C'D'
is a translation of
CD
. Write the translation rule.
-

Answer:

-4/7

Step-by-step explanation:

The slope of the given line is [tex]\frac{3-(-4)}{4-0}=\frac{7}{4}[/tex].

Perpendicular lines have slopes that are negative reciprocals of each other, so the answer is [tex]-4/7[/tex].

The slope of every line perpendicular to the line passing through (4, -3) and (0, -4) is -4.

We have,

Let's first find the slope of the given line passing through (4, -3) and

(0, -4):

slope = (change in y) / (change in x)

= (-4 - (-3)) / (0 - 4)

= (-4 + 3) / (-4)

= -1 / (-4)

= 1/4

The slope of the given line is 1/4.

Now, to find the slope of a line perpendicular to this line, we take the negative reciprocal of the slope:

[tex]slope_{perpendicular} = -1 / slope[/tex]

= -1 / (1/4)

= -4

Therefore,

The slope of every line perpendicular to the line passing through (4, -3) and (0, -4) is -4.

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The number of party popper she bought is 32 and the number of balloons she bought is 18.

The first step is to form a system of equations using the information provided in the question.

0.20x + 0.50y = $20 equation 1

x + y = 52 equation 2

The solution using the elimination method :

Multiply equation 2 by 0.20

0.20x + 0.20y = 10.40 equation 3

Subtract equation 3 from equation 2 :

0.30y = 9.60

Divide both sides of the equation by 0.30

y = 9.60 / 0.30

y = 32

The solution using the substitution method:

Make x the subject of the formula in equation 2

x = 52 - y equation 3

Substitute for x in equation 1 :

0.20(52 - y) + 0.50y = $20

10.40 - 0.20y + 0.50y = $20

Combine similar terms together

0.50y - 0.20y = $20 - $10.40

0.30y = $9.60

y = 9.60 / 0.30

y = 32

x = 50 - 32

x = 18

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From the base of the wall, the bottom of the ladder is 10.6 feet away

information given in the question

hypotenuse = 16 foot long ladder

opposite = 12 foot high wall

adjacent =  How far away from the base of the wall is the bottom of the ladder = ?

The problem is solved using the Pythagoras theorem is applicable to right angle triangle.  the formula of the theorem is

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required distance

16² = 12² + x²

256 = 144 + x²

256 - 144 = x²

x² = 112

x = √112

x = 10.583

the ladder is  10.6 feet away from the base of the wall

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Answer:

18 tiles

Step-by-step explanation:

There are 20 tiles in total.  Red is 6 of the 20, or 6/20.  That is 3/10 or 30%

Each draw has a 30% chance of being red.  30% or 20 tiles is 1.8 tiles.  Over 30 draws, that would mean a total of 600 tiles are drawn,  The overall chance of red is still 30%, so after 30 draws, the number of red tiles would be predicted to be 30% of 600:

 (0.30)*(600) = 18 tiles will be red.

Answer:

-6y + 13.3 = 0

y = 13.3/6

Step-by-step explanation:

This equation don't need any step-by-step explanation :). Hope it helps!

The given triangle is been reflected according to rule (x, y)→(−x, y) and the new coordinates are (-8, 2), (-3, 4), (-2, 7).

A reflection is a type of transformation that involves flipping a shape, known as the preimage, across a line, known as the line of reflection, to produce a new shape (called the image).

We can picture what would happen if you turned the form across the line to graph a reflection.

So, we have a triangle with coordinates:

(8, 2), (3, 4), (2, 7)

Now, we will reflect it according to the rule:

(x, y)→(−x, y)

Then, the coordinates will be:

(-8, 2), (-3, 4), (-2, 7)
(Refer to the graph attached below)

Therefore, the given triangle is been reflected according to rule (x, y)→(−x, y) and the new coordinates are (-8, 2), (-3, 4), (-2, 7).

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Answer:

13.3 ft

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a square}\\\\$A=s^2$\\\\where:\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\\\end{minipage}}[/tex]  [tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a triangle}\\\\$A=\dfrac{1}{2}bh$\\\\where:\\ \phantom{ww}$\bullet$ $b$ is the base. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]

The surface area of a square-based pyramid is made up of:

Given:

Find the area of the square base and the area of one of the triangles by substituting the given values into the formulas:

[tex]\textsf{Area of the square base} = 5^2 = 25\; \sf ft^2[/tex]

[tex]\textsf{Area of one of the side triangles} = \dfrac{1}{2} \cdot 5 \cdot l= 2.5l \; \sf ft^2[/tex]

Substitute these values along with the given total surface area into the formula and solve for l:

[tex]\begin{aligned}\textsf{Total Surface Area}&=\sf square+4\;triangles\\\implies 158&=25+4\left(2.5l)\\158&=25+10l\\133&=10l\\l&=\dfrac{133}{10}\\l&=13.3\; \sf ft\end{aligned}[/tex]

Therefore, the missing length is 13.3 feet.

In mathematics, linear programming is a technique for maximizing operations under certain restrictions.

Using the mathematical modeling technique of linear programming, a linear function is maximized or minimized depending on the restrictions it is subjected to. This method has proved helpful for directing quantitative judgments in business planning, industrial engineering, and—to a lesser extent—in the social and physical sciences.

In mathematics, linear programming is a technique for maximizing operations under certain restrictions. Maximizing or minimizing the numerical value is the primary goal of linear programming. It comprises of linear functions that are subject to restrictions in the form of inequalities or linear equations.

Therefore, the correct answer is option A. this is a binding constraint, so there is no slack or surplus.

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Answer:

[tex]x = 15 $^{\circ}$ ; z = 74$^{\circ}$[/tex]

Step-by-step explanation:

First, combine all like terms. Like terms are terms that have the same amount of the same variables:

[tex]m$\angle$(5x - 1) + m$\angle$(7x + 1) = 180$^{\circ}$\\\\[/tex]

[tex]m$\angle$(5x + 7x) + (1 - 1) = 180$^{\circ}$[/tex]

[tex]12x + 0 = 180$^{\circ}$[/tex]

Next, isolate the variable, x. Divide 12 from both sides of the equation:

[tex]12x = 180\\\frac{12x}{12} = \frac{180}{12}\\ x = \frac{180}{12}\\ x = 15 $^{\circ}$[/tex]

Next, plug in 15 for x in one of the given expressions. If you choose the right one (7x + 1), you will solve using the straight angle theorem. If you choose the bottom one (5x - 1), you will solve using the vertical angle postulate. Both will give you the same answer for x.

Firstly, if you want to solve using the straight angle theorem. The straight angle theorem is defined that all straight angles are 180 degrees. Solve using the straight angle theorem. Set both angle measurements equal to 180°:

[tex](z) + (7x + 1) = 180[/tex]

Plug in 15 for x and solve for the parenthesis:

[tex]z + 7(15) + 1 = 180 $^{\circ}$\\[/tex]

First, multiply 7 with 15:

[tex]z + (7 * 15) + 1 = 180 $^{\circ}$\\z +105 + 1 = 180$^{\circ}$\\[/tex]

Next, simplify by combining like terms:

[tex]z + (105 + 1) = 180 $^{\circ}$\\z + 106 = 180$^{\circ}$[/tex]

Next, isolate the variable, z, by subtracting 106 from both sides of the equation:

[tex]z + 106 = 180 $^{\circ}$\\z + 106 (-106) = 180 (-106)\\z = 180 - 106\\z = 74$^{\circ}$[/tex]

Your answer:

[tex]x = 15 $^{\circ}$ ; z = 74$^{\circ}$[/tex]

~

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The given statement "the coefficients of dummy variables in multiple regression models must always be positive." is True.

Regression model:

In statistics, regression model means a statistical technique that relates a dependent variable to one or more independent variables.

Given,

Here we have the statement the coefficients of dummy variables in multiple regression models must always be positive.

Now, we have to find whether the given statement is true or not.

In order to find the statement creditability, we must know the definition of the terms coefficient and dummy variables.

Dummy variable refers the variable that takes values of 0 and 1, where the values indicate the presence or absence of something

Where as the coefficient means a number or symbol by which another number or symbol is multiplied.

Based on this definition we have found that the given statement is true.

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Therefore, the limitations census of entire population can be described in  major points like  it can be Since surveys rely on self-reporting, some misrepresentation or mistake is unavoidable and further more

A key component of the U.S. Federal Statistical System, the United States Census Bureau, or Bureau of the Census, is in charge of gathering information on the population and economy of the United States.

Here,

Therefore ,the limitations of generalizing census findings back to the entire population are:-

The homeless population is underrepresented in the findings even though every home is required to complete a census report. This is because they are frequently impossible to reach, interview, and count.

People who do not speak either English or Spanish as their first language and whose primary language is one of those two are more likely to be overlooked in the census.

Since surveys rely on self-reporting, some misrepresentation or mistake is unavoidable.

The population fluctuates constantly, so it is unlikely that the population on the day the census results are released would closely resemble the population as described in the census.

Those who entered the country illegally but intend to stay do not submit a report.

Therefore , there are 5 major limitation described above .

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Answer: I believe that this statement is very true. People shouldn’t be pushing others down when instead they could be pushing themselves up, improving them to be better.

Step-by-step explanation:

Answer:

THAT VERY RIGHT INSTEAD OF PEOPLE HELPING THEMSELVES THEY SPEND THEIR TIME CRITICIZING OTHERS KUDO TO U

Answer:

  0 < x < 4.5

Step-by-step explanation:

You want the reasonable domain of V(x) = (8.5 -2x)(11 -2x).

The equation describes volume (V) and cut length (x), so both need to be positive. Volume will be positive when ...

  8.5 -2x > 0

  4.25 > x

The reasonable domain is 0 < x < 4.5.

All of the following statements are true:

a. Effective listening is vital to success in selling.

b. visual aids play a part in the listening process.

c. people can talk approximately twice as fast as they can listen.

d. you should listen closely to everything you hear.

e. listening refers to the process of trying to detect sounds.

Listening is the act of paying attention to sounds that are happening around you. It involves both hearing the sounds and interpreting what they mean. Good listening skills are important for many reasons, including being able to communicate effectively with others and understand instructions. To listen effectively, you need to be able to focus on the speaker and try to understand their perspective, rather than just waiting for your turn to talk.

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The value of the double integral ∫∫[tex]\frac{y^{2} }{x^{2} +y^{2} }[/tex] dA is 131.95.

We know that in polar coordinates, the circle become r = 4 and r = 16. These are the limits on the radius. Clearly the limits on the angle are

0 ≤ θ ≤ 2π.

Therefore we get,

∫∫ [tex]\frac{y^{2} }{x^{2} + y^{2} }[/tex] dA = ∫ ∫ r²sin²θ / r² dr dθ

                  = ∫ sin²θ dθ ∫ r dr

                  = [ [tex]\frac{1}{2}[/tex]θ - [tex]\frac{1}{4}[/tex]sin(2θ)]₀²ⁿ[ [tex]\frac{1}{2}[/tex] r²]₄¹⁰

                  = [tex]\frac{1}{4}[/tex] (2π)(10² - 4²)

                  = 42π

∫∫ [tex]\frac{y^{2} }{x^{2} + y^{2} }[/tex] dA = 131.95.

What is Polar coordinates?

When each point on a plane of a two-dimensional coordinate system is decided by a distance from a reference point and an angle is taken from a reference direction, it is known as the polar coordinate system.

Polar coordinates are useful in calculating the equations of motion from a lot of mechanical systems. Polar coordinate means the magnitude and direction of a vector.

Polar coordinate system of locating points in a plane with reference to a fixed point O and a ray from the origin usually chosen to be the positive x-axis.

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On solving the provided question, we got to know that, Blenders sold as a percentage of food processors sold is 30/20, or 3/2.

Since equations are essentially questions, efforts to systematically find answers to those questions have been the driving force behind the development of mathematics. From straightforward algebraic equations that just require addition or multiplication to differential equations, exponential equations that use exponential expressions, and integral equations, there are many different types of equations that range in complexity.

Compared to mixers, the dealer sold twice as many food processors.

Let M be the quantity of mixers sold.

Therefore, 2M is the quantity of food processors sold.

A total of 60 of the three appliances were sold by the dealer.

M + 2M = 3M

Thus, 3M is a representation of the whole sales of mixers and food processors.

60 appliances were purchased in total, thus 60 - 3M equals the quantity of blenders purchased.

Everything was sold by the merchant for a total of $4,200.

We get: (30)(M) + (120)(2M) + (50)(60 - 3M) = 4,200

30M + 240M + 3000 - 150M = 4200

130M + 3000 = 4200

120M = 1200

M = 10

The retailer so sold 10 mixers.

This indicates that the vendor sold 20 food processors and 30 food processors.

Blenders sold as a percentage of food processors sold is 30/20, or 3/2.

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A random sample of 277 individuals will result in a sample mean waist size of at least 86.3 cm is 0.0749.

In the given question,

18-year-old American males stated that the sample mean waist circumference was 86.3 cm.

The populations mean waist size is 85 cm.

The population standard deviation is 15 cm.

We have to find, a random sample of 277 individuals will result in a sample mean waist size of at least 86.3 cm.

H(0): μ = 85

H(A): μ > 85

Sample mean(X) = 86.3

Standard deviation(σ) = 15

Standard error of mean =σ/√n

Standard error of mean (SE) = 15/√277

SE = 15/16.6433

SE = 0.9013

z = (X- μ)/SE

z=(86.3-85)/0.9013

z = 1.4424

P(z > 1.4424) = 0.0749

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The right question is;

The National Health Statistics Reports dated Oct. 22, 2008 stated that for a sample size of 277. 18-year-old American males stated that the sample mean waist circumference was 86.3 cm.

Suppose that the population mean waist size is 85 cm and that the population standard deviation is 15 cm. how likely is it that a random sample of 277 individuals will result in a sample mean waist size of at least 86.3 cm? (Round your answers to four decimal places.)

Answer:

x = 8/3

y = 10/3

Step-by-step explanation:

We add (1) and (2) to get 3x = 8. This means that x = 8/3. We substitute it back into (1) to get 8/3 + y = 6 which shows that y = 10/3

The locations on the function's graph that are most near the specified point f(x) = x2, (0,9) are approximately 3 units to the right and left, respectively, or (sqr8.5, 8.5).

The initial estimate would be rough to the right and left by around 3 units, or (sqr8.5, 8.5), rounded to the nearest decimal place.

Visually, it is most likely just below y=9 and just below x=3. Additionally, roughly (-3, 9) slightly lower than 3 and 9

Connect the parabola's nearest point to the point at (0,9). Where the two intersect, its slope is the negative inverse of the parabola's slope. The derivative's slope is 2x for the equation f(x) = x2. -1/2x is its inverse negative. The line from (0,9) to the parabola's nearest point has a slope that is perpendicular to the tangent to the parabola at that location.

Get the equation of the line joining (0,9) and the nearest point (x,y) on the parabola using the point-slope formula: 8.5 or y=-1/2 + 9 = (-1/2x)(x)

The closest point's y coordinate is that. The square root of 8.5, including both positive and negative square roots, is the closest point's x coordinate (-sqr8.5, 8.5)

Sqr8.5 =[tex]\sqrt{8.5}[/tex], or approximately 2.91 or -2.91

The process entails finding the equation for the line connecting (0,9) with the parabola's nearest point and then setting the two equations equal. Set the line equation to y=(-1/2x), the parabola equation. The parabola equation is y=[tex]x^{2}[/tex] and the line equation is x + 9.

Equalize them, then find x using the square of the result. The closest point is at x,y. There are two places that are equally far from (0,9), both of which are as close as they can be to 3 at (3,9). (0,9). At the parabola point, that line is not perpendicular to the tangent line (3,9). The line must be perpendicular to the tangent line, which is the slope of the parabola, in order to be closest.

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Answer:

slope of original line; m = -3/-4

                                         =3/4

slope of parallel line = 3/4

slope of perpendicular line = m1*m2=-1

                                               =(3/4)*m2=-1

                                               =-4/3

equation passes through point (4,-3) is : 3x + 4y = -12

The simplified expression of the statement is -41.66

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

negative 17 plus the quantity negative 3 and seven tenths plus 9 and 15 hundredths end quantity divided by 5 all times 4 squared minus 4 and 7 tenths

Rewrite properly

So, we have

(-17 - 3.7 + 9.15)/5 * 4² - 4.7

Evaluate the sum and the difference in the expression

So, we have

-11.55/5 * 4² - 4.7

Evaluate the exponent and the quotient

-2.31 * 16 - 4.7

So, we have

-36.96 - 4.7

Evaluate

-41.66

Hence, the solution is -41.66

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The complex numbers are

a.  11 - 3i

b. 2 + i

c. 5 - 6i

A complex number is a number in the complex plane. It is written in the form r = a + bi where a and b are real numbers and i = √(-1). Also, a is the real part and ib is the complex part of the complex number

a. Given that the complex number is denoted by r = a + ib where

Since we have for the given complex number

So, r = real part + imaginary part = 11 + (-3i)

= 11 - 3i

So, the complex number is 11 - 3i

b. Given that the complex number is denoted by r = a + ib where

Since we have for the given complex number

So, r = real part + imaginary part = 2 + i

= 2 + i

So, the complex number is 2 + i

c. Given that the complex number is denoted by r = a + ib where

Since we have for the given complex number

So, r = real part + imaginary part = 5 + [-6√(-1)]

= 5 - 6√(-1)

= 5 - 6i (since i = √(-1))

So, the complex number is 5 - 6i

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The data does contradict with the prior evidence

To determine whether the data presented here are significantly inconsistent with previous assumptions, a statistical test was performed to verify that the observed relationship between tendon length and cranial volume was significantly greater than the expected relationship. You have to decide if they are different.

To do this, fit a line to the data using linear regression analysis and test the hypothesis that the slope of the line is equal to 20 cm3/mm. If the p-value for this hypothesis test is less than 0.05, you can conclude that the data are inconsistent with previous assumptions at the 0.05 significance level.

It is crucial to realize that this analysis assumes that the relationship between tendon length and cranial volume is linear.

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A biconditional statement is a statement that may be stated in the form “p if and only if q.” This implies “if p, then q” and “if q, then p.”

A biconditional statement is one that can be expressed as "p if and only if q," which implies "if p, then q" and "if q, then p."

For example, "If the polygon is a square, then it has four equal sides and four right angles," and "If a polygon has four equal sides and four right angles, then it is a square," are two examples of biconditional statements.

A biconditional statement is a combination of a conditional statement and its converse written in the if and only if form.

Two line segments are congruent if and only if they are of the same length.

Therefore, the biconditional statement is a statement that may be stated in the form “p if and only if q.” This implies “if p, then q” and “if q, then p.”

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Answer: T  = 1

Step-by-step explanation:

As 6/9 is equivalent to 2/3, then 1/1.5 is similar to 10/15, which is also 2/3

Answer:

t = 1

Step-by-step explanation:

Given equation,

→ (6/9) = (t/1.5)

Now the value of t will be,

→ (6/9) = (t/1.5)

→ (t/1.5) = (6/9)

→ t = (6/9) × 1.5

→ t = (6 × 1.5)/9

→ t = 9/9

→ [ t = 1 ]

Hence, the value of t is 1.

The type of analysis used to identify the source of the bias is known as Differential Item Functioning Analysis.

Analysis

In statistics, analysis is to break a topic or concept down into its parts in order to inspect and understand it, and to restructure those parts in a way that makes sense to you.

Given,

Here we need to find the type of analysis used to identify sources of bias.

While we looking into the given question, we have used by ETS.

And it identifies items that are specifically biased against any ethnic, racial or gender group.

And we also know that the first analysis equates groups on the basis of overall scores.

By using these groups it evaluates differences in performance between sub groups on particular items.

And the Items that differ significantly between the groups are thrown out.

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1. The equation of the straight line is y = -x -1.

2. The equation of the point-gradient form is 3x -y - 10.

3. The equation of the straight line that is parallel to the line y = x-2 and goes through the point (0,1) is y = x + 1.

What is a straight line?

A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher-dimensional environments, they are one-dimensional things. In daily language, a line segment with two points designating its endpoints is also referred to as a "line."

Here, we have

1. The slope-intercept form of the equation of a line is:

y = mx + b

We are fortunate to be given the y-intercept, the point(0,-1) therefore, the value, b, in the slope-intercept form is -1:

y = mx - 1

Substitute the other point(-1,0) into the equation and then solve for the value of m:

0 = -m - 1

m = -1

y = -x -1

Hence, the equation of the straight line is y = -x -1.

2. We know that the equation of a line passing through the point (x₀, y₀  ) whose slope is m is (y -  y₀) = m(x -x₀)

The equation of a line passing through the point(2,-4) and the slope is 3.

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

y + 4 = 3x - 6

3x -y - 10

Hence, the equation of the point-gradient form is 3x -y - 10.

3. Consider the given equation: y = x-2

Since, the line is parallel to given line. so slope will be same.

slope = 1

We know that the second line will also have a slope of 1, and we are given the point (0,1). We can set up an equation in slope-intercept form and use these values to solve for the y-intercept.

y = mx + b

1 = b

Now, we put the value of b in the equation and we get

y = x + 1

Hence, the equation of the straight line that is parallel to the line y = x-2 and goes through the point (0,1) is y = x + 1.

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The value after simplifying the number 10^3(10)^4 is 10⁷.

The simplification of given number can be done through the rule of exponent -

[tex] {a}^{m} [/tex] × [tex] {a}^{n} [/tex] = [tex] {a}^{m+n} [/tex], where m and n are the powers of a.

Now, keeping the values in formula -

Value = [tex] {10}^{3} [/tex] × [tex] {10}^{4} [/tex]

Based on the rule, the simplified for these powers will be

Value = [tex] {10}^{3+4} [/tex]

Performing addition of powers on Right Hand Side of the equation

Value = [tex] {10}^{7} [/tex]

Alternatively, the numbers can be expanded and multiplied. Further write the result in scientific notation as above. However, it will a long method which is not practical for very large numbers.

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