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An expression for the amount of money that Alicia earns in a day is 40y-3g.

Given that, Alicia runs a small business mowing yards in the summer. For every yard she mows, she earns $40. However, she spends part of this money on gasoline for her lawnmower. Each gallon of gasoline costs $3.

We need to find an expression for the given situation.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Now, expression =40y-3g

Therefore, an expression for the amount of money that Alicia earns in a day is 40y-3g.

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Answer: $40y − $3g

Step-by-step explanation:

Answer:

G

Step-by-step explanation:

27 + 28 = 55

the smaller integer is 27

In the random sample of 17 students in this group, the probability of the average height being 73-75 inches is about 0.014, or 1.4%.  

Let the heights be normally distributed with a mean of 70 inches and a standard deviation of 3 inches.

If we sample 17 students from this group, the distribution of the sample mean will also be approximately normal, with a mean of 70 inches and a standard deviation of 3/sqrt(17) inches (according to the central limit theorem).

This sample average interval can be normalized by the following formula:

z = (x - μ) / (σ / sqrt(n))

where x =sample mean,

μ = population mean,

σ= population standard deviation,

and n = sample size.

For the lower bound of 73 inches, the standardized values ​​are:

z1 = (73 - 70) / (3 / sqrt(17)) ≈ 2.25

For the upper limit of 75 inches, the standardized values ​​are:

z2 = (75 - 70) / (3 / sqrt(17)) ≈ 3.87

Find the probability that the sample mean is between these two values. This probability can be found by finding the area under the standard normal curve between z1 and z2 using a standard normal distribution table or calculator.

P(2.25 < z < 3.87) ≈ 0.014

So, in her random sample of 17 students in this group, the probability of the average height being 73-75 inches is about 0.014, or 1.4%.  

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The value of the double integral (4x − 9y) dA over the region D bounded by the circle with center at the origin and radius 2 is -48.

To evaluate the double integral (4x − 9y) dA over the region D bounded by the circle with center at the origin and radius 2, we need to use polar coordinates.

In polar coordinates, the equation of the circle with center at the origin and radius 2 is given by r = 2. Therefore, the limits of integration for r are 0 and 2, and the limits of integration for θ are 0 and 2π.

The element of area in polar coordinates is given by dA = r dr dθ. Therefore, we can rewrite the double integral in terms of polar coordinates as follows

∬D (4x − 9y) dA = ∫₀² ∫₀²π (4r cosθ - 9r sinθ) r dθ dr

= ∫₀² r² (4cosθ - 9sinθ) dθ dr [Using the properties of integrals]

The integral with respect to θ is zero for sinθ and cosθ over a full period. Therefore, we have

∬D (4x − 9y) dA = ∫₀² r² (4cosθ - 9sinθ) dθ dr

= 4∫₀² r² cosθ dθ dr - 9∫₀² r² sinθ dθ dr

Integrating with respect to θ, we get

∫₀² r² cosθ dθ = [2r² sinθ]₀²π = 0

∫₀² r² sinθ dθ = [-2r² cosθ]₀²π = 4r²

Substituting these values in the original equation, we get

∬D (4x − 9y) dA = 4∫₀² r² cosθ dθ dr - 9∫₀² r² sinθ dθ dr

= 4(0) - 9(4r²) dr

= - 36 ∫₀² r² dr

= -36 [r³/3]₀² = -48

Therefore, the value of the double integral is -48.

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The given question is incomplete, the complete question is:

Evaluate the double integral. (4x − 9y) dA, D is bounded by the circle with center the origin and radius 2

Answer:

The answer would be y = 120.

Step-by-step explanation:

If x is always 1/4 of y, then if x equals 30, y would be 4 times the amount of x. I hope this helps you! :)

there are 1365 possible committees that can be formed from this group of 15 people, regardless of gender.

To form a committee of 4 people from a group of 9 women and 6 men, we need to consider all possible combinations of 4 people, regardless of gender.

The number of ways to choose 4 people from a group of 15 (9 women and 6 men) is given by the combination formula:

C(15,4) = 15! / (4! * (15-4)!) = 15! / (4! * 11!) = (15 * 14 * 13 * 12) / (4 * 3 * 2 * 1) = 1365

Therefore, there are 1365 possible committees that can be formed from this group of 15 people, regardless of gender.

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The equation that can be used to solve for the number of classes, cc, for which Class AA and Class BB cost the same is 5cc + 10 = 8cc.

To solve for the number of classes, cc, for which Class AA and Class BB cost the same, we can use the following equation:

5cc + 10 = 8cc

In this equation, 5cc represents the fee structure for Class AA, and 8cc represents the fee structure for Class BB. The + 10 represents an additional flat fee for Class AA that is not present in Class BB.

To solve for cc, we can simplify the equation by combining like terms:

10 = 3cc

Next, we can solve for cc by dividing both sides of the equation by 3:

cc = 10/3

Therefore, Class AA and Class BB will cost the same when there are 10/3 or approximately 3.33 classes. Since we cannot have a fraction of a class, we can round up to 4 classes as the answer.

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In statistical hypothesis testing, the P-value is a significant factor. It is the probability of obtaining a test statistic at least as extreme as the one calculated from the data, assuming the null hypothesis to be true. If the null hypothesis is false, the P-value is the probability of a type I error. It is the probability of rejecting the null hypothesis when it is true.

To interpret the P-value correctly, a P-value of 0.054 means that if the null hypothesis is correct, there is a 5.4% probability that the sample will produce a test statistic as extreme as, or more extreme than the one that was observed. If the calculated P-value is higher than the significance level, which is usually 0.05 or 0.01, we cannot reject the null hypothesis.

In the given situation, the sample provides insufficient evidence to reject the owner's claim that the mean weight of Gala apples this year is heavier than usual because the calculated P-value is higher than the significance level. Hence, the correct option is that the P-value suggests that there is not sufficient evidence to reject the null hypothesis.

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Answer: 3

Step-by-step explanation:

      First, we will write a mathematical equation for the phrase given.

-> Let n be "a number"

             four subtracted from twice a number is two

             four subtracted from twice a number = 2

             (twice a number) - 4 = 2

             2n - 4 = 2

      Now, we will solve this equation by isolating the variable.

             2n - 4 = 2

             2n = 6

             n = 3

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Answer:

a/2=3

We simplify the equation to the form, which is simple to understand  

a/2=3

We move all terms containing a to the left and all other terms to the right.  

+ 0.5a=+3

We simplify left and right side of the equation.  

+ 0.5a=+3

We divide both sides of the equation by 0.5 to get a.  

a=6

The total cost if Wacky Widget Company makes 230 widgets is $31,600.

The total cost is the sum of the rent (fixed cost) and the variable costs. The variable costs includes the cost of materials and labor.

Total cost = rent + (cost of labor and materials x number of widgets)

$4000 + [(77 + 43) x 230]

$4000 + (120 x 230)

$4000 + $27,600

= $31,600

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The total cost if Wacky Widget Company makes 230 widgets is $31,600 if each widget requires $77 worth of materials and $43 worth of labor.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have:

The Wakey Widget Company is planning to produce widgets. The company has rented space for its manufacturing operation at $4,000 per month.

Let's suppose the total cost is $x

We can frame a linear equation in one variable:

x = 4000 + 77x230 + 43x230

x = 4000 + 17710 + 9890

x = $31,600

Thus, the total cost if Wacky Widget Company makes 230 widgets is $31,600 if each widget requires $77 worth of materials and $43 worth of labor.

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The correct graph of the system of equations is D) The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 12.

What is the system of equations?

A system of equations is a set of two or more equations with the same variables. The goal of a system of equations is to find the values of the variables that simultaneously satisfy all the equations in the system.

The given equations are

3x + y = 12

x + 4y = 4

To graph the system of equations, we can start by finding the x-intercepts and y-intercepts of each line.

The x-intercept is the point where the line crosses the x-axis, which means that the y-value is 0. To find the x-intercept, we can set y = 0 and solve for x:

3x + y = 12

3x + 0 = 12

3x = 12

x = 4

So, the x-intercept of the first line is (4, 0).

Next, we can find the y-intercept, which is the point where the line crosses the y-axis, meaning that the x-value is 0. To find the y-intercept, we can set x = 0 and solve for y:

3x + y = 12

0 + y = 12

y = 12

So, the y-intercept of the first line is (0, 12).

We can repeat this process for the second line to find its x-intercept and y-intercept:

x + 4y = 4

x + 4 * 0 = 4

x = 4

So, the x-intercept of the second line is (4, 0).

Next, we can find the y-intercept by setting x = 0:

x + 4y = 4

0 + 4y = 4

4y = 4

y = 1

So, the y-intercept of the second line is (0, 1).

Now that we have found the x-intercepts and y-intercepts of each line, we can plot these points on a coordinate plane and draw lines through them to obtain the graph of the system of equations.

The graph shows a line with an x-intercept at (4, 0) and a y-intercept at (0, 12). There is a second line with an x-intercept at (4, 0) and a y-intercept at (0, 1).

Therefore, the correct graph of the system of equations is D) The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 12.

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Answer:

  $4050

Step-by-step explanation:

You want to know how much money Lynn had left after she spent 16% and 30% of her $7500 on food and drink, respectively.

After spending a total of 16% +30% = 46% of her money, the amount remaining is 100% -46% = 54% of the original amount. That would be ...

  0.54 · $7500 = $4050

Lynn had $4050 left.

Report on Commonalities Among Three Chosen Regions

For this assignment, three regions of the world have been selected to identify commonalities among them. The chosen regions are North America, Europe, and East Asia. Through internet research, several commonalities have been identified that are shared among these regions. Below are five commonalities found:

Economic Development:

All three regions, North America, Europe, and East Asia, are characterized by significant economic development. They are home to some of the world's largest economies, such as the United States, Germany, China, and Japan. These regions exhibit high levels of industrialization, technological advancement, and trade activities. Their economies contribute significantly to global GDP and are major players in international commerce.

Technological Advancement:

Another commonality among these regions is their emphasis on technological advancement. They are known for their innovation, research and development, and technological infrastructure. Companies and industries in these regions are at the forefront of technological advancements in fields such as information technology, automotive manufacturing, aerospace, pharmaceuticals, and more.

Cultural Diversity:

North America, Europe, and East Asia are culturally diverse regions, with a rich tapestry of different ethnicities, languages, and traditions. Immigration and historical influences have contributed to the diversity seen in these regions. Each region has a unique blend of cultural practices, cuisines, art, music, and literature. This diversity creates vibrant multicultural societies and fosters an environment of cultural exchange and appreciation.

Democratic Governance:

A commonality shared among these regions is the prevalence of democratic governance systems. Many countries within these regions have democratic political systems, where citizens have the right to participate in the political process, elect representatives, and enjoy individual freedoms and rights. The principles of democracy, rule of law, and respect for human rights are important pillars in these regions.

Education and Research Excellence:

North America, Europe, and East Asia are known for their strong education systems and institutions of higher learning. These regions are home to prestigious universities, research centers, and educational initiatives that promote academic excellence. They attract students and scholars from around the world, offering a wide range of educational opportunities and contributing to advancements in various fields of study.

In conclusion, the regions of North America, Europe, and East Asia share several commonalities. These include economic development, technological advancement, cultural diversity, democratic governance, and education and research excellence. Despite their geographical and historical differences, these regions exhibit similar traits that contribute to their global significance and influence.

Answer:

For this assignment, three regions of the world have been selected to identify commonalities among them. The chosen regions are North America, Europe, and East Asia. Through internet research, several commonalities have been identified that are shared among these regions. Below are five commonalities found:

Economic Development:

All three regions, North America, Europe, and East Asia, are characterized by significant economic development. They are home to some of the world's largest economies, such as the United States, Germany, China, and Japan. These regions exhibit high levels of industrialization, technological advancement, and trade activities. Their economies contribute significantly to global GDP and are major players in international commerce.

Technological Advancement:

Another commonality among these regions is their emphasis on technological advancement. They are known for their innovation, research and development, and technological infrastructure. Companies and industries in these regions are at the forefront of technological advancements in fields such as information technology, automotive manufacturing, aerospace, pharmaceuticals, and more.

Cultural Diversity:

North America, Europe, and East Asia are culturally diverse regions, with a rich tapestry of different ethnicities, languages, and traditions. Immigration and historical influences have contributed to the diversity seen in these regions. Each region has a unique blend of cultural practices, cuisines, art, music, and literature. This diversity creates vibrant multicultural societies and fosters an environment of cultural exchange and appreciation.

Democratic Governance:

A commonality shared among these regions is the prevalence of democratic governance systems. Many countries within these regions have democratic political systems, where citizens have the right to participate in the political process, elect representatives, and enjoy individual freedoms and rights. The principles of democracy, rule of law, and respect for human rights are important pillars in these regions.

Education and Research Excellence:

North America, Europe, and East Asia are known for their strong education systems and institutions of higher learning. These regions are home to prestigious universities, research centers, and educational initiatives that promote academic excellence. They attract students and scholars from around the world, offering a wide range of educational opportunities and contributing to advancements in various fields of study.

In conclusion, the regions of North America, Europe, and East Asia share several commonalities. These include economic development, technological advancement, cultural diversity, democratic governance, and education and research excellence. Despite their geographical and historical differences, these regions exhibit similar traits that contribute to their global significance and influence.

In this scenario, the shape of the sampling distribution of X-bar is approximately normal.

The sampling distribution of the sample mean, X-bar, can be determined by the Central Limit Theorem. In this case, since the sample size is large (n = 64) and the underlying distribution (X) is approximately normal, the sampling distribution of X-bar will also be approximately normal. The Central Limit Theorem states that regardless of the shape of the population distribution, as the sample size increases, the sampling distribution of X-bar tends to become more and more normal. Therefore, in this scenario, the shape of the sampling distribution of X-bar is approximately normal.

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After doing the calculation we can conclude that the volume of the composite figure is 837 cubic inches.

The volume of a cube is defined as the total amount of cubic units that it fills. Volume can be defined as the whole area that an object takes up. The volume of such a cube can be calculated using the equation a3, where an appears to indicate the cube's edge.

The following formula can be used to get the rectangular prism's volume:

Volume = length x width x height

The dimensions in this instance are 10 inches long, 9 inches wide, and 9 inches high. Hence, the rectangular prism's volume is:

Volume of rectangular prism = 10 x 9 x 9 = 810 cubic inches

The volume of the pyramid that was cut from the prism can be calculated using the formula:

Volume equals (1/3) of base area times height.

Since the base of the pyramid is a square with sides of 9 inches, its base area is:

Base area of cut pyramid = 9 x 9 = 81 square inches

The height of the pyramid is 2 inches, so its volume is:

Volume of cut pyramid = (1/3) x 81 x 2 = 54 cubic inches

The volume of the pyramid that was added to the opposite base of the prism can also be calculated using the same formula:

Base area of added pyramid = 9 x 9 = 81 square inches

Volume of added pyramid = (1/3) x 81 x 3 = 81 cubic inches

To find the volume of the composite figure, we need to subtract the volume of the cut pyramid from the volume of the rectangular prism and then add the volume of the added pyramid:

Volume of composite figure = Volume of rectangular prism - Volume of cut pyramid + Volume of added pyramid

Volume of composite figure = 810 - 54 + 81 = 837 cubic inches

Therefore, the volume of the composite figure is 837 cubic inches.

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The required number of children and adults for sitting in the theater are 300 and 50 respectively.

A equation is supposed to be linear equation in two factors in the event that it is written as hatchet + by + c=0, where a, b and c are genuine numbers and the coefficients of x and y, i.e an a and b separately, are not equivalent to nothing. For instance, 10x+4y = 3 and - x+5y = 2 are straight equation in two factors.

Let be consider number of children be x and that of adults is y.

We have,

x + y = 350-------(1)

y = 350 - x

And 5x + 10y = 2000------------------(2)

Put value of y in equation (2)

5x + 10( 350 - x) = 2000

5x + 3500 - 10x = 2000

-5x = -1500

x = 300

Then

y = 350 - x = 350 - 300 = 50

Thus, There will be 300 children and 50 adults in the  theater .

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We know that function f(x) is given by

where the slope is the coefficient of the variable x, that is, the slope,m, is

Since g(x) is given by

we have that

where the slope is equal to 6, in other words

Therefore, the slope of the graph of g(x) is 6 times the slope of the graph of f(x).

Since the y-intercept of f(x) is zero, then the y-intercept of g(x) is zero too. Then, the answer is: the y-intercept does not change.

The correct answer is c. sequence diagram.

A sequence diagram is a type of UML (Unified Modeling Language) diagram that graphically documents a use case by showing the classes involved, the messages exchanged between these classes, and the timing of the messages.

This diagram illustrates the interactions between objects in a system in a particular order, hence the name "sequence diagram."Sequence diagrams are commonly used in software engineering to help developers understand and visualize the interactions between different components in a system.

They are particularly useful in designing and testing complex systems and in identifying potential issues with message timing or sequencing. Overall, sequence diagrams help to ensure that a system is designed and implemented correctly, and that all components work together as intended.

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Answer:

Step-by-step explanation:

Let x be the number

I hope this helps!

Answer:

13

Step-by-step explanation:

12 + 13 = 25

10+10=20

20+3+2=25

Answer:

22.4

Step-by-step explanation:

a^2 + b^2 c^2

20^2 + b^2 = 30^2

400 + b^2 = 900

b^2 = 500

b = 22.4

The simplification of the given fraction which is solved as a fraction would be =-13/12

A fraction is defined as the expression that represents the whole of a value in the form of a numerator and denominator.

The fraction given;

-8/24+ -18/24

The Lowest common denominator of the given fraction is 24

= -8-18/24

= -26/24

= -13/12

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The value at x = 1 of the local linearization L(x) of (1+x)^4 at x=0L(0.1) = 1 + 4(0.1) = 1.4.

Finding the equation of the tangent line to the (1+x)4 graph at x=0 is necessary before we can determine the value of the local linearization of (1+x)4 at x=1 at x=1.

The following is the formula for a function's local linearization at x=a:

L(x) = f'(a) Plus f(a) (x-a)

where f'(a) is f(x) derivative's calculated at x=a.

Accordingly, for (1+x)4, we have:

f(x) = (1+x)^4

f'(x) = 4(1+x)^3

a = 0

When we enter these numbers, we obtain:

f(0) = (1+0)^4 = 1

f'(0) = 4(1+0)^3 = 4

The expression for the tangent line to the (1+x)4 graph at x=0 is as follows:

L(x) = 1 + 4x

Simply substituting x=1 into the equation of the tangent line yields the number at x=1:

L(1) = 1 + 4(1) = 5

Therefore, the local linearization of (1+x)4 at x=0 therefore has a value of 5 at x=1.

We can enter x=0.1 into the equation of the tangent line to obtain L(0.1):

L(0.1) = 1 + 4(0.1) = 1.4.

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To find the amount of interest earned, we can subtract the initial investment from the final balance.

The initial investment is $230, and the final balance is $285.20. Therefore, the interest earned is:

Interest = Final balance - Initial investment

= $285.20 - $230

= $55.20

So, the interest earned on the investment is $55.20. This represents the additional amount gained on top of the initial investment over the period of eight years, considering a 3% interest rate.

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Answer:

  x - 4y = 0 . . . in standard form

  y = (1/4)x . . . in slope-intercept form

Step-by-step explanation:

The slope of the given line is ...

  m = (y2 -y1)/(x2 -x1) = (9 -(-7))/(-1 -3) = 16/-4 = -4

The slope of the perpendicular line is the negative reciprocal of this:

  desired slope = -1/m = -1/-4 = 1/4

This can be used in the point-slope form of the equation of a line:

  y -h = m(x -k) . . . . . line with slope m through point (h, k)

Your perpendicular line has a slope of 1/4 and goes through point (4, 1), so its equation can be written as ...

  y -1 = (1/4)(x -4)

  y = (1/4)x -1 +1

  y = (1/4)x

In standard form, this is ...

  4y = x

  x -4y = 0

Answer:

Therefore, the shaded portion of the figure represents 44% of the increase in area of the rectangle.

Step-by-step explanation:

The increase in area of the rectangle is represented by the shaded portion of the figure. The shaded portion is the difference between the area of the original rectangle and the area of the new rectangle. The area of the original rectangle is l * w, where l is the length of the rectangle and w is the width of the rectangle. The area of the new rectangle is (1.2l) * (1.2w) = 1.44 * l * w. The difference between these two areas is 0.44 * l * w, which is the shaded portion of the figure.

The percentage increase in area is calculated by dividing the increase in area by the original area and multiplying by 100%. In this case, the increase in area is 0.44 * l * w and the original area is l * w. The percentage increase in area is therefore 0.44 * 100% = 44%.

Therefore, the shaded portion of the figure represents 44% of the increase in area of the rectangle.

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Answer:

I got x=4 sorry if im wrong

Step-by-step explanation:

Answer:

The answer is x=4 because it is.

Step-by-step explanation:

x=4

The net pay amount for January would be $86,761.

Given the following information: Gross earnings in Vaughn Company were $114,000. All earnings are subject to 7.65% FICA taxes. Federal income tax withheld was $16,500, and state income tax withheld was $2,000.To calculate the net pay for January, first, we have to calculate the deductions:Gross earnings are:$114,000The FICA taxes for the earnings will be:7.65% of $114,000 = 0.0765 × $114,000 = $8,739State income tax withheld was $2,000Federal income tax withheld was $16,500Deductions are: 8,739 + 2,000 + 16,500 = $27,239The net pay amount for January would be:$114,000 - $27,239 = $86,761Answer: $86,761.

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