If M is a centroid of triangle WOR and YR = 11, what is the length of WR?​

1. f(x) - cubic function -- polynomial , g(x) - linear function

similar

The function f(x) = x³+x²-3x+4 is a polynomial function and g(x) = 2ˣ-4 is an exponential function.

Domain: -∞ < x < ∞

Range: -∞ < y < ∞

y-intercept = 4

x - intercepts = -2.68

Function g(x)

Domain: x > 0

Range: -4 < y < ∞

y - intercept = -4

x - intercepts = none

By comparing the key features above, we can conclude that the common features in both functions are their range

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The value of x will be 1.17 inches and the maximum volume of the box is 1.6 cubic inches.

Volume is a measurement of three-dimensional space that is occupied. It is frequently numerically quantified using SI-derived units or various imperial or US customary units. The definition of length is linked to the definition of volume.

Given that the rectangular box is made from cardboard the thickness is x.

The length of the box will be,

L = 4.5 - 3x

The width of the box will be,

W = 4 - 2x

The thickness of the box is,

H = x

The volume of the box will be calculated as,

V = ( 4.5 - 3x) ( 4 - 2x ) (x)

V = ( 4.5 - 3x) ( 4 - 2x ) (x)

V = ( 18 - 12x - 9x + 6x² ) x

V = 6x³ -21x² + 18x

For maximum volume differentiate the volume with respect to x and get the value of x,

dV / dx = d / dx (  6x³ -21x² + 18x ) = 0

d / dx (  6x³ -21x² + 18x ) = 0

18x² - 42x + 12 = 0

3x² - 7x + 6 = 0

Solve the above quadratic equation as,

x = [ -b ±√(b² - 4ac) ] / 2a

x = [ -7 ± √ (-7² - 4 x 3 x 6 ) ] / ( 2 x 3 )

x = 1.17

The value of x is 1.17 inches by solving the above quadratic equation. The maximum volume will be calculated as,

V = 6x³ -21x² + 18x

V = 6(1.17)³ -21(1.17)² + 18(1.17)

V = 9.6 - 28.7 + 21.06

V = 1.96 cubic inches

The maximum volume is 1.96 cubic inches and the value of x is 1.17 inches.

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Answer:

x + x - x = x

explanation:

give us the actual formula lol

A car manufacturer wants to lean about the brand preferences, then the company should survey a sample of all electric car owners.

A survey is a set of questions used in human subject research with the goal of gathering specific information from a particular population. Surveys can be carried out via the phone, by mail, online, at street corners, and even in shopping centers. Surveys are employed to collect data or learn more in areas like demography and social research.

Survey research is frequently used to evaluate ideas, beliefs, and emotions. Surveys may have narrow, specialized objectives, or they may have more general, extensive objectives.

As the manufacturer wants to learn about the brand preferences of electric car owners that what type of things people like nowadays, or what kind of improvement he can do in his model or design or other things, he should prefer a sample of all electric car owners.

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Answer:

144cm²

Step-by-step explanation:

If the square is perfectly even on all sides, the you first need to divide 48 by 4, as a square has 4 sides.

48/4 = 12cm

Then, to find the area, you need to multiply 12 by 12.

12 cm x 12 cm = 144cm²

Hope this helps :)

A z-score tell us about an individual observation in a data set is, the number of standard deviations an observation is away from the mean.

The value of the z-score tells you how many standard deviations you are away from the mean. If a z-score is equal to 0, it is on the mean. A positive z-score indicates the raw score is higher than the mean average. For example, if a z-score is equal to +1, it is 1 standard deviation above the mean.

A z-score is the value of an observation expressed in standard deviation units. The sign of the score indicates whether it is above (positive) or below (negative) the mean, and the value quantifies how many standard deviations the score is from the mean.

The purpose of z-scores is to identify and describe the exact location of each score in a distribution & to standardize an entire distribution to understand & compare scores from different tests.

Z-scores or Z-statistics represent a statistical technique of measuring the deviation of data from the mean. There are different formula used for Z-score or Z-statistics depending upon what is measured. Z-statistics is generally used with Z-test which is a hypothesis testing statistical technique.

Therefore,

A z-score tell us about an individual observation in a data set is, the number of standard deviations an observation is away from the mean.

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The statement "cross-tabulation can only be used for two variables; each variable must have well-defined labels " is false

The cross tabulation is defined as the tool that is used in statistics to categorical data. We can also says that  that present the results of the entire group of respondents

The given statement is "cross-tabulation can only be used for two variables; each variable must have well-defined labels "

The cross tabulation method can be used to represent two or more variables. The cross tabulation table has x axis as one variable and y axis as another variables

The cross tabulation can be used for two or more variables

Therefore, the the given statement is false

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Answer: 500

Step-by-step explanation:

280 + 220 is 500

Answer:

The number is 500.

Step-by-step explanation:

Let's assume that,

→ Missing number = x

Forming the equation,

→ x = 220 + 280

Now the value of x will be,

→ x = 220 + 280

→ [ x = 500 ]

Hence, the number is 500.

The point of the compass located in order to make the arcs is points X and Y.

An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference. A curve contains an arc. A circle contains an arc. For instance, a quarter-circle and a semicircle are both examples of arcs. A minor arc is one that is smaller than half of the circle it is a part of, or less than a semicircle, whereas a major arc is one that is more than half of its circle.

Given

The following figure was drawn using a straightedge and a compass.

The point of the compass located in order to make the arcs:

1. points X and Y

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The solution of the equation is x = 6±2√11.

What is a quadratic equation?

The quadratic formula in elementary algebra is a formula that yields the answer to a quadratic problem. In addition to the quadratic formula, other methods of solving quadratic equations include factoring, completing the square, graphing, and others.

Here, we have

Given: x² - 12x = 8

Now, we factorize the given equation and find the solution.

x² - 12x = 8

x² - 12x - 8 = 0

We apply here the quadratic formula.

= (-b ±√b²-4ac)/2

= (12 ±√12²-4×1×(-8))/2

= (12±√144+32)/2

= (12±√176)/2

= (12±4√11)/2

= 6±2√11

Hence, the solution of the equation x² - 12x = 8 is 6±2√11.

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In case A:

The amount to be paid = $41.75

In case B :

The amount to be paid = $41.76

So, the Case A is better option.

Finding the right answer using the round off to nearest hundredth.

How to change any value to it's nearest hundredth ?

Rounding to the nearest hundredth means the rounding of any decimal number to its nearest hundredth value. In decimal, hundredth means 1/100 or 0.01. For example, the rounding of 2.167 to its nearest hundredth is 2.17.

Steps to find nearest hundredth of any value:

Step 1:

Since we need to round the given decimal number to the nearest hundredth, we mark the digit at the hundredths place.

Step 2:

Then, we observe the 'thousandths' place digit, which lies to the right of the hundredths column.

Step 3:

If the digit at the thousandths place is less than 5, we write the hundredths place digit as it is and remove all the digits to its right.

Step 4:

If the digit at the thousandths place is 5 or more than 5, we add 1 to the digit at the hundredths place, that is, we increase the hundredths place by 1 and remove all the digits to its right.

Case A :

The price for each gallon = $3.479

So, the total price for 12 gallon = $41.748

In case A total amount is rounded off

So, the price = $41.75

Case B :

The price for each gallon = $3.479

Rounding off the price for each gallon = $3.48

So, the total amount for 12 gallon = $41.76.

So, the case A is better option.

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Answer:

D

Step-by-step explanation:

when we have the zeroes, we can build the polynomial by multiplying factors that will turn the functional value to 0 at exactly these points.

f(x) = (x - 3)(x + 6)(x - 1)

we don't need to do the full multiplications to see that the constant term of the polynomial is the result of the multiplication of all 3 constant terms of the factors :

-3 × +6 × -1 = +18

and therefore, D is the correct answer (as it is the only answer option with +18 as constant term).

The proposition ststement is: the only prime number that is odd is 2.

The correct answer is an option (d)

In this question we have been given some statements.

we need to identify the proposition statement.

We know that a proposition is a declarative statement. In mathematics proposition gives a clear inference of whether a sentence is true or false. The proposition statement cannot be stated in two ways. The statement must be either correct or incorrect.

a) get me a glass of milkshake.

It is a commanding statement.

b) god bless you!

It is a type of optative statement.

c) what is the time now?

It is a question sentence.

d) the only odd prime number is 2.

It is a false proposition statement.

Therefore, option (d) is a proposition statement.

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The remainder of polynomial g(x) divides (x - 3) that is  g(x) / (x - 3) is 0.

What is polynomial?

A polynomial is a mathematical expression made up of variables, constants, and exponents that are combined using addition, subtraction, multiplication, and division operations.

Given: g(x) = 2x^3 + 5x^2 - 28x - 15

(x - 3) is a factor of g(x).

We have to find the remainder of g(x) / (x - 3).

Consider,

                 2x^2 + 11x + 5

         [tex]\sqrt[(x-3)]{2x^3+5x^2 -28x -15}[/tex]

          -    2x^3 -6x^2

____________________________

                      11x^2 - 28x

               -      11x^2 - 33x

____________________________

                               5x - 15

                          -    5x - 15

_______________________________

                                      0

Hence, the remainder of polynomial g(x) divides (x - 3) that is

g(x) / (x - 3) is 0.

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The equations found for the number of tickets sold when 22 tickets are sold on Monday and 30 per day after are sold by Madelyn, and 53 tickets are sold on Monday and 20 per day after that are;

Tickets sold by Madelyn is; y = 22 + 30·x

Tickets sold by Kaia is; y = 53 + 20·x

A system of equation obtained from the details in the question can be presented as follows

y = 22 + 30·x...(1)

y = 53 + 20·x...(2)

The appropriate method for solving the system is to equate equivalent values of one of the variable obtained from each equation in the system.

The solution of the system of equation is; x = 3.1, which indicates that it takes about 3.1 days for the number of tickets sold by Madelyn and Kaia to be equivalent.

An equation consists of two expressions that are joined by the 'equals to' (=) sign.

The number of tickets for the Winter Dance Madelyn sold = 22

Number of tickets per day Madelyn sold after that = 30 per day

Number of tickets Kaia sold on Monday = 53

Number of tickets per day Kaia sold after that = 20 per day

Let x represent the number of days since Monday, and let y represent the number of tickets sold

Therefore;

The number of tickets Madelyn sold, y = 22 + 30·x

The number of tickets Kaia sold, y = 53 + 20·x

The system of equations from the specified information is the equation for the number of tickets Madelyn sold and the number of tickets Kaia sold combined, which can be presented as follows;

y = 22 + 30·x...(1)

y = 53 + 20·x...(2)

The method of solving the equations is by plugging in the value of y from equation (1) in equation (2), as follows;
22 + 30·x = 53 + 20·x

30·x - 20·x = 53 - 22 = 31

10·x = 31

x = 31 ÷ 10 = 3.1

The meaning of the solution of the system of equation, x = 3.1, is that the number of days for the number of tickets sold by Madelyn and Kaia to be the same is about 3 days

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Answer:

-2

Step-by-step explanation:

Given,

g(x) = f(4)

or, 2 - 4x = 3*4 - 2

or, 2 - 4x = 10

or, 2 - 10 = 4x

or, -8 = 4x

or, x = -2

The proof for the Base Angles Theorem is explained below:

A triangle's opposite angles are congruent if its two sides are congruent. We shall build the angle bisector through the vertex angle of an isosceles triangle in order to demonstrate the Base Angles Theorem. We created two congruent triangles by building the angle bisector, and then we utilized CPCTC to prove that the base angles are congruent. Base angles: The angles that include the base of an isosceles triangle are known as the "base angles."

Any triangle with at least two congruent sides is said to be isosceles. Legs are the isosceles triangle's congruent sides. The base is the other side. Base angles are the angles formed between the base and the legs.

Given: [tex]\bar{ LM}[/tex]≅ [tex]\bar{LN}[/tex]

Prove: ∠M≅∠N

According to the figure,

Given,

[tex]\bar{ LM}[/tex]≅ [tex]\bar{LN}[/tex]

By the definition of mid-point,

O is the mid-point of [tex]\bar{MN}[/tex]

Now, by joining the two points determine and draw a line of [tex]\bar{LO}[/tex]

Now, Again by the definition of mid-point

[tex]\bar{MO}[/tex]≅[tex]\bar{NO}[/tex]

Now, by using reflexive property,

[tex]\bar{LO}[/tex]≅ [tex]\bar{LO}[/tex]

By SSS rule,

ΔLMO≅ΔLNO

By CPCTC rule,

∠M≅∠N

Hence proved.

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Answer: The answer is $s$ > 7, which represents the number of seconds that can pass for the temperature in the cryotherapy chamber to drop below -20°F.

Step-by-step explanation: The temperature in the chamber will drop below -20°F when it reaches -20°F + 2.5°F = -17.5°F.

The temperature in the chamber is currently 0°F, so we can represent this situation with the inequality 0 - (2.5 * $s$) < -17.5, where $s$ is the number of seconds that can pass.

We can simplify this inequality by multiplying both sides by -1 to get the following: 2.5 * $s$ > 17.5.

Dividing both sides by 2.5, we get the final inequality: $s$ > 7.

Therefore, the number of seconds $s$ that can pass for the temperature in the cryotherapy chamber to drop below -20°F is greater than 7 seconds.

Answer: Y=mx+b

Step-by-step explanation:

Luka will require 24 cups of water to make lemonades as calculated from the data given.

The quantity of sugar which he use is twice the amount of lemon which he us ,

= 2 x 3 = 6

and ,

as we know the amount of water is 4 times as much as lemon juice

Therefore, amount of water

= 4 * 6

= 24

A quantity in a Maths equation is a number or variable plus any algebraic combination of additional quantities. In an equation like x + 6 = 15, four values are represented.

A quantity can be described as the amount of something or how much of it there is. Quantity can also be used to refer to the size of something (its magnitude), whether in terms of numbers, units of measurement, or just relative size.

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Answer:

i think that answer is correct

Step-by-step explanation:

Parent function is represented by the graph is

B. The quadratic parent function

What is Parent function?

A parent function in mathematics is the most basic function within a family of functions that nonetheless upholds the definition of the entire family. For instance, displaystyle y=x2 is the simplest function in the family of quadratic functions with the general form displaystyle y=ax2+bx+c.

A parent function is an equation in the simplest form of a family of functions. There are many forms of parent functions such as: Linear functions: f(x)=x f ( x ) = x , where the degree of the function is 1 and represents a straight line.

The simplest parabola is y = x2, whose graph is shown at the right. The graph passes through the origin (0,0), and is contained in Quadrants I and II. This graph is known as the "Parent Function" for parabolas, or quadratic functions.

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Using the given data, the number of suspects is; 7

The union of two sets A and B is the set of all those elements which are either in A or in B, and which is denoted as A ∪ B.

However, the intersection of two sets A and B is defined as the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B.

Now, we are told that;

Total number of people in the office = 30 people

Number of people wearing a white button down shirts = 22

Number of people wearing black pants = 16

Number of people wearing a multicolored tie = 7

Thus, by definition of intersection of sets, if the suspect was wearing black pants, a white button-down shirt, and a multicolored tie, then;

The number of suspects =  A ∩ B ∩ C = 7 people

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Step-by-step explanation:

it is the process of changing rows to columb

Answer:G(x) = 3/4 |x|, nevertheless that is the same that G(x) = |3/4x|.

Step-by-step explanation:

Note that given that 3/4 is less than 1 the original function is compressed.

- Take care <3

The probability that a randomly chosen person from the united states can donate blood to maria is 0.50

considering blood to be of types A,B,AB and O

further all blood groups are equi probable

Probability of blood type A  = probability of blood type B = probability of blood type AB = probability of blood type O = x

Probability of blood type A  + probability of blood type B + probability of blood type AB + probability of blood type O = 1

⇒ 4x = 1

⇒ x = 1/4

Probability that a random person will have blood of type B or O = x+x

= 1/4 + 1/4

= 1/2

= 0.50

Hence we get the required answer.

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The answer to each part is -

        y = mx + c    

        where -

        [m] : slope of line
        [c] : y - intercept                    

Given is the graph of a straight line as shown.

[A] - A second equation for the system so it has infinitely many solutions can be the one that overlaps the line given. So the second equation can be written as follows. The points are -

(0, 4) and (4, 1)

Let the line be -

y = mx + c

m = (1 - 4)/(4 - 0) = -3/4

m = -3/4

So, the equation will be -

y = (-3/4)x + 4

[B] -

For no solution, the line will be parallel to the given line. The equation of the line is → y = (-3/4)x + 4. The equation whose graph goes through (0, 1) so the system has no solutions as : y = (-3/4)x + 1.

Therefore, the answer to each part is -

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The points where the inequality x+ 5y <-30 intercepts is ( 30, 0 ) and (0,6).

Here given the inequality.

x + 5y ≤ 30

To find the x-intercepts.

We have to substitute 0 for y and solve x to determine the x-intercepts.

x + 5 × 0 = 30

By solving the equation.

x = 30

( 30, 0 ) is the x-intercepts.

To find the y-intercepts.

By substituting 0 for x and solving y will get the y-intercept(s).

0 + 5y = 30

5y =30

y = 30/5

y = 6

In the point form, y-intercept.

Y-intercept(s): ( 0, 6 )

(30, 0) is the x-intercept.

Y-intercepts at : ( 0, 6 ).

The points in which the inequality x+ 5y <-30 intercepts is (30, 0) and (0,6).

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As AB is the perpendicular bisector of IK so we conclude that the right option is AJ=BJ.

A precise drawing in which a line is split in half by another line that is at a 90-degree angle to the original line is known as a perpendicular bisector. To divide into two equal portions is to bisect. When two lines intersect at a straight angle, they are perpendicular.

A line that precisely divides a line segment connecting two locations in half at a 90 degree angle is known as a perpendicular bisector. Finding the midpoint and negative reciprocal of two points, then entering these solutions into the equation for a line in slope-intercept form, will get the perpendicular bisector of the two points.

Option J can not be true as A can not be the midpoint of IK as A is not on IK.  Because J is on the IK as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. Hence, J is assumed as the midpoint of IK.

Option H i.e IJ = JK can not be true because AJ does not necessarily equal to BJ.

Option G i.e m∠IAJ  also does not true necessarily true. The reason is simple i.e AJ is arbitrary.

So, Option f i.e AJ = BJ is the correct Answer as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. So it can be assumed that that J is the midpoint as but it doesn't necessarily mean that IJ = JK, also it is true that perpendicular lines meet at 90 degree. Hence, statement F i.e AJ = BJ  is true.

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As AB is the perpendicular bisector of IK so we conclude that the right option is AJ=BJ.

What is perpendicular bisector?

A precise drawing in which a line is split in half by another line that is at a 90-degree angle to the original line is known as a perpendicular bisector. To divide into two equal portions is to bisect. When two lines intersect at a straight angle, they are perpendicular.

What is the perpendicular of two points?

A line that precisely divides a line segment connecting two locations in half at a 90 degree angle is known as a perpendicular bisector. Finding the midpoint and negative reciprocal of two points, then entering these solutions into the equation for a line in slope-intercept form, will get the perpendicular bisector of the two points.

Option J can not be true as A can not be the midpoint of IK as A is not on IK.  Because J is on the IK as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. Hence, J is assumed as the midpoint of IK.

Option H) i.e IJ = JK can not be true because AJ does not necessarily equal to BJ.

Option G)  i.e  m∠IAJ  also does not true necessarily true. The reason is simple i.e AJ is arbitrary.

So, Option f)  i.e AJ = BJ is the correct Answer as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. So it can be assumed that that J is the midpoint as but it doesn't necessarily mean that IJ = JK, also it is true that perpendicular lines meet at 90 degree. Hence, statement F i.e AJ = BJ  is true.

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