Complete the frequency table for the following set of data. You may optionally click a number to shade it out.

The measure of angle Q is 70°

A parallelogram is a quadrilateral with two pairs of parallel sides.

Some of the properties of a parallelogram are ;

1. They have two pair of parallel lines

2. The opposite sides are equal

3. The sum of the adjascent sides is 180°

Since we have known that the sum of the adjascent sides of a parallelogram is 180°, then we can say that;

6x+4 + 10x = 180

16x = 180 -4

16x = 176

x = 11

angle Q = 6x +4

Q = 6(11)+4

Q = 70°

Therefore the value of angle Q is 70°

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The missing values for the inverse matrix A⁻¹ are:

The solution is:

In Mathematics and Geometry, a square matrix refers to a type of matrix that is composed of an equal number of both rows and columns. Generally speaking, m × m matrix is typically referred to as a square matrix of order m.

Next, we would convert the system of three linear equations in standard form to matrix form as follows;

[tex]\left[\begin{array}{ccc}1&1&1\\10&-20&98\\5&10&-10\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}200\\250\\500\end{array}\right][/tex]

By using technology, the solutions to this system of three linear equations include the following:

x = -9200

y = 7025

z = 2375.

By using technology, the inverse of this matrix is given by;

[tex]A^{-1}=\left[\begin{array}{ccc}-78&2&11.8\\59&-1.5&-8.8\\20&-0.5&-3\end{array}\right][/tex]

Therefore, the missing values are as shown in the inverse of this matrix A⁻¹ above.

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The correct answer is D. No because 23 and 25 are not supplementary.

In the given diagram, it is stated that the measures of angles 23 and 27 are 45°, and the measure of angle 25 is 135°. To determine if lines C and D are parallel, we need to analyze the angles formed by these lines.

If the alternate interior angles or corresponding angles are congruent, then the lines are parallel. However, in this case, we don't have enough information about the angles formed by lines C and D to make that determination.

The fact that angle 23 and angle 27 are congruent (both measuring 45°) doesn't provide any information about the relationship between lines C and D. Similarly, the measure of angle 25 being 135° doesn't give us any insight into the parallelism of lines C and D. Therefore, we cannot conclude that lines C and D are parallel based on the given information, and the correct answer is D.

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The size of the matrix is 2 × 3.

The matrix is: B. of no special type.

The additive inverse of the matrix is:  [tex]\left[\begin{array}{ccc}7&-6&4\\3&-4&2\end{array}\right][/tex]

In Mathematics and Geometry, a square matrix is a type of matrix that is composed of an equal number of both rows and columns. Generally speaking, m × m matrix is typically referred to as a square matrix of order m.

In this context, we can reasonably infer and logically deduce that this matrix is of no special type because the number of rows in are not the same as the number of columns.

2 rows by 3 columns;

m × n = 2 × 3

From additive inverse postulate, we have the following:

A + (-A) = 0

[tex]\left[\begin{array}{ccc}-7&6&-4\\-3&4&-2\end{array}\right]+\left[\begin{array}{ccc}7&-6&4\\3&-4&2\end{array}\right]=0[/tex]

-A =  [tex]\left[\begin{array}{ccc}7&-6&4\\3&-4&2\end{array}\right][/tex]

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The amount of Bruno's yearly pay deducted for FICA is approximately

A. $4,524.15. The closest option provided is A. $4521.15.

To calculate the amount of FICA deducted from Bruno's yearly pay, we need to consider the specific FICA tax rates for Social Security and Medicare.

As of 2021, the Social Security tax rate is 6.2% on income up to a certain threshold, and the Medicare tax rate is 1.45% on all income.

Given that Bruno's gross income per pay period is $4925 and he is paid monthly, we can calculate the yearly gross income as follows:

Yearly gross income = $4925 * 12 = $59,100

To calculate the FICA deduction, we need to find the sum of the Social Security and Medicare taxes. Using the respective tax rates mentioned earlier:

Social Security deduction = $59,100 * 6.2% = $3,667.20

Medicare deduction = $59,100 * 1.45% = $856.95

Adding these two deductions together:

FICA deduction = $3,667.20 + $856.95 = $4,524.15

Therefore, the amount of Bruno's yearly pay deducted for FICA is approximately $4,524.15.

The closest option provided is A. $4521.15.

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6x² - 6x + 5 is the algebraic expression that is a polynomial with a degree of 2.

The algebraic expression that is a polynomial with a degree of 2 is:

6x² - 6x + 5

A polynomial expression is a sum of terms where each term consists of a coefficient multiplied by one or more variables raised to non-negative integer exponents. The degree of a polynomial is determined by the highest exponent of the variable in any term of the polynomial.

In the expression 6x² - 6x + 5, the highest exponent of the variable x is 2 in the term 6x². The other terms have lower exponents, with -6x having an exponent of 1 and 5 having an exponent of 0. Therefore, the degree of the polynomial is 2, which is the highest exponent in the expression.

Hence, 6x² - 6x + 5 is the algebraic expression that is a polynomial with a degree of 2.

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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 equation in the box with x replacing [tex]4^{\frac{1}{5} }[/tex] in the equation can be presented as follows;

An equation is a statement that indicates that two expressions are equivalent, by joining them with an '=' sign.

The details in the diagram indicates; x = [tex]4^{\frac{1}{5} }[/tex]

Required, to rewrite the equation in the box by plugging in x to substitute [tex]4^{\frac{1}{5} }[/tex] in the equation

The equation in the box can be presented as follows;

[tex]\underline{(4^{\frac{1}{5} })^5 = 4}[/tex]

Plugging in x = [tex]4^{\frac{1}{5} }[/tex] in the above equation, we get;

[tex]\underline{(4^{\frac{1}{5} })^5 =x^5 = 4}[/tex]

Therefore, the equation in the box becomes;

x⁵ = 4

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Answer:

3√41

Step-by-step explanation:

a^2+b^2=c^2

rearrange this to make x (a or b it doesn't matter) the subject

√b=c^2-a^2

now substitute this in:

√b=25^2-16^2

=369

then simple do the square root

√369

=3√41

Hope this helps!

The correct answer is C. 2.

To determine the slope of a line, we need to calculate the change in the y-coordinates divided by the change in the x-coordinates between two points on the line. In this case, we have the points (0, -5) and (3, 1).

The change in the y-coordinates is 1 - (-5) = 6, and the change in the x-coordinates is 3 - 0 = 3.

Therefore, the slope of the line is the ratio of the change in the y-coordinates to the change in the x-coordinates, which is 6/3 = 2.

Hence, the slope of the line graphed is 2.

Therefore, the correct answer is C. 2.

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Answer:x=bx2 is the answer

Step-by-step explanation:

The probability that the 5 starting members of the basketball team are lined up from shortest to tallest is 1/120. Option A.

To calculate the probability that the 5 starting members of the basketball team are lined up from shortest to tallest, we need to determine the number of favorable outcomes (arrangements where the players are lined up from shortest to tallest) and divide it by the total number of possible outcomes.

Since the order matters and we want the players to be arranged from shortest to tallest, there is only one favorable outcome. The shortest player must be in the first position, followed by the second shortest, and so on, until the tallest player is in the last position.

The total number of possible outcomes is given by the number of permutations of 5 players, which is denoted as 5!.

Therefore, the probability is:

Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

Probability = 1 / 5!

Probability = 1 / (5 * 4 * 3 * 2 * 1)

Probability = 1 / 120 Option A is correct.

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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 two angles are related in that they are supplementary angles

Supplementary angles would add tuo to 180 degrees according to the angle Theorem.

Adding the two given angles :

These angles are supplementary

The angles aren't vertical in that , vertical angles should have the same vertex. Complementary angles on the other hand add to 90 degrees. While the angles doesn't share the same side, hence, they aren't adjacent.

Hence, the angles are related as they are supplementary angles .

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True because corresponding sides and angles of the triangles are congrent.

The simplification of 3 hours : 45 m is 4 minutes : 1 minutes.

Ratio refers to a number representing a comparison between two named quantities.

3 hours : 45 m

Convert hours to minutes:

1 hour = 60 minutes

3 hours = 180 minutes

3 hours : 45 m = 180 minutes : 45 minutes

= 180/45

= 4 / 1

= 4 : 1

Ultimately, 3 hours : 45 m is 4 minutes ratio 1 minutes.

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The diagram to the right BC is parallel to DE.

Here, AD=15,

DB=12,

AE=10, and

EC=8.

We need to determine if BC||DE or not.

angle ADE = 180 - 90  = 49.106 degree.

Now, using the triangle BDC, we can find the value of sin[angle CDB] as follows.

angle CDB = angle DAB = angle ABD = 180 - angle ADE - angle EDC

To determine if BC is parallel to DE, we can use the concept of proportional sides of the triangle.

From the information given, AD = 15, DB = 12, AE = 10, and EC = 8.

If BC is parallel to DE, then by the intercept theorem (also known as Thales' theorem), the Die segments AD/DB and AE/EC must be the same.

Let's calculate these ratios:

AD/DB = 15/12 = 5/4

AE/EC = 10/8 = 5/4

AD/DB = AE/EC = 5/ 4, so we can conclude that: BC is parallel to DE.

The reason for this is that if two ratios are equal, it means that the corresponding sides of the triangle formed by the intersecting lines are proportional, which is a characteristic of parallel lines.

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The function g(x) is obtained by stretching the logarithmic function f(x) vertically by 7, reflecting it over the x-axis and y-axis, and shifting it up by 2 units. The equation for g(x) is -7*log₆(-x) + 2.

To find the equation of the function g(x), we can apply a series of transformations step by step. First, we stretch the function vertically by a factor of 7 by multiplying it by 7. This gives us the function g₁(x) = 7*log₆(x).

Next, we reflect the function g₁(x) over the x-axis by multiplying it by -1. This results in the function g₂(x) = -7*log₆(x).

To reflect the function g₂(x) over the y-axis, we replace x with -x, giving us the function g₃(x) = -7*log₆(-x).

Lastly, we shift the function g₃(x) up by 2 units by adding 2 to it. This gives us the final equation for g(x) as g(x) = -7*log₆(-x) + 2.

In summary, the function g(x) is obtained by vertically stretching the logarithmic function f(x) by a factor of 7, reflecting it over the x-axis, reflecting it over the y-axis, and then shifting it up by 2 units.

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Answer:

The given linear equation is -5x-3y=-7. To graph the equation, we need to find three points that satisfy the equation and then plot them on the graph.

Let's find the x and y intercepts first.

At x = 0, we have -3y = -7, which gives us y = 7/3. So the y-intercept is (0, 7/3).

At y = 0, we have -5x = -7, which gives us x = 7/5. So the x-intercept is (7/5, 0).

Now, let's choose another point. We can choose any value for x or y and solve for the other variable. Let's take x = 1.

-5(1) - 3y = -7

-3y = -2

y = 2/3

So the third point is (1, 2/3).

Now we can plot these three points on the graph and draw a line passing through them.

Here's the graph:

|

|

| . (1, 2/3)

|

| .

| (0, 7/3)

|

|_________________________

| |

7/5 -7/15

Step-by-step explanation:

Already explained

The graph with the upward parabola plotted in quadrant 1 of a coordinate plane, with the vertex at (3, -1), and left and right slopes at (2, 1) and (4, 1), matches the quadratic function f(x) = (x - 3)^2 - 1.T

To match the graph with the quadratic function it represents, we need to analyze the given information about the graph.
The graph shows an upward parabola plotted in quadrant 1 of a coordinate plane. This means that the parabola opens upwards.
The vertex of the parabola is given as (3, -1), which means that the axis of symmetry is a vertical line passing through x = 3, and the vertex is the lowest point on the parabola.
The left slope of the parabola is given as (2, 1), which means that the slope on the left side of the vertex is positive and equal to 1.
The right slope of the parabola is given as (4, 1), which means that the slope on the right side of the vertex is also positive and equal to 1.
Based on this information, we can determine the quadratic function that matches the graph.
The vertex form of a quadratic function is given by f(x) = a(x - h)^2 + k, where (h, k) represents the vertex.
In this case, the vertex is (3, -1), so the equation can be written as f(x) = a(x - 3)^2 - 1.
Since the parabola opens upwards, the coefficient of a must be positive.
The left and right slopes of the parabola are both equal to 1, which means that the coefficient a must be equal to 1.
Therefore, the quadratic function that matches the graph is f(x) = (x - 3)^2 - 1.

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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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the period of y = 3cot(x) remains as π. the period of y = 3cot(4x - 3x) is also π.

To find the period of the function y = 3cot(4x - 3x), we need to determine the length of one complete cycle of the function.

First, let's simplify the expression inside the cotangent function: 4x - 3x = x.

Now, the cotangent function has a period of π, which means it repeats every π units.

To find the period of the given function y = 3cot(x), we need to determine how the variable x affects the period. Since the coefficient of x is 1, it means that the period is not affected by any scaling or stretching.

In summary, the period of the function y = 3cot(4x - 3x) is π, which means the function repeats every π units along the x-axis.

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Answer:

Refer to the step-by-step explanation, please follow along very carefully. Answers are encased in two boxes.

Step-by-step explanation:

Given the following function, find it's derivative using the definition of derivatives. Evaluate the function when θ=1, 11, and 3/11

[tex]p(\theta)=\sqrt{11\theta}[/tex]

[tex]\hrulefill[/tex]

The definition of derivatives states that the derivative of a function at a specific point measures the rate of change of the function at that point. It is defined as the limit of the difference quotient as the change in the input variable approaches zero.

[tex]f'(x) = \lim_{{h \to 0}} \dfrac{{f(x+h) - f(x)}}{{h}}[/tex][tex]\hrulefill[/tex]

To apply the definition of derivatives to this problem, follow these step-by-step instructions:

Step 1: Identify the function: Determine the function for which you want to find the derivative. In out case the function is denoted as p(θ).

[tex]p(\theta)=\sqrt{11\theta}[/tex]

Step 2: Write the difference quotient: Using the definition of derivatives, write down the difference quotient. The general form of the difference quotient is (f(x+h) - f(x))/h, where "x" is the point at which you want to find the derivative, and "h" represents a small change in the input variable. In our case:

[tex]p'(\theta) = \lim_{{h \to 0}} \dfrac{{p(\theta+h) - p(\theta)}}{{h}}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11(\theta + h)} - \sqrt{11\theta} }{h}[/tex]

Step 3: Take the limit:

We need to rationalize the numerator. Rewriting using radical rules.

[tex]p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11(\theta + h)} - \sqrt{11\theta} }{h} \\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11\theta + 11h} - \sqrt{11\theta} }{h}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} }{h}[/tex]

Now multiply by the conjugate.

[tex]p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} }{h} \cdot \dfrac{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} } \\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{(\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} )(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )}{h(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )} \\\\\\[/tex]

[tex]\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{11h}{h(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{11}{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }[/tex]

Step 4: Simplify the expression: Evaluate the limit by substituting the value of h=0 into the difference quotient. Simplify the expression as much as possible.

[tex]p'(\theta)= \lim_{h \to 0} \dfrac{11}{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{\sqrt{11}\sqrt{\theta+(0)} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{\sqrt{11}\sqrt{\theta} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11\theta} }[/tex]

[tex]\therefore \boxed{\boxed{p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta} }}}[/tex]

Thus, we have found the derivative on the function using the definition.

It's important to note that in practice, finding derivatives using the definition can be a tedious process, especially for more complex functions. However, the definition lays the foundation for understanding the concept of derivatives and its applications. In practice, there are various rules and techniques, such as the power rule, product rule, and chain rule, that can be applied to find derivatives more efficiently.[tex]\hrulefill[/tex]

Now evaluating the function at the given points.  

[tex]p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}; \ p'(1)=??, \ p'(11)=??, \ p'(\frac{3}{11} )=??[/tex]

When θ=1:

[tex]p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(1)= \dfrac{\sqrt{11} }{2\sqrt{1}}\\\\\\\therefore \boxed{\boxed{p'(1)= \dfrac{\sqrt{11} }{2}}}[/tex]

When θ=11:

[tex]p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(11)= \dfrac{\sqrt{11} }{2\sqrt{11}}\\\\\\\therefore \boxed{\boxed{p'(11)= \dfrac{1}{2}}}[/tex]

When θ=3/11:

[tex]p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(\frac{3}{11} )= \dfrac{\sqrt{11} }{2\sqrt{\frac{3}{11} }}\\\\\\\therefore \boxed{\boxed{p'(\frac{3}{11} )= \dfrac{11\sqrt{3} }{6}}}[/tex]

Thus, all parts are solved.

The total number of pizzas sold at the end of 5 hours would be = 520.

To calculate the total number of pizzas sold, the following steps needs to be taken as follows;

The current total number of pizza sold by the restaurant = 80

The percentage increase of the number sold = 5% of 80

That is ; 5/100 × 80

= 400/100 = 4

The total number of hours spent = 5 hours

The additional number of pizzas = 5×4 = 20

Therefore,the total number of pizzas = 500+20 = 520.

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Answer: B

Step-by-step explanation: Hope this helps:)

Potential problems with increasing the minimum wage include job loss, increased cost of living, business closures, regional disparities, and potential skill depreciation. It is important to carefully consider the potential consequences and assess the trade-offs before implementing any changes to the minimum wage.

1. Job Loss: Increasing the minimum wage can lead to job losses, especially for low-skilled workers. Employers may not be able to afford paying higher wages and may choose to reduce their workforce or automate certain tasks. This could result in unemployment and make it harder for individuals to find jobs.
2. Cost of Living: While increasing the minimum wage may help some workers, it could also lead to higher costs of goods and services. Employers may pass on the increased labor costs to consumers, which could result in inflation. This could offset the benefits of higher wages as the cost of living increases.
3. Business Closures: Small businesses, in particular, may struggle to absorb the increased labor costs associated with a higher minimum wage. This could result in business closures, leading to job losses and potentially reducing job opportunities for individuals.
4. Regional Disparities: A nationwide increase in the minimum wage may not account for regional differences in living costs. While a higher minimum wage may be reasonable in some areas with high costs of living, it may be excessive in other regions. This could lead to unintended consequences, such as businesses relocating to areas with lower labor costs.
5. Skill Depreciation: If the minimum wage is increased significantly, there is a risk that it may discourage individuals from pursuing higher education or acquiring additional skills. Some individuals may find it more economically viable to rely on minimum wage jobs rather than investing time and money into further education or training.

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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! =)