what is the coefficient of the x^4 y^3 term in the expansion of (x-2y)^7?

The length and width of the rectangle are 16 cm and 90 cm respectively

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P = 2 ( Length + Width )

Given data ,

Let the perimeter of the rectangle be P = 212 cm

Now , the equation will be

The length of the rectangle be = L

And , length is an even integer and the width is 5 times the next consecutive even integer

So , the width of the rectangle W = 5 ( L + 2 )

Substituting the values in the equation , we get

Perimeter of rectangle P = 2 ( Length + Width )

212 = 2 ( L + 5 ( L + 2 ) )

On simplifying the equation , we get

106 = L + 5L + 10

6L = 96

Divide by 6 on both sides of the equation , we get

L = 16 cm

So , W = 5 ( L + 2 )

W = 5 x 18

W = 90 cm

Hence , the length and width of rectangle is 16 and 90 respectively

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Answer: a. In this situation, 0 likely represents sea level or the baseline from which water levels are measured.

b. To find the average water level relative to high tide, you need to take the average of high tide and low tide.

Since high tide is 5 feet higher than low tide, you can assume that low tide is 0 ft. Therefore, the high tide is 5 ft.

The average of two values is the sum of the values divided by the number of values. So average of 0ft and 5ft is (0+5)ft / 2 = 2.5 ft.

Therefore, an integer that represents the average water level relative to high tide would be 2.5 ft.

It's worth noting that relative to high tide means how much the average water level varies (higher or lower) from the high tide, so the answer was not an integer in this case.

The right angle, 99, 171, and 159 are four of the angles. It follows that the x and y angles, which are also equal, must both equal 201/2.

A place where two lines converge creates an angle. They are quantified in degrees and are denoted by the symbol °. Four essential types are reflex, acute, right, and obtuse angles. A circle has 360 degrees. One terminal exists when two rays (half-lines) are merged form an angle. The rays are referred to as the angle's sides, occasionally as its legs, and occasionally as its arms, while the latter is referred to as the angle's vertex. The place where all points of an angle converge is known as the vertex.

given

A polygon's internal angle measurements are equal to (n-2) * 180, where n is the number of sides.

Therefore, 4 * 180 = 720 is the total of the internal angles of this 6-sided object.

The remaining two equal angles are 720 - 90 - 99 - 171 - 159 = 201 .

The right angle, 99, 171, and 159 are four of the angles. It follows that the x and y angles, which are also equal, must both equal 201/2.

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The angles are congruent and the ratios of sides are equal, then the polygons are similar.

What is the similarity of polygons?

The similarity of polygons refers to the relationship between two or more polygons in which the corresponding angles are congruent (equal in measure) and the corresponding side lengths are in proportion.

We have,

Polygon 1:

Opposite Sides 24 = 24, 12=12,

Angles = 90°

Polygon 1:

Opposite Sides 16 = 16, 8=8,

Angles = 90°

This means that if two polygons are similar, their corresponding angles will have the same measure, and their corresponding side lengths will be in the same ratio. In other words, the ratio of any pair of corresponding sides of similar polygons will be the same.

For example, two triangles are similar if the ratio of their corresponding sides is the same, and their corresponding angles are equal. Similarly, two quadrilaterals are similar if the ratio of their corresponding sides is the same and their corresponding angles are equal.

It's important to note that similarity is a stronger relationship than congruence, because in congruence all the sides and angles must have the same measure, while in similarity only the angles and ratios of sides are the same.

Additionally, the similarity of a polygon can be determined by measuring the angles of the polygon, and comparing the ratios of the corresponding sides.

If the angles are congruent and the ratios are equal, then the polygons are similar.

Hence, the angles are congruent and the ratios of sides are equal, then the polygons are similar.

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Answer:rotational

Step-by-step explanation:

it would not be a line because a line is a line and other make no sense

A digital clock will show that the number of the hour is less than the number of the minute for 12 different displays, starting at 10:00 AM and ending at 4:00 PM.

These displays are:

10:01 AM, 10:12 AM, 10:23 AM, 10:34 AM, 10:45 AM, 11:02 AM, 11:13 AM, 11:24 AM, 11:35 AM, 12:03 PM, 12:14 PM, and 12:25 PM.

For example, 10:01 AM and 11:23 AM.

From 10:00 AM to 12:59 PM, the hour will always be a single digit, so we can check the minutes to see if they are double digit.

From 10:00 AM to 10:59 AM, the minute has to be greater than the hour. So, we can pick the minutes starting from 01 to 59 and check whether the hour is less than the minute which gives us 12 such displays

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As per the following diagram, the angle measures of triangle EFC is 118°

The term angle in math is known as a figure which is formed by two rays or lines that shares a common endpoint.

Here we have given that an artist uses colored tape to divide sections of a mural and she needs to cut a piece of paper to cover triangle EFC while she works on other sections.

According to the diagram, here we know that the value of

=> DE = EF

And the value of

=> EB = FB

Here we know that the value of the angles,

=> ∠EDB = ∠EFB = 90°

Thus implies that the angles,

=> ∠DFB = ∠FEB = 31°

Then the value of the angle is calculated as,

=> ∠EDB =∠EFB = 90° - 31°

=> ∠EDB = ∠EFB = 59°

Then the value of the angle ABC is calculated by sum the values of the angles, then we get,

=> ∠ABC = ∠EDB + ∠EFB = 59 + 59 = 118°

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The equation of the polynomial function is (a)  h(x) = x^3 - 2x^2 - 5x - 6

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

x –2 0 1 2 3

h(x) 0 –12 0 8 0

The x-intercepts are where y = 0

So, we have

x = -2, x = 1 and x = 3

The multiplicity is 1

So, we have

h(x) = (x + 2)(x - 1)(x - 3)

Expand

= (x + 2)(x^2 - 4x + 3)

This gives

= x(x^2 - 4x + 3) + 2(x^2 - 4x + 3)

So, we have

= x^3 - 4x^2 + 3x + 2x^2 - 8x + 6

Evaluate the like terms

= x^3 - 2x^2 - 5x - 6

So the equation is h(x) = x^3 - 2x^2 - 5x - 6

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The option that describes the center and variability of simulation A and simulation B is The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B. The correct answer is C.

Considering the details provided in the query,

The two simulations will be run with sampling proportions from a population with a true percentage of 0.325.

Simulacrum A:

100 samples were used.

Tests: 1500

Exercise B -

50 samples total.

2000 trials

Due to the relationship between simulations A and B, they are now nearly equal.

1500 x 100 is the overall sample size for Simulation A.

= 150000

The simulation B sample size is 2000 x 50.

= 100000

We can observe from the simulations A and B calculations above that when comparing the,

Sample Size = Comparison of Simulations A and B

Simulation B + Simulation = Variability

Your question is incomplete but most probably your full question was

In a recent survey, the proportion of adults who indicated mystery as their favorite type of book was 0.325. Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325. Simulation A will consist of 1,500 trials with a sample size of 100. Simulation B will consist of 2,000 trials with a sample size of 50. Which of the following describes the center and variability of simulation A and simulation B?

A) The centers will roughly be equal, and the variabilities will roughly be equal.

B) The centers will roughly be equal, and the variability of simulation A will be greater than the variability of simulation B.

C) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B.

D) The center of simulation A will be greater than the center of simulation B, and the variability of simulation A will roughly be equal to the variability of simulation B.

E) The center of simulation A will be less than the center of simulation B, and the variability of simulation A will be greater than the variability of simulation B.

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The date Mr. Remy Osta will resume duty after his 50 days leave which lasted from February 10, 2008 is March 31, 2008

A leap year is a year which has 366 days, that is, the days in February are 29 days.

So,

From February 10, 2008

The days remaining in February is 19 more days

The days of march is 31 days

Hence,

19 days + 31 days

= 50 days

Therefore, Mr. Remy Osta will resume duty on March 31, 2008

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The first and second expressions are equal. The second expression is not synonymous. The third expression is interchangeable. The fourth expression is incorrect.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign. Example of a word: the sum of 8 and 3. Example of a word: The product of 8 and 3 equals 11. 8 + 3 is an expression.

Here,

According to image,

First expression is equivalent. Second expression is not equivalent. Third expression is equivalent. Forth expression is not equivalent.

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3/4 divided by 2 in the fraction is equal to 3/8.

A fraction is used to represent the portion of the whole quantity. Also, we know that every integer is a rational number and any whole number can be written in the form of n/1, where n is any whole number.

On the given data, we need to use the concept of the division of fractions.

3/4 ÷ 2

=3/4 × 1/2 [ Reciprocal of 2 is 1/2]

=3/8

Therefore, 3/4 divided by 2 in the fraction is equal to 3/8.

Once you have your final fraction, just divide the numerator by the denominator to get your answer in decimal form: 3/8=0.375

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Answer:

9/4

Step-by-step explanation:

Use the process of elimination. Divide each number's numerator by its denominator; if the outcome repeats itself, it isn't a terminating decimal. Therefore, when you divide 9/4, it equals 2.25, which is a terminating decimal.

For the given equation of the line 2x + 3y = 6 , the slope = -2 /3,

the x-intercept = 3 and the y-intercept = 2.

As given in the question,

Given equation of the line is :

2x + 3y = 6

Standard equation of the line with slope 'm' and y -intercept = c

y = mx + c

Convert the given equation into standard form we get,

2x + 3y = 6

⇒ y = (-2/3)x + 6/3

⇒y = (-2/3)x + 2

Slope of the line = -2/3

y - intercept when x = 0

y = 2

x - intercept when y = 0

x = 3

Therefore, for the given equation of the line the slope , x- intercept ,and y-intercept is equal to (-2/3) , 3 , and 2 respectively.

The above question is incomplete, the complete question is:

Determine the slope, x-intercept and y-intercept of the line given by the equation 2x + 3y = 6?

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Solutions can be divided into supersaturated, unsaturated, and saturated solutions based on how well the solute dissolves in the solvent.

A homogeneous mixture with the major ingredients solute and solvent is referred to as a solution.

Solutions can be divided into supersaturated, unsaturated, and saturated solutions based on how well the solute dissolves in the solvent.

Supersaturated solution: The excess solute will crystallize quickly in a supersaturated solution because it contains a lot of solute at a temperature where it will be decreased.

Unsaturated solution: When a solvent can dissolve any more solute at a specific temperature, the solution is said to be unsaturated.

Saturated solution: A saturated solution is one in which a solvent can no longer dissolve any more solute at a particular temperature.

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Answer:

Infinitely many solutions.

Step-by-step explanation:

y=5x+2

2y-4=10x

----------------

2(5x+2)-4=10x

10x+4-4=10x

10x=10x

Step-by-step explanation:

1.y = x * (1-0.4)

2.y = x - 0.4x

3.x = y / (1-0.4)

4.x = y + 0.4y

The equation 1 and 2 correctly represent the situation. In the first equation, we are multiplying the initial amount of water (x) with (1-0.4) which is the percentage of the water that is remaining after drinking 40% of it. In the second equation, we are subtracting 0.4x from x, which is equivalent to multiplying x by (1-0.4).

The equation 3 and 4 are not correct, as they are trying to calculate the initial amount of water from the remaining amount, but it's not possible to know the initial amount once it has been consumed.

You have 0.6X amount water remaining.

The amount of water remaining in the water bottle is X minus 40%. This means that if you had X amount of water at start you now have 60% of X left.  That is, you have 0.6X amount of water remaining.

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Answer:

I don't care for the points

Step-by-step explanation:

The answer is the last one

A 3:2 image ratio refers to the proportion of the width to the height of an image or screen. It means that for every 3 units of width, there are 2 units of height.

The aspect ratio 3:2 is commonly used in digital photography, particularly for DSLR cameras and some mirrorless cameras.

In photography, the 3:2 aspect ratio is considered a standard format, it's the same as the traditional 35mm film frame, it's also the same as the aspect ratio of most modern digital cameras. It allows photographers to capture a wide range of scenes and subjects, and it's also a good option for cropping and printing photos.

For example, if an image's resolution is 3000x2000 pixels, it means that it has a 3:2 aspect ratio. The width of the image is 3000 pixels and the height is 2000 pixels, so 3000/2000 = 3/2

It's worth noting that the aspect ratio of 3:2 is a compromise between the wider aspect ratio of 16:9, used for video and some photography, and the taller aspect ratio of 4:3, used for more traditional photography.

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Answer: $20.95

Due to credit rating being fair:

Secured APR = 7.00%

Loan amount = sale price + tax - down payment

New car  =  [tex]19027 + (19072 x 0.045) - 1200 = 18730.24[/tex]

Used car = [tex]15635 + (15635 x 0.045) - 1200 = 15138.575[/tex]

---------------------------------------------------------------------------

Monthly interest = loan amount [tex]x 0.07 x 1/12[/tex]

New car = [tex]18730.24 x 0.07 x 1/12 = 109.26[/tex]

Used car = [tex]15138.575 x 0.07 x 1/12 = 88.31[/tex]

Thus, the difference is [tex]109.26 - 88.31 = $20.95[/tex]

The area of the triangle is 54 square centimetres, which is calculated by multiplying the base (12 cm) and height (9 cm) and dividing by 2.

A = (12 cm * 9 cm) / 2

A = (108 cm²) / 2

A = 54 cm²

The area of a triangle is calculated by multiplying the base of the triangle and its height, and then dividing the result by 2. To calculate the area of the triangle with a base of 12 cm and a height of 9 cm, first the base and height must be multiplied together. 12 cm multiplied by 9 cm equals 108 cm². Then, the result of the multiplication, 108 cm², must be divided by 2. 108 cm² divided by 2 equals 54 cm². Therefore, the area of the triangle is 54 cm². To summarize, the area of a triangle is found by multiplying the base and height of the triangle, and then dividing the result by 2. In this case, the area of the triangle with a base of 12 cm and a height of 9 cm is 54 cm².

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Answer:

Here are two data points that can be used to represent this relationship:

(x1, y1) = (8, $320) - this data point represents that when Susan works 8 hours, she gets paid $320.

(x2, y2) = (12, $440) - this data point represents that when Susan works 12 hours, she gets paid $440.

Step-by-step explanation:

In this situation, the independent variable is the number of hours that Susan works, and the dependent variable is the amount of money that she gets paid.

Here are two data points that can be used to represent this relationship:

(x1, y1) = (8, $320) - this data point represents that when Susan works 8 hours, she gets paid $320.

(x2, y2) = (12, $440) - this data point represents that when Susan works 12 hours, she gets paid $440.

We can use these two data points to represent the relationship between the number of hours that Susan works and the amount of money that she gets paid. It shows that, As her work hours increase, her pay increases as well.

Answer:

the answer is 45°

Step-by-step explanation:

because they mirror eachother

Answer:

Step-by-step explanation:

I'm not sure but I think that is 45

There are 0.16 gallon is used to paint each chair.

What is gallon?

A unit of volume for measuring liquids. 1 gallon = 4 quarts = 8 pints = 16 cups = 128 fluid ounces. 1 US gallon = 231 cubic inches = 3.785411784 liters.

as given, Four gallon of paint are used to paint 25 chair.

i.e. 4 gallon ⇒ 25 chairs

and If each chair used the same amount of paint then how many gallon are used to paint each?

i.e. how many gallons ? ⇒ 1 chair

∴ 4 gallon ⇒ 25 chairs

∴ 25 chairs ⇒ 4 gallon

∴ 1 chairs ⇒ 4 / 25 gallon

∴ 1 chairs ⇒ 0.16 gallon

Therefore, there are 0.16 gallon is used to paint each chair.

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A system of equations consisting of a linear equation and a quadratic equation has infinitely many solutions is not true.

Linear equations are equations that graph as a line, while the quadratic equations are that graph as a parabola. Lines and parabolas in the xy-plane are convenient representations of linear and quadratic systems, respectively. One solution to the system is shown by each point where the line and parabola intersect. It is possible for a line and a parabola to intersect zero, one, or two times. This indicates that a linear and quadratic system may have zero, one, or two solutions.

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Equation  that represents Chris's total income I = ($5.75+$17.5)h , where X is the number of hours he works in a day.

Equation is a mathematical statement that expresses the equality between two or more expressions.

Equation are different types such as equation with one variables and equation with two variables. The equation is used to determine the unknown values.

Chris salary  $5.75 per hour.

During his work time he serves two groups.

The average tip per group = $8.75

Tips earned from two groups = $8.75 × 2 = $17.5

Then Chris total income in one hour = $5.75 + $8.75

Let Chris works h hours

Chris total income if he works total h hours in a day

I = ($5.75+$17.5) h

Hence, I = ($5.75+$17.5) h is the equation that determines Chris total income.

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The correct measure of center to determine which shop typically sells the most amount of coffee per hour will be C. Coffee Ground, with a mean value of about 5 gallons.

The mean is calculated by adding all the data points together and dividing by the number of data points.

When comparing the mean values of the two shops, Coffee Ground has a higher value of 5 gallons compared to Wide Awake's mean value of about 4.5 gallons. This indicates that Coffee Ground typically sells more coffee per hour on average.

The correct option is C.

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The total playground area is 280 square meter, if the dome cover an area of 1+2/3 = 5/3 square meter.

The area covered by the dome = 5/3 square meter

The area covered by the dome is 5/840 times of the total playground area.

Let the total area of the playground = A

5/3 = 5/840 × A

A = (5 × 840)/(3 × 5)

A = 280 square meter

--The given question is incomplete, the complete question is " Ben like to go in the covered dome, when he feels overexcited. The dome covers an area of 5/3 square meter, which is 5/840 of the total playground area. What is the total playground's area?"--

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If the rate of the change in the input to the change in the output is the same for every point in the table, then the table represents a linear function.

If a table of values shows a constant rate of change, it is linear.

A non-vertical graph that is a straight line is linear. An equation that can be written in the form y=mx+b is linear. If a table of values shows a constant rate of change, it is linear.

Linear relationships can be modeled using the slope-intercept form y=mx+b, As x increases, y increases by a proportional amount.

A linear function is a linear relationship that obeys the rules of a function and has a graph that forms a straight line. Function notation is used to express a linear relationship when there are clearly defined inputs and outputs.

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The inverse function of f(x) = (x - 5)/3 is f^-1(x) = 3x + 5.

Solution:

To find the inverse of a function, we need to switch the x and y variables, and then solve for y.

Starting with f(x) = (x - 5)/3, we can switch the x and y variables to get y = (x - 5)/3.

We can then solve for x by multiplying both sides by 3, giving us 3y = x - 5.

We can then add 5 to both sides to get 3y + 5 = x, which is the inverse of our original function.

Therefore, the inverse of f(x) = (x - 5)/3 is f^-1(x) = 3x + 5.

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