What is the value of n in the equation 1/2(n-4)-3=3− (2n + 3)?

The measure of angle Q is equal to 70 degrees.

In Mathematics and Geometry, a parallelogram is a geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.

Generally speaking, the the sum of all the interior angles of a parallelogram is equal to 360 degrees and as such, we have the following:

(6x+4) + (6x+4) + 10x + 10x = 360

32x + 8 =360

32x =360-8

32x=352

x = 11

Now, we can determine the measure of angle Q as follows;

Q = 6x + 4

Q = 6(11) + 4

Q = 66 + 4

Q = 70 degrees.

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Answer: The usual dose for an 18-month-old weighing 21 pounds is 48 mg of ibuprofen.

Step-by-step explanation: To find the usual dose of ibuprofen for a child, we need to follow these steps:

Therefore, the usual dose for an 18-month-old weighing 21 pounds is 48 mg of ibuprofen. Hope this helps, and have a great day! =)

Answer:

1244 DCD

Step-by-step explanation:

The exact value of sinθ in simplest form, with cosθ = 2/5 and θ in Quadrant IV, is -√21/5.

To find the exact value of sinθ, we can use the Pythagorean identity: sin²θ + cos²θ = 1. Since we know the value of cosθ, we can substitute it into the equation and solve for sinθ.

Given that cosθ = 2/5 and θ is in Quadrant IV, we know that the cosine is positive in Quadrant IV, and the sine is negative. Let's proceed with the calculations:

sin²θ + cos²θ = 1

sin²θ + (2/5)² = 1 (Substituting cosθ = 2/5)

sin²θ + 4/25 = 1 (Simplifying)

sin²θ = 1 - 4/25 (Subtracting 4/25 from both sides)

sin²θ = 21/25 (Simplifying)

Taking the square root of both sides, considering that sinθ is negative in Quadrant IV:

sinθ = -√(21/25)

Since we want to express the answer in simplest form, we can simplify the radical:

sinθ = -√21/√25

The square root of 25 is 5, so we can simplify further:

sinθ = -√21/5

Therefore, the exact value of sinθ in simplest form, given that cosθ = 2/5 and θ is in Quadrant IV, is -√21/5.

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Answer: (A)  independent or (D) not mutually excusive

Step-by-step explanation: Just think about it, what card you draw from a deck doesn't depend on anything. Not mutually exculisve means the same as indendent.

The 23rd term of the arithmetic sequence is -8.

To find the 23rd term of an arithmetic sequence, we need to know the common difference (d) of the sequence.

Given that the 14th term is 37 and the 5th term is 82, we can use this information to find the common difference.

The formula for the nth term of an arithmetic sequence is:

Term n = a + (n - 1) * d,

where a is the first term and d is the common difference.

Using the information provided, we can set up two equations based on the given terms:

Equation 1: a + (14 - 1) * d = 37, (14th term is 37)

Equation 2: a + (5 - 1) * d = 82. (5th term is 82)

Simplifying the equations, we have:

Equation 1: a + 13d = 37,

Equation 2: a + 4d = 82.

We can solve this system of equations to find the values of a and d. Subtracting Equation 2 from Equation 1, we have:

(a + 13d) - (a + 4d) = 37 - 82,

13d - 4d = -45,

9d = -45,

d = -5.

Now that we have the common difference, we can find the first term (a) using Equation 2:

a + 4d = 82,

a + 4(-5) = 82,

a - 20 = 82,

a = 82 + 20,

a = 102.

Now, we can use the formula for the nth term to find the 23rd term:

Term 23 = a + (23 - 1) * d,

Term 23 = 102 + 22 * (-5),

Term 23 = 102 - 110,

Term 23 = -8

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A recent survey conducted on a sample of 425 individuals revealed that 102 of them had visited the cinema within the past month.

This data suggests that approximately 24% of the surveyed population had engaged in movie going activities during the specified period.

The findings highlight a significant proportion of the respondents who have recently enjoyed the cinematic experience.

However, it is important to note that this data is based on a limited sample size and may not be representative of the entire population.

Further research and surveys involving a larger and more diverse sample are recommended to obtain a more accurate understanding of movie attendance trends.

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Answer:

explanation provided in the picture

Step-by-step explanation:

the answer is x= 55°

hopefully this helps ! :)

The reduced row echelon form of a matrix allows us to determine whether the associated linear system is consistent or inconsistent, unique or has infinitely many solutions.

In reduced row echelon form, a matrix has the following properties:

Each leading entry (the leftmost nonzero entry) of a row is equal to 1.

Each leading entry is the only nonzero entry in its column.

All entries below a leading entry are zeros.

The leading entry in each row is to the right of the leading entry in the row above it.

Based on these properties, we can make the following conclusions about the solution to the associated linear system:

Consistency: If there are no rows of the form [0 0 ... 0 | b] (where b is a nonzero constant), meaning there are no contradictory equations, the linear system is consistent. In other words, there is at least one solution.

Uniqueness: If there are no free variables (columns without leading entries), meaning each column corresponds to a pivot column, the linear system has a unique solution. This means there is only one set of values for the variables that satisfies all the equations.

Infinite solutions: If there are one or more free variables, the linear system has infinitely many solutions. This occurs when there are more variables than equations or when there are dependent equations.

The reduced row echelon form provides an organized representation of the linear system that simplifies the process of determining its solution. By analyzing the structure of the matrix, we can determine the consistency, uniqueness, and the nature of the solution set.

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The present age of the elder brother is in a ratio of 23 to the present age of the younger brother, which can be simplified to a ratio of 5 to 4.

Let's assume the present age of the elder brother is E years, and the present age of the younger brother is Y years. According to the given information, the difference in their ages is 5 years, which can be expressed as E - Y = 5.

Six years ago, the elder brother's age was E - 6, and the younger brother's age was Y - 6. According to the second given condition, the product of their ages at that time was 696, which can be expressed as (E - 6)(Y - 6) = 696.

To find the ratio of their present ages, we need to solve the two equations simultaneously. We can start by expanding the second equation:

(E - 6)(Y - 6) = 696

EY - 6E - 6Y + 36 = 696

EY - 6E - 6Y = 660

Now we can substitute the value of E - Y from the first equation into the second equation:

(E - Y) - 6E - 6Y = 660

5 - 6E - 6Y = 660

-6E - 6Y = 655

Simplifying the equation:

6E + 6Y = -655

Now we have a system of linear equations:

E - Y = 5

6E + 6Y = -655

Solving these equations, we find that the present age of the elder brother (E) is 23 years and the present age of the younger brother (Y) is 18 years.

Therefore, the ratio of the present age of the elder brother to the younger brother is 23:18, which can be simplified to 5:4.

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To estimate the probability of rolling a score of 4 on the next roll based on the recorded data, we need to examine the frequency of rolling a score of 4 and calculate the expected number of 2s in 400 rolls.

Unfortunately, the provided information does not include the table or any specific data regarding the frequency of rolling a score of 4. Without this information, we cannot estimate the probability accurately or calculate the expected number of 2s.

To determine the expected number of 2s in 400 rolls, we would need to know the probability distribution of rolling a 2 with the biased dice. This information is crucial to make a reasonable estimate.

Without further details, it is not possible to provide a specific answer to how many 2s you would expect to get in 400 rolls.

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The value of the equation that defines the function is f(x) = 3(5/3)ˣ

From the question, we have the following parameters that can be used in our computation:

(0, 3) and (1, 5)

An exponential function is represented s

y = abˣ

Where,

a = y when x = 0

So, we have

y = 3bˣ

Using the other point, we have

3b = 5

This gives

b = 5/3

So, we have

f(x) = 3(5/3)ˣ

Hence, the equation defining f is f(x) = 3(5/3)ˣ

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The x-intercept in function B is one-third as large as the x-intercept in function A.

The x-intercepts of two functions, A and B, are compared in terms of their relative sizes and distances. According to the given information, the x-intercept in function B is one-third as large as the x-intercept in function A. This means that the value of the x-coordinate at which function B intersects the x-axis is one-third of the value of the x-coordinate at which function A intersects the x-axis.

Conversely, we can say that the x-intercept in function A is three times as large as the x-intercept in function B. The x-coordinate at which function A intersects the x-axis is three times the value of the x-coordinate at which function B intersects the x-axis.

However, the information does not provide any direct comparison of the distances between the x-intercepts of the two functions. Therefore, we cannot determine whether the distance between the x-intercepts in function A is half or twice the distance between the x-intercepts of function B based on the given information.

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The formula for the area of the base (B) of a triangular pyramid is given by option C: B = ½bh.

In a triangular pyramid, the base is a triangle, and the area of a triangle is calculated using the formula ½bh, where b represents the length of the base of the triangle and h represents the corresponding height. Therefore, the formula for the area of the base (B) is B = ½bh.

The base of a triangular pyramid is a two-dimensional shape, and its area is determined by the length of the base and the height perpendicular to it. The formula B = ½bh is commonly used to find the area of a triangle, which applies to the base of the pyramid in this case.

The ½ factor accounts for the fact that the base is a triangle, and the product of the base length (b) and the corresponding height (h) yields the area of the triangle. Hence, option C correctly represents the formula for the base area of a triangular pyramid.

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There are 21 different city combinations possible for Peter's summer traveling.

To determine the number of different city combinations possible for Peter's summer traveling, we need to calculate the number of combinations of choosing 5 cities out of the 7 available cities.

Since the order in which he visits the cities does not matter, we are dealing with combinations rather than permutations.

The formula to calculate the number of combinations is given by the binomial coefficient, also known as "n choose k," denoted as C(n, k) or (nCk).

In this case, we have 7 cities to choose from, and Peter will visit 5 cities. Thus, we can calculate the number of city combinations as follows:

C(7, 5) = 7! / (5! * (7-5)!)

= 7! / (5! * 2!)

= (7 * 6 * 5!) / (5! * 2)

= (7 * 6) / 2

= 42 / 2

= 21

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