building is 120 meters tall. A scale model of the building uses a scale of 1 entimeter = 6 meters. How tall is the model?

The positive externality of carpooling with friends is reduced traffic on the road. Hence, option C is the correct option.

Carpooling is a very useful method of reducing traffic as well as pollution and is quite simple as well. It involves the usage of only one common vehicle that can be used by people who commute to the same destination. It's helpful since it means a lot of people will use only one vehicle and hence, there will be less traffic and pollution.

In the given problem as well, since these friends are gonna carpool to work, they will use the same vehicle and so, lead to less traffic. So, option C is the correct option.

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The 5x factored out will be 5x(4x+3)

What is the Greatest Common Factor?

The greatest common factor, which is the product of two or more numbers, is the largest number (GCF). A natural number is created by dividing them by the biggest number (factor). There are a few factors that both share once all the number's factors have been identified. The greatest common factor is the one with the largest number among the common factors. The highest common factor is another name for the GCF (HCF)

The factors of 20x2 (all the values that will divide into 20x2:  

1, 2, 4, 5, 10, 20, x, 2x, 4x, 5x, 10x, 20x, x2, 2x2, 4x2, 10x2, 20x2

The factors of 15x:

 1, 3, 5, 15, x, 3x, 5x, 15x

The greatest ("largest") one that is common ("in both lists"):

5x

So, with the 5x factored out:    5x(4x+3)

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The full question

Factor out the greatest common factor.

20x2 + 15x

Answer:

y = $24,500 * (1 + 0.03x)

Step-by-step explanation:

Please find the attachment for detail

Answer:

26771.8115

Step-by-step explanation:

24500(1.03)=25235 then continue doing this 2 more times and you get 26771.8115

The mass of  1 box of the weight of 20 boxes of apples is 84 kg.

Given that,

The weight of a single bag of apples = 350 grams.

No. of bags hold by one box = 12

The total weight of a single box is 12 x 350 grams = 4200 grams.

Now we multiply the weight of a single box (4200 g) by 20, which gives us 4200 g x 20 = 84,000 grams.

Since the final answer is asked in kilograms, we divide the weight in grams by 1000, which gives us 84,000 g ÷ 1000 = 84 kilograms.

Therefore, the total weight of 20 boxes of apples would be 84 kilograms.

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The function is defined by m(x)=f(x)/2g(x) is m′(5))=[tex]\sqrt[3]{3/2}[/tex] on graph.

A function is a relation that is "well-behaved," by which we mean that, given a starting point, we know the exact one ending spot to go to; given an x-value, we get only and precisely one corresponding y-value. As a result, even though all functions are relations [since they pair information], not all relations are functions. Family members who behave well are a subset of all your relations, just as well-behaved functions are a subset of all mathematical relations.)

f(x)=2x+3,XE[-1,2]

-2/3x+25/3, XE[2,8]

g(x)=√x^2−x+3 XE

m′(5))=[tex]\sqrt[3]{3/2}[/tex]

The thing to notice here is that f(x) is expressed differentially in different domain.

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The answer to these questions is "7," but before we get there, let's define the instantaneous rate and its further computation.

A rate at a specific time is called an immediate rate.The negative ball of the reactant concentration curve with respect to time t is calculated by calculating the pitch of the product amounting with respect to time t.

Given:

at X = 3

y = 21 according to the graph.

In light of this, given that X = 3 and the instantaneous rate of changes,

that is half.

Consequently, y/x = 21/3 = 7 is the instantaneous rate of change.

The final response is "7," as a result.

The answer to these questions is "7," but before we get there, let's define the instantaneous rate and its further computation.

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there are 31680 yards in 18 miles

Answer:

31680

Step-by-step explanation:

After considering all his earnings and savings, we found that Chris started with $120 in his savings.

Let's assume that Chris saved x dollars. According to the equation, he spent half of his savings, so he spent 0.5 * x dollars on video games. After earning an additional $20 cutting grass, his total savings became 0.5 * x + 20 = 60. To solve for x, we can subtract 20 from both sides of the equation, which gives us 0.5 * x = 40.

Then, we can divide both sides of the equation by 0.5 to obtain x = 80. This means that Chris started with $80 in savings, which he then doubled by spending half of his savings and adding $20 earned from cutting grass, resulting in $120 in total savings.

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lim (x → a) f(x) = ∞ , The limit does not exist and is neither ∞ nor - ∞

The vertical line test is used to verify function. That is, a graph must have a unique y value for it to be referred to as a function for a certain (unique) value of x. If for a particular x, and y values are coming it means it is not a function. If it crosses y-axis twice it means for a particular x value , two different value of y will exist. And that is not possible for a function

From the graph, we know that limit at point a is:

lim (x→a) f(x) exists if and only if

lim (x →a⁺) f(x) = lim (x→a⁻) f(x) and ≠ ∞

∴ right hand side limit = left hand side limit

lim (x →a⁺) f(x) = - ∞

lim (x →a⁻) f(x) = - ∞

∴ lim (x → a) f(x) = ∞

thus, option B is the correct answer.

The limit does not exist and is neither ∞ nor - ∞

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39.52 cm² of the surface area of the box​ increase.

Given data :

H = 31 cm

the surface area of the box​ increase ;

= 2( 31 x 8.7 + 31 x 16 + 16 x 8.7) + 2 ( 31.8 x 8.7 + 31.8 x 16 + 16 x 8.7 )

= 2 ( 8.7 + 16 ) x ( 31.8 - 31 )

= 2 x 24.7 x 0.8

= 39.52 cm²

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The pair of slopes of -3/4 and 4/3 represent perpendicular lines

An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.

The standard form of a linear equation is:

Ax + By = C

Where A, B and C are constants

The slope intercept form of a linear equation is:

y = mx + b

Where m is the slope and b is the y intercept

The slope of the line passing through points (x₁, y₁) and (x₂, y₂) is:

m = (y₂ - y₁) / (x₂ - x₁)

Two lines are said to be perpendicular if the product of their slope is -1.

Given two lines with slope of -3/4 and 4/3:

Product of their slope = (-3/4) * (4/3) = -1

The lines with slope of -3/4 and 4/3 is perpendicular

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The volume of the cylindrical shell will be 20 cubic unit using integration.

Integration is the process of calculating an integral. Integrals are used by mathematicians to compute a range of useful quantities, such as areas, volumes, displacement, etc. Usually, when we talk about integrals, we mean definite integrals. Indefinite integrals are used for antiderivatives. Integration is one of the two primary calculus topics in mathematics, along with differentiation (which measure the rate of change of any function with respect to its variables).

An integral that has both the upper and lower boundaries is said to be definite. Only a real line may be used for X to lay. A Riemann Integral is another name for the Definite Integral.

n example of an Integral is:

f(x)dx, from a to b.

Indefinite integral

∫f(x)dx = F(x) + C

Where C is any constant and the function f(x) is called the integrand.

Now,

As we can see in image

Volume = ∫x³.dx from 1 to 3  Using integration formula

=x⁴/4

=81/4-1/4

=80/4

volume =20 cubic unit

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The value of v in the variation is 21.1

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

Joint variation from p to s and v^2

So, we have

p = ksv^2

Substitute the known values in the above equation, so, we have the following representation

18 = k * 9 * 15^2

So, we have

k = 2/225

When s = 81 and p = 32, we have

32 = 2/225 * 81 * v^2

This gives

v^2 = 72000/162

So, we have

v = 21.1

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The more appropriate measures of center and spread or the data set would be:

The median and interquartile range (IQR) should be used when analyzing data that has a non-normal distribution. They are particularly useful when working with data sets that contain outliers or skewness.

The median provides an indication of the central tendency of the data, representing the value that separates the data into two equal parts, with half the data being below and half the data being above that value. The IQR, on the other hand, provides information about the spread of the data and can be used to identify outliers.

The data here has the extreme figure of 24 which is an outlier and so not compatible with the mean. The median is therefore better. The interquartile range would be better for spread due to the outlier as well.

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The 4 in 64.723 has a value that is 10 times greater than the value of the 4 in 9.048.

The values of the 4 in 64.723 and 9.048 are not directly comparable because they represent different places in the number and have different values as a result.

In 64.723, the 4 is the hundredths place, which means it represents 0.04. In this case, the value of the 4 is 0.04.

In 9.048, the 4 is the thousandths place, which means it represents 0.004. In this case, the value of the 4 is 0.004.

To compare the two values of 4, we can divide the value in 64.723 by the value in 9.048:

0.04 / 0.004 = 10

So the value of the 4 in 64.723 is 10 times the value of the 4 in 9.048. This means that the 4 in 64.723 has a value that is 10 times greater than the value of the 4 in 9.048.

Therefore, the 4 in 64.723 has a value that is 10 times greater than the value of the 4 in 9.048.

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The 4 in 64.723 has a value that is 10 times greater than the value of the 4 in 9.048.

The values of the 4 in 64.723 and 9.048 are not directly comparable because they represent different places in the number and have different values as a result.

In 64.723, the 4 is the hundredth place, which means it represents 0.04. In this case, the value of the 4 is 0.04.

In 9.048, the 4 is the thousandths place, which means it represents 0.004. In this case, the value of the 4 is 0.004.

To compare the two values of 4, we can divide the value in 64.723 by the value in 9.048:

0.04 / 0.004 = 10

So the value of the 4 in 64.723 is 10 times the value of the 4 in 9.048. This means that the 4 in 64.723 has a value that is 10 times greater than the value of the 4 in 9.048.

Therefore, the 4 in 64.723 has a value that is 10 times greater than the value of the 4 in 9.048.

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Answer:

x = 63° , y = 83°

Step-by-step explanation:

In a trapezium

each lower base angle is supplementary to the upper base angle on the same side , then

x + 117° = 180° ( subtract 117° from both sides )

x = 63°

the sum of the 3 angles in the outer triangle = 180° , that is

x + y + 34° = 180° ( substitute x = 63° )

63° + y + 34° = 180°

97° + y = 180° ( subtract 97° from both sides )

y = 83°

The missing value of the first coordinate x is 9.

Slope is simply expressed as change in y over the change in x.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Given the data in the question;

Point A (x,8)

Point B (4,-7)

Slope m = 3

Plug the given coordinates into the slope formula and and solve for x.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

3 = ( -7 - 8 )/( 4 - x )

Cross multiply

3( 4 - x ) = ( -7 - 8 )

12 - 3x = -7 - 8

12 - 3x = -15

-3x = -15 - 12

-3x = -27

x = -27 / -3

x = 9

Therefore, the value of x is 9.

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The directions used to translate the original triangle to a new triangle are translation to the right on the x-axis by 2 units and then it is down on the y-axis by 3 units.

The transformation, or f: X X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one way or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point.

The directions used to translate the original triangle to a new triangle are:

First the graph is translated to the right on the x-axis by 2 units and then it is translated down on the y-axis by 3 units.

The new coordinates of the triangle are:

A' = (-1, -2)

B' = (-2, 0)

C' = (0, 0)

Hence, the directions used to translate the original triangle to a new triangle are translation to the right on the x-axis by 2 units and then it is down on the y-axis by 3 units.

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The required simplified solution of the given expression is 2x⁶.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
= -2x³(-x³)

Since we know that, -a × - a = a²,
= 2x³⁺³
= 2x⁶

Thus, the required simplified solution of the given expression is 2x⁶.

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The type of correlation is determined by the relationship between variables in terms of the proportion of change between them that is multiple proportion.

A proportion is the relationship between two quantities, often expressed as a ratio or fraction.

"Simple correlation" refers to the relationship between two variables, where a change in one variable is associated with a change in the other variable in a consistent manner.

"Multiple correlation" refers to the relationship between three or more variables. In this type of correlation, the proportion of change in one variable is associated with the proportion of change in other variables.

"Zero correlation" refers to the absence of any relationship between two variables. In this type of correlation, there is no consistent proportion of change in one variable that is associated with a change in the other variable.

Therefore correct option is (b).

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So Condition 1 has reduced the possibilities for existing Enet = 0 positions to Region (I) (to the left of both charges) and Region (III) to the right of both charges.

The X-axis is sometimes known as the horizontal axis, and the Y-axis is the vertical axis.

There are a few main approaches to this issue. I'll explain it in terms of electric fields. This is due to the defining equation's ability to link the electrostatic force's expression, FE, to a region's net electric field, E:

FE = qE

where q is a charge that has been added to the electric field; in this case, it is a charge of 1 C. The only way FE can equal zero at some place when q is not zero (and q=0 would be a simple case, anyway) is if the net electric field E is zero at that location.

This is true regardless of the size and nature of the charge you were putting there.

Therefore, given this scenario, where can the net electric field E = 0? At every point in space surrounding the charge, each charge generates its own electric field, which either points in the direction of the charge (for negative charges) or away from the charge (for positive charges). The following equation determines the size of the electric field, |E|, produced by a point charge at a distance r from the charge:

|E| = kq/r2

At every point in space surrounding the two charges stated in the issue, an electric field is produced by one of them. The vector sum of the field from each charge present at a given point is the net electric field at that location. There are two requirements for the two fields to cancel each other out:

1. Each charge's electric fields must be directed in opposite directions.

2. Each charge's electric fields must be of equal strength.

We can examine the two situations independently. Since the first one (regarding directions) may frequently weed out a lot of potential responses through scrutiny, I frequently start there.

For instance, if you were to create a diagram with the two charges as indicated on the x-axis and then choose any location off of the x-axis, it would be clear that this position does not satisfy Condition 1. This is so that the (+)10 C charge's electric field will point away from the 10 C charge from that location. And from there, the -5 C charge's electric field will point in its direction. These two electric field vectors won't even coincide for any position off the x-axis. Since they cannot point in the same direction, even if their magnitudes are equal, they cannot cancel out. Thus, the third response from above is disproved.

Therefore, let's examine the x-axis. The electric fields for points on this line point in the same direction, so they could potentially point in different directions. But how is that even possible? We can divide a line with two charges into three regions: (I) to the left of both charges, (II) in the space in between the charges, and (III) to the right of both charges.

Therefore, So Condition 1 has narrowed the range of potential locations where Enet = 0 is present to Region (I) (to the left of both charges) and Region (III) (to the right of both charges).

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The median lies outside the span of the box is always false.

Boxplots are particularly helpful for immediately determining a collection of data's location, dispersion, symmetry, or skewness as well as for comparing these characteristics between two or more data sets. Building a boxplot is straightforward.

A box and whisker plot, often known as a box plot, shows a data set's five-number summary. The minimum, first quartile, median, third quartile, and maximum make up the five-number summary.

In a box plot, we draw a box from the first quartile to the third quartile. A vertical line goes through the box at the median. The whiskers go from each quartile to the minimum or maximum.

Thus, The median lies outside the span of the box is always false.

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According to the given information, the mystery polygon is most likely a right trapezoid.

Li's mystery polygon has 4 sides and no pairs of parallel sides, which means it is a quadrilateral. Based on the angles given, 90 degrees, 63 degrees, 120 degrees, and 87 degrees, the mystery polygon is a trapezoid. A trapezoid is a quadrilateral with exactly one pair of parallel sides and no two angles that add up to 180 degrees.

A trapezoid with two right angles (90 degrees) is called a right trapezoid. Since Li's mystery polygon has one angle that measures 90 degrees, it is likely a right trapezoid. The other angles, 63 degrees, 120 degrees, and 87 degrees, do not match the angles of any other specific type of quadrilateral. Therefore, based on the information given, the mystery polygon is most likely a right trapezoid.

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350° and 350° - 360° are coterminal angles with magnitudes less than 2π.

What is coterminal?

In mathematics, two angles are called coterminal if they have the same magnitude (measure) but different orientations. This means that they represent the same angle but start from different points on the unit circle.

An angle is coterminal with another angle if it has the same magnitude but a different orientation. To find a positive angle less than 2π that is coterminal with a given angle, you can add or subtract multiples of 2π until you get an angle in the desired range.

For example, if the given angle is 350 degrees, you can subtract 2π from it to get a positive angle less than 2π:

350° - 360° = -10° + 360° = 350°

So, 350° and 350° - 360° are coterminal angles with magnitudes less than 2π.

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The amount of the commission earned by Zachary on the $635 sale is $196.85.

A commission is a percentage of a sale earned by a sales person.

Given that;

Since commission is a percentage of a sale earned

Commission amount = sale price × commission

Plug in the given values and simplify

Commission amount = $635 × 31%

Note that; 31% is the same as 31/100

Commission amount = $635 × 31/100

Commission amount = $635 × 0.31

Multiply $635 and 0.31

Commission amount = $196.85

Therefore, the amount of commission is $196.85.

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The area in a square meter is 5$. We can equate the two expressions for the length of the edge of the square and solve for x:

$4x - 15 = 20 - 3x$

$7x = 35$

$x = 5$

The length of one edge of the square is 5 meters, so the area of the square is $5^2 = 25$ square meters. Therefore 5$ is the solution for the $4x-15$ and  20 - 3x$ equation. 15 and 3 will exchange their places to form 7$ and 35$ and 5$ is the end result of the problem that is given.

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Answer:

55x+20

Step-by-step explanation:

Answer:

Simplification 5(11x+4)

Step-by-step explanation:

42x-23+13x+43

42x +20 + 13x

Combine like terms

42x+20+13x

55x+20

Common factor

55x+20

5(11x+4)

The equation of the parabola is give as;

f (x) = x² − 2x − 8

Let y =  x² − 2x − 8

Complete the square on right sides of the equation.

y = (x - 1)² + 9

Comparing with the standard equation of the parabola.

y = a(x - h)² + k

Thus, vertex of the parabola are found as:

(h, k) = (1, - 9)

Since 'a' has a positive value, the parabola opens upwards.

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