The average distance between the Sun and Neptune is 4450 x 100 km. Express this distance in AU
with two significant figures.

The coordinate points on the first quadrant represent the possible dimensions of the rectangle with an area of 32 m².

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

Given are two figures as shown in the image attached.

{ 1 } -

The image in question {12} cannot be proved congruent by AAS congruence rule.

{ 2 } -

For the triangles shown in question {13}, we can prove the triangles congruent by AAS rule as -

90° = 90°    { Equal right angles }

Sides opposites to right angles are equal. So, the angles opposite to these angles {let x° and  y°} will be equal. We can write -

x° = y°

Two equal sides given

Hence, triangles are proved AAS congruent rule.

Therefore, the triangles along with their respective congruency proofs are given above.

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Answer:

height = 12

Step-by-step explanation:

The formula for the area of a triangle is: [tex]\frac{1}{2}(b*h)[/tex] = A

A = area of a triangle

b = base

h = height

The problem states that the area (A) of triangle is 48, and the base (b) is 8, so we can plug those values into the equation above:

48 = [tex]\frac{1}{2}(8*h)[/tex]

Let's solve for h now:

48 = [tex]\frac{1}{2}8h[/tex]

48 = 4h

h = 48/4

h = 12

Answer:

12 inches

Step-by-step explanation:

Formulae (Area of a triangle): 1/2 × Measure of Base × Measure of Height

Given Information:

Substitute the information into the formula to create an equation;

Solve the equation to find out the measure of the height;

Therefore, the measure of the height is 12 inches.

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The linear system l has one solution. This can be determined by examining the augmented matrix to find the row echelon form. The row echelon form is a matrix with zeroes below the leading entries and all the leading entries are in different columns.

By converting the augmented matrix into the row echelon form, we can identify the number of variables and the number of equations. Since there are three equations and three variables in the row echelon form, the linear system l has one solution. The row echelon form of the given augmented matrix is

[tex]$\begin{bmatrix}1&-3&2&3\\0&-5&-9&-10\\0&0&4&5\end{bmatrix}$[/tex]

By counting the number of equations and variables in the row echelon form, it can be seen that there is only one solution for the linear system l. This is because the number of equations is equal to the number of variables, indicating that there is a single solution.

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the linear system l has an augmented matrix which is a row equivalent to the following. how many solutions does l have?

 [tex]$\begin{bmatrix}1&-3&2&3\\-3&8&-11&-14\\2&-7&5&7\end{bmatrix}$[/tex]

Answer:

Step-by-step explanation:

(0, 7) and (-1, 6)

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only C) The diagonals bisect each other, and E) The diagonals are perpendicular are the two conditions that prove that a quadrilateral is a rectangle.

What is the quadrilateral?

A quadrilateral is a four-sided polygon, which means it has four straight edges and four angles. Quadrilaterals can come in many different shapes and sizes and can be classified based on their properties. Some common examples of quadrilaterals include squares, rectangles, parallelograms, rhombi, and trapezoids.

A quadrilateral is a rectangle if it satisfies the following conditions:

C) The diagonals bisect each other.

E) The diagonals are perpendicular.

A) Both pairs of opposite sides are congruent, is not a necessary condition for a quadrilateral to be a rectangle, as a rectangle can have different side lengths.

B) One pair of opposite sides is longer than the other pair of sides, is not a necessary condition for a quadrilateral to be a rectangle, as a rectangle can have equal side lengths.

D) The diagonals are congruent, is not a necessary condition for a quadrilateral to be a rectangle, as a rectangle can have diagonals of different lengths.

So, only C) The diagonals bisect each other, and E) The diagonals are perpendicular are the two conditions that prove that a quadrilateral is a rectangle.

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The level of measurement used for the temperature is given as follows:

Interval.

There are four levels of measurement for the data, given as follows:

The measures of central tendency for each level are given as follows:

For the temperature, we obtain the arithmetic mean, hence it has the level of measurement of interval.

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The federal income tax withheld for Doug, given the fact Doug is married and claims 1 allowance is $ 149.

Using the Married Persons Weekly Payroll table, you can find the bracket that Doug Smalley belongs in which is $1, 350 - $ 1, 360.

When looking at this bracket, we see that the federal income tax withheld for a person in this bracket, who claims 1 withholding allowance, is $ 149.

The federal income tax for Doug Smalley who earns $ 1, 352.75 a week in 2016, is therefore $ 149.

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The full question is:

Use the Married Persons Weekly Payroll table to find the federal income tax withheld. Doug smalley, a meteorologist, is married, earns $1,352.75 a week, and claims 1 allowance.

The Pythagorean Theorem holds true for both triangles, then the triangles are not only similar, but also congruent.

Triangle xyz has sides of length x, y, and z and triangle pqr has sides of length p, q, and r.

To determine if triangle xyz is similar to triangle pqr, we must calculate the ratios of corresponding sides. This is done using the formula:

Ratio of sides = (Side length x) / (Side length y)

We can calculate the ratios for each side of the triangles and compare them. If the ratios are equal for all sides, then the triangles are similar. For example, if the ratio of side x to side y in triangle xyz is equal to the ratio of side p to side q in triangle pqr, then the triangles are similar. If the ratios are not equal for all sides, then the triangles are not similar.

We can use the Pythagorean Theorem to determine if the triangles are not only similar, but also congruent. The Pythagorean Theorem states that a2 + b2 = c2, where c is the longest side and a and b are the other two sides. If the Pythagorean Theorem holds true for both triangles, then the triangles are not only similar, but also congruent.

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The statement that is not true about samples is: "samples picked randomly are more representative of a population."

To determine this:

While random sampling is one way to ensure that a sample is representative of a population, it is not the only way. There are other methods of sampling such as stratified sampling, cluster sampling, and systematic sampling that can also be used to obtain a representative sample.

It is important to note that, even with random sampling, a sample may not be representative of the population if the sample size is too small or if there is a significant amount of bias in the sampling process.

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Answer:

45 fewer chapter books

Step-by-step explanation:

Picture books: 27 x 11= 297

Chapter books: 21 x 12= 252

297-252= 45

The scale factor for the dilation in this problem is given as follows:

2.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

As the side lengths are changed, with a dilation the figure loses it's congruence relative to the original figure.

The equivalent side lengths in this problem are given as follows:

The dilated triangle is triangle DAB, hence the scale factor is obtained as follows:

k = 8/4 = 2.

(that is, the side lengths of triangle DEF were multiplied by 2 to generate triangle DAB).

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Answer:

x=1

Step-by-step explanation:

4(5x-3)-3(2x-5)=17

20x-12-6x+15=17

14x+3=17

     -3.  -3

14x=14

/14.  /14

x=1

The machine can make 20 soda bottles each minute.

In Mathematics and Geometry, the slope of any straight line simply refers to the rate of change and it can be calculated by using this mathematical equation (expression);

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

From the information provided above, we have the following data points located on the line:

Substituting the given points into the slope formula, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (140 - 100)/(7 - 5)

Slope (m) = 40/2

Slope (m) = 20.

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For your data, the regression equation for Y is:

Y = 2.09697X - 0.55152

A linear function in mathematics is one that has either one or two variables and no exponents. It is a function with a straight line as its graph.

Given, a data set

x: -5, -3, 4, 1, -1, -2, 0, 2, 3, -4

y: -10, -8, 9, 1, -2, -6, -1, 3, 6, -8

Sum of X = -5

Sum of Y = -16

Mean X = -0.5

Mean Y = -1.6

Sum of squares (SSₓ) = 82.5

Sum of products (SP) = 173

Regression Equation = Y = bX + a

b = SP/SSₓ = 173/82.5 = 2.09697

a = Mₓ - bMₓ = -1.6 - (2.1*-0.5) = -0.55152

Y = 2.09697X - 0.55152

For x = 2.5 the value of y:

y = 2.09697* 2.5 - 0.55152

y = 4.69

Therefore, For your data, the regression equation for Y is:

Y = 2.09697X - 0.55152

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The equation in slope-intercept form for this line is y = -5/4x + 3.

What is the slope-intercept form of the line?

The slope-intercept form is a way of representing the equation of a straight line in the form y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis). The slope of a line represents the steepness of the line, and the y-intercept represents the point at which the line crosses the y-axis.

A line can be represented by two points (x1, y1) and (x2, y2) the slope can be calculated by the formula:

m = (y2 - y1) / (x2 - x1)

In this case, the line passes through the point (-8, -9) and has a slope of -5/4, we can use the point-slope form of the equation of a line to find the equation of this line:

y - y1 = m(x - x1)

y - (-9) = (-5/4)(x + 8)

y = (-5/4)x + (-9) + (2*9)

y = (-5/4)x + 3

Hence, the equation in slope-intercept form for this line is y = -5/4x + 3.

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The linear functions for each diagonal are given as follows:

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

For diagonal BD, the points are given as follows:

D(-3,-3) and B(3,3).

The slope is given by the change in y divided by the change in x, hence:

m = (3 - (-3))/(3 - (-3)) = 1.

Hence:

y = x + b.

When x = 3, y = 3, hence the intercept b is given as follows:

y = x.

The diagonals are perpendicular, meaning that the multiplication of their slopes is of -1, hence the slope of AC is of:

m = -1.

Hence:

y = -x + b

When x = -3, y = 3, hence the intercept b is given as follows:

3 = 3 + b

b = 0.

Hence the equation is:

y = -x.

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The design of the experiment is Completely randomized over two factors (fertilizer and location).

Randomization is a statistical technique used in experimental design to ensure that all possible combinations of the factors being studied are represented in the study groups. It is used to eliminate bias and control for confounding variables that may affect the outcome of an experiment.

The researcher randomly assigned the tomato plants to be planted on either the sunny or the shady side of the hill. This creates two groups or two levels of the factor "location". She also randomly assigned the tomato plants to one of three groups based on the amount of fertilizer given, creating three groups or three levels of the factor "fertilizer".

The random assignment of plants to the different groups for both factors helps to ensure that any differences in the yield of tomatoes is due to the independent variables (fertilizer and location) being tested, and not due to other extraneous factors.

Therefore, The design of the experiment is Completely randomized over two factors (fertilizer and location).

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The best interpretation for the given standard deviation as per given information is given by :

Option D. On an average, the number of breakdowns per day varies from the mean by about 0.28.

As given in the question,

Therefore, the best interpretation of standard deviation is :

Option D. On an average, the number of breakdowns per day varies from the mean by about 0.28.

The above question is incomplete , the complete question is:

The quality control manager at a factory records the number of equipment breakdowns each day. Let the random variable Y represent the number of breakdowns in one day. The standard deviation of Y is 0.28. Which of the following is the best interpretation of the standard deviation?

A. The number of breakdowns on a randomly selected day is expected to be 0.28.

B. The number of breakdowns on a randomly selected day will be 0.28 away from the mean.

C. The average number of breakdowns per day for a random sample of days is expected to be 0.28

D. On average, the number of breakdowns per day varies from the mean by about 0.28.

E. The number of breakdowns per day for a random sample of days is expected to be 0.28 away from the mean.

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For the creation of y, we first need to know the placement of the numbers and then write an R code to create a subset for the same.

To create another vector y which contains all the numbers between 3 and -3 in order of appearance, we first need to know exactly what is the order of the appearance of 3 and -3.

Hence we will write the R code

which(x == 3)

which(x == -3)

These commands will return us the specific position of the numbers 3 and -3

Let us assume that 3 is the fourth number and -3 is the 31st number. Then we will write y as a function that contains the subset of x from the fourth to the 31st number as follows.

y <- x[4:31]

Typing this command will give us the required subset.

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Complete Question

Let x be a numeric vector and suppose you want to extract all the entries of x that are between -3 and 3 (including both boundaries -3 and 3). Create a new vector y which consists of all entries of x between -3 and 3 (including -3 and 3), in order of appearance as in vector x. For example, if X = c(-5, 7, 9, 3, 14, 9, 5, 10, -2, 0, 12) then, printing y should read у [1] 0 3 -2 0

Since lim a n/b n does not exist, it means that the ratio between a n and b n can be larger or smaller depending on the terms.

This implies that the rate of growth of a n and b n are not necessarily the same. If the series b n diverges, it means that the terms of b n increase without bound. Therefore, the terms of a n will also increase without bound, and sum a n will also diverge.

Formally, if lim a n/b n = ∞, then ∑ a n is divergent. We can prove this by contradiction. Suppose ∑ a n converges. Then by the comparison test, lim a n/b n must converge and be finite, which is a contradiction. Therefore, ∑ a n must diverge.

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According to the information ∠1 and ∠2 are complementary to each other.

∠1 ⊥ ∠2
Since PR is parallel to VO and RO is parallel to PV, it follows that PR is congruent to RO. This means that ∠1 and ∠2 are supplementary angles and thus, complementary.
Since PR // VO and RO // PV, then by the Transitive Property of Congruence, VO // PV.

Since PR ≅ RO and VO // PV, then by the Corresponding Angles Postulate, ∠1 ≅ ∠2.

Since ∠1 and ∠2 are congruent, then by the definition of complementary angles, ∠1 and ∠2 are complementary.

Thus, ∠1 and ∠2 are complementary.

∴ ∠1 and ∠2 are complementary

Congruent refers to something that is "absolutely equal" in terms of size and shape. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, and stack them on top of one another.

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Answer:1325

Step-by-step explanation:

The general solution of a linear second order homogeneous equation is represented as the combination of two particular solutions.

This is because the linear second order homogeneous equation is of the form ax2+bx+c=0 and has two distinct roots, i.e. x1 and x2. The general solution of the equation can be written as y=C1y1+C2y2, where C1 and C2 are constants and y1 and y2 are the two particular solutions. The particular solutions can be derived from the two distinct roots of the equation using the formula y1=e^(x1*t) and y2=e^(x2*t). The constants C1 and C2 can be found by solving the linear combination of the two particular solutions for the given initial conditions of the equation. This gives the general solution of the linear second order homogeneous equation as a combination of the two particular solutions.

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The original matrix's rank > the augmented matrix's rank. So the option C "the solution set is empty" is correct.

The matrix is

[tex]\left [ \begin{matrix}1 & 7&3 & -4\\ 0& 1& -1 & 3\\ 0& 0 & 0& 2\\ 0&0 & 1&1 \end{matrix} \right ][/tex]

To determine the solution set we simplify the given matrix by performing the row operations.

[tex]R_{4}\leftrightarrow R_{3}[/tex]

[tex]\left[\left.\begin{matrix}1 & 7 &3 \\ 0& 1 & -1\\ 0& 0 & 1\\ 0&0 &0 \end{matrix}\right|\begin{matrix}-4\\ 3\\ 1\\ 2\end{matrix}\right][/tex]

The rank of main matrix = 3

The rank of augmented matrix = 4

The rank of main matrix < The rank of augmented matrix

So, there is no solution. The solution set is empty.

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The complete question is:

The augmented matrix of linear system has been reduced by row operations to the form shown. Continue the appropriate row operations and describe the solution set of the original system:

[tex]\left [ \begin{matrix}1 & 7&3 & -4\\ 0& 1& -1 & 3\\ 0& 0 & 0& 2\\ 0&0 & 1&1 \end{matrix} \right ][/tex]

Select the correct choice below and; if necessary; fill in the answer boxes to complete your choice.

A: The solution set has exactly one element

B. The solution set has infinitely many elements

C. The solution set is empty

Answer: The area of the floor can be found by multiplying the width and the length.

Area of the floor = (6x - 9)(6x + 9) = 36x^2 - 63x - 81

The area of each tile can be found by evaluating the expression 24x^2 - 12x - 36.

Area of each tile = 24x^2 - 12x - 36

To find out how many tiles are needed to cover the floor we need to divide the area of the floor by the area of each tile.

Number of tiles needed = (36x^2 - 63x - 81) / (24x^2 - 12x - 36)

The division is simplified by canceling out common factors between the numerator and denominator, the number of tiles is a fraction that can't be simplified any further.

So the answer is (36x^2 - 63x - 81) / (24x^2 - 12x - 36) tiles are needed to cover the floor.

Step-by-step explanation:

Answer: The sum is -15

Step-by-step explanation:

The equations for the sides of the parallelogram would be

8x - 6 = 9x

y + 10 = 11y

Option (A) and (C) are correct.

What is a parallelogram?

A parallelogram is a four-sided shape with opposite sides that are parallel and congruent. In other words, opposite sides of a parallelogram are of equal length and parallel to each other. Additionally, opposite angles in a parallelogram are also congruent. It has two pairs of parallel sides. It can be thought of as a rectangle with opposite sides that are not necessarily at right angles to each other.

As the property of the parallelogram says

"Opposite sides of the parallelogram are equal"

So we can write

8x - 6 = 9x

y + 10 = 11y

Hence, The equations for the sides of the parallelogram would be

8x - 6 = 9x

y + 10 = 11y

Option (A) and (C) are correct.

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The required  inequality to represent the possible number of cakes sold ​is Cupcakes ≥ 144.

The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has diverse meanings to different people, it is prone to misunderstanding in public discourse.

Write an inequality to illustrate the potential amount of cakes sold if the business sold 144 cupcakes. ​

So,

Bakery can sold 144 cupcakes and more

Cupcakes ≥ 144

Thus, required inequality is Cupcakes ≥ 144.

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The area under the density curve from 15 to 100 is 0.80.

With pdf f and cdf f, consider X to be a continuous random variable.

By definition, integrating the pdf yields the cdf: F(x)=x∫−∞f(t)dt.

By differentiating the cdf, one may find the pdf according to the Fundamental Theorem of Calculus: f(x) = ddx[F(x)]

An interval or group of intervals makes up the sample space of a continuous random variable, X.

1- 0.20 0.80

[tex]\int\limits^[/tex] f(x) dx from 0 to 100 = 1

[tex]\int\limits^[/tex]  f(x) dx from 0 to 15 + int 15 ^ 100 =1

[tex]\int\limits^[/tex]  d from 15 to 100 =1-0.20=0.80.

The area under the density curve from 15 to 100 is 0.80.

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The inequality to determine the number of 100-kilogram crates that can be loaded into the shipping container is 27500 ≤ 5400 + 100x

A shipping container will be used to transport several 100-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 27500 kilograms. Other shipments weighing 5400 kilograms have already been loaded into the container.

Therefore, the inequality that can be used to determine x, the number of 100-kg crates that can be loaded into the shipping container can be calculated as follows:

27500 ≤ 5400 + 100x

where

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