follow the order of operations, which is PEMDAS: Parentheses, Exponents, Multiplication, and Division (performed left to right), and Addition and Subtraction (performed left to right).

Since there are no parentheses or exponents in this expression, we start with multiplication and division. In this case, we have to multiply 233 by 5, which gives us 1165. Then, we add 547 to 1165, which gives us 1712. Finally, we subtract 142 from 1712, which gives us the final answer of 1752. Therefore, the result of the expression 547 + 233 × 5 - 142 is 1752, which can be obtained by following the order of operations and performing the arithmetic operations in the correct order.

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Here, we will use the method of steepest descent to find the minimiser of the function f(x1, x2, x3). The steepest descent method is an iterative optimization algorithm used to find the local minimum of a function.

Step 1: Initialize the starting point (x1, x2, x3) and set the initial values.
Step 2: Compute the gradient of the function f(x1, x2, x3) with respect to each variable (x1, x2, x3). The gradient is a vector that points in the direction of the steepest increase of the function.
Step 3: Calculate the step size, which determines how far along the descent direction we move. This can be done using various techniques, such as line search or a constant step size.
Step 4: Update the current point by moving in the direction of the negative gradient (steepest descent direction) with the computed step size. The new point will be (x1_new, x2_new, x3_new).
Step 5: Check the convergence criteria. If the change in the function value or the variables is below a certain threshold, stop the iteration process. Otherwise, return to Step 2 with the updated point.
By following these steps, the method of steepest descent will help us find the minimizer of the function f(x1, x2, x3).

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Rounding to three decimal places, the probability that exactly 7 Americans out of a sample of 15 own an answering machine is approximately 0.170.

To find the probability that exactly 7 of the 15 Americans selected at random own an answering machine, we can use the binomial distribution formula:

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

where P(X = k) is the probability of getting exactly k successes, n is the sample size, p is the probability of success, and (n choose k) is the binomial coefficient which represents the number of ways to choose k successes out of n trials.

In this case, n = 15, p = 0.69 (the proportion of Americans who own an answering machine), and k = 7. Thus, the probability of getting exactly 7 Americans who own an answering machine out of a sample of 15 is:

P(X = 7) = (15 choose 7) * 0.69^7 * (1 - 0.69)^(15 - 7)

Using a calculator or statistical software, we can evaluate this expression to find:

P(X = 7) ≈ 0.170

This means that if we were to repeat this survey many times with samples of size 15, we would expect approximately 17% of the samples to have exactly 7 Americans who own an answering machine.

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With the given parameters, the width of the 80% CI for the normal distribution's mean is roughly 1.5.

The following formula can be used to determine the width of an 80% confidence interval (CI) for the mean of a normal distribution with unknown variance, the sample mean 9, sample variance 6, and sample size 15:

width = t * (s / √(n))

where s is the sample standard deviation (the square root of the sample variance), n is the sample size, and t is the value from the t-distribution with n-1 degrees of freedom for an 80% CI (from a t-table or calculator).

We must first determine the sample standard deviation:

s = √(6) ≈ 2.45

Then, we can find the worth of t from a t-table or mini-computer for a 80% CI with 14 levels of opportunity (15-1):

Lastly, these numbers can be used to calculate the 80% CI width:

With the given parameters, the width of the 80% CI for the normal distribution's mean is roughly 1.5.

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The two numbers in the system of equation is 5 and 13.

A group of multiple-variable equations that must all be solved concurrently make up a system of equations. Finding values for the variables that satisfy every equation in a system of equations is the objective. Each equation in the system reflects a connection between the variables. In order to find a singular solution or a group of solutions, systems of equations can be solved using a variety of methods, such as substitution or elimination. In many disciplines, including mathematics, physics, engineering, and economics, systems of equations can occur.

Let us suppose the two numbers as x and y.

x + y = 18

x - y = -8

The second equation can be written as:

x + 8 = y

Substitute the value of y in equation 1:

x + x + 8 = 18

2x = 10

x = 5

Substitute the value of x to get y:

x + y = 18

5 + y = 18

y = 13

Hence, the two numbers in the system of equation is 5 and 13.

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