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The probability that all adjacent points differ in colour is [tex]\frac{1}{5}[/tex].

What is probability ?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

Have given ,

We have first three colour Green that is g1 , g2 and g3

And We have next three colour red that is r1 , r2 and r3

The probability that all adjacent points differ in colour = 3! * [tex]^{4}C_{3}[/tex] 3! / 6!

=> [tex]\frac{ 3! * 4! *3!}{6!}[/tex]

=> [tex]\frac{1}{5}[/tex]

The probability that all adjacent points differ in colour is [tex]\frac{1}{5}[/tex].

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Given polynomials are,

[tex]\rm{f(x)=x^2+px+q}[/tex]

[tex]\rm{g(x)=x^2+mx+n}[/tex]

According to Remainder Theorem, if (x + a) is a factor of f(x), then,

[tex]\longrightarrow\rm{0=f(-a)}[/tex]

[tex]\longrightarrow\rm{0=(-a)^2+p(-a)+q}[/tex]

[tex]\longrightarrow\rm{0=a^2-pa+q\quad\dots(1)}[/tex]

Similarly, if (x + a) is a factor of g(x), then,

[tex]\longrightarrow\rm{0=g(-a)}[/tex]

[tex]\longrightarrow\rm{0=(-a)^2+m(-a)+n}[/tex]

[tex]\longrightarrow\rm{0=a^2-ma+n\quad\dots(2)}[/tex]

Subtracting (2) from (1),

[tex]\longrightarrow\rm{0=(a^2-pa+q)-(a^2-ma+n)}[/tex]

[tex]\longrightarrow\rm{0=a^2-pa+q-a^2+ma-n}[/tex]

[tex]\longrightarrow\rm{0=(m-p)a+q-n}[/tex]

[tex]\longrightarrow\rm{0=(m-p)a-(n-q)}[/tex]

[tex]\longrightarrow\rm{(m-p)a=n-q}[/tex]

[tex]\longrightarrow\rm{\underline{\underline{a=\dfrac{n-q}{m-p}}}}[/tex]

Hence Proved!

Answer:-21788

Step-by-step explanation:

Answer:

9 ways

Step-by-step explanation:

2 × $1

1 × $1 + 4 × $0.25

1 × $1 + 2 × $0.25 + 5 × $0.10

1 × $1 + 10 × $0.10

8 × $0.25

6 × $0.25 + 5 × $0.10

4 × $0.25 + 10 × $0.10

2 × $0.25 + 15 × $0.10

20 × $0.10

I count 9 ways.

The shift in the line's y coordinate relative to its x coordinate is known as the slope of a line. The slope of the given line graph is 3.

The slope of a line is defines as the change in the y coordinate of the line to the x-coordinate. Mathematically, the slope of a line is expressed according to the formula below:

Slope = y₂-y₁/x₂-x₁

Using the following coordinate from the given graph (0, 0) and (1, 3), we will substitute the coordinates into the formula to have:

Slope = 3-0/1-0

Simplify to have:

Slope = 1/3

Slope = 3

Hence the slope of the given line graph is 3.

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For a given collection of data, the median is 7.

The median is the value in the center of a data collection, which means that 50% of the data points have a value less than or equal to the median, and 50% of the data points have a value greater than or equal to the median. The median is the value in the center of a group of numbers. The median corresponds to the 50th percentile of the collection of numbers. In other terms, the median is the value in the center of a group of numbers where half of the values are less than the median and half are more than the median.

Here,

First we have to arrange the numbers in ascending order.

3,5,6,7,8,9,10,12

There are 8 terms.

8 is an even number

So the median term is 8÷2=4th term

4th term =7

The median for given set of observations is 7.

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There is no mode in the given data.

To find: Mode of the given data.

Given data is 1, 2, 3, 4

Mode: The mode of data is the observation having the highest frequency in a set of data. There is a possibility that more than one observation has the same frequency, i.e. a data set could have more than one mode. In such a case, the set of data is said to be multimodal.

The data is already arranged in ascending order. Therefore, there is no need to arrange the data in increasing order.

Constructing the frequency for given data:

Number:       1  2  3  4  5

Frequency:   1  1   1   1   1

Since the frequency of all the numbers are same, therefore, there is no specific mode for the given set of data distribution.

Conclusively, if no numbers in the data distribution are repeated, then there is no mode for such observation.

Therefore, there is no mode for given data.

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Therefore, the solution to the given problem of the equation whose factors are (3x - 1)(x + 1).

Examine the equation.

An equation is a mathematical statement that is created by connecting two expressions using the equivalent sign. An example of an equation is 2x - 5 = 15. This equation's solution reveals that the value of the variable x is 5.

According to the given question:

Given : 3x² + 2x - 1

Factorizing using splitting the middle term

= 3x² + 3x - x - 1

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

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

Therefore , the solution to the given problem of the equation whose factors are (3x - 1)(x + 1) .

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The graph peaks at t=2 hours and the peak concentration is 337.4mg

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division.

Given here, P(t) = 0.5t++3.45t³ - 96.65t² + 347.7t, when 0 ≤ t ≤ 6

Clearly from the graph the medicine peaks at t=2 hours and the peak concentration therefore is = 0.5×2++3.45×2³ - 96.65×2² + 347.7×2

                                            = 1+27.6-386.6+695.4

                                            = 337.4mg

Hence, The graph peaks at t=2 hours and the peak concentration is 337.4mg

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The possible rational zeros of f(x) = [tex]x^{4} + 2x^{3} - 3x^{2} - 4x +20[/tex] are ±1, ±2, ±4, ±5, ±10, ±20.

What is mean of rational zero ?

A rational zero is a rational number, which is a number that can be written as a fraction of two integers. An irrational zero is a number that is not rational, so it has an infinitely non-repeating decimal.

By Rational Zero Theorem,

If P(x) is a polynomial with integer coefficients and if is a zero of P(x) i.e.,(P( ) = 0),

then p is a factor of the constant term of P(x)

q is a factor of the leading coefficient of P(x)

Possible value of rational zero is p/q

Have given, f(x) = [tex]x^{4} + 2x^{3} - 3x^{2} - 4x +20[/tex]

Here, constant term, p = +20

Leading coefficient, q = +1

The factors of the constant term +20 are ±1, ±2, ±4, ±5, ±10, ±20.

The factor of the leading coefficient is ±1.

Therefore , The possible rational zeros of f(x) = [tex]x^{4} + 2x^{3} - 3x^{2} - 4x +20[/tex] are ±1, ±2, ±4, ±5, ±10, ±20.

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The volume of vinegar in each container is 200 milliliters.

Since the total volume of vinegar in the five containers is one liter, and a liter is equal to 1000 milliliters, the volume of vinegar in each container is 1000/5 = <<1000/5=200>>200 milliliters.

The amount of space a container encloses, or how much room is inside of it, is measured by its volume. The volume of a box is easily calculated using the following formula: Volume of a box with dimensions H, W, and L is equal to L×W×H. Many different units can be used, however because of the way this formula is stated, the volume would have length to the third power dimensions. For instance, if the container's measurements are given in meters, the capacity of the box will be given in meters cubed, or m³.

The volume of vinegar in each container is 200 milliliters.

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Since the total volume of vinegar in the five containers is one liter, and a liter is equal to 1000 milliliters, the volume of vinegar in each container is 1000/5 = <<1000/5=200>>200 milliliters.

A container's volume is a measure of how much space it contains or how much space is inside of it. The following formula makes calculating a box's volume simple: LWH is the volume of a box having the dimensions H, W, and L. Although many various units can be used, the volume would have length to the third power dimensions due to the way this formula is written. For instance, the capacity of the box will be specified in meters cubed, or m3, if the container's dimensions are given in meters.

The volume of vinegar in each container is 200 milliliters.

Answer:

[tex]f(x)=2(x+3)(x-5)[/tex]

Step-by-step explanation:

Using the roots, [tex]f(x)=a(x+3)(x-5)[/tex].

Using the point [tex](1,-32)[/tex] to solve for [tex]a[/tex],

[tex]-32=a(4)(-4) \\ \\ -32=-16a \\ \\ a=2 \\ \\ \\ \therefore f(x)=2(x+3)(x-5)[/tex]

All integers are also rational numbers.

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the area of 4 cm circle is 12.568 cm² whose radius is 2 cm

the round shaped figure having a fixed center and specific diameter is called circle.

area of a circle having known radius is calculated by the formula

A =πr²

r is the radius of circle

in the above question 4cm circle refer the diameter of circle is 4cm

so, radius is r= 2 cm

Area = 3.142x2²

12.568 square cm

hence, area is 12.568 square centimeters.

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Answer:

i just want the points

Step-by-step explanation:

No, AAS ( Angle , Angle , Side) congruence postulate is not same as ASA (Angle, Side, Angle) congruence postulate, because in AAS consists one equal side between both triangles either it PR = AC or PQ = AB . But ASA must include side equality in this case i.e BC = QR and both are not same.

Two triangles are said to be congruent if they have all three same angles as well as same sides. AAS and ASA are basic methods through which we can prove that two triangles are congruent. So, to check that wheather both methods are same we will take one example of two triangles. So, consider two triangles, ∆ABC and ∆PQR as seen above in figure, ∠ ABC = ∠ PQR = 40° and ∠ACB = ∠ PRQ = 80° and AC = QR

According to AAS rule, if two pairs of corresponding angles with opposite or non- including side is same and the equality in opposite sides are equal to each other then the triangles are congruent. We have ,

∠ PRQ = ∠ ACB , ∠ABC = ∠PQR

and either PR = AC or PQ = AB.

if the above three conditions are satisfied then ∆ABC congruent to ∆PQR.

According to ASA rule , if two angles of one triangle with one side contained between two angles are respectively equal to two angles of another triangle and one side contained between them , then triangles are congruent. We have, ∠ R =∠C , ∠B = ∠Q and BC = QR

if the above three conditions are satisfied then both triangles are congruent. As we see clearly both congruence postulates are not same.

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Answer:

in the 50th cube I think it's 250, because your just adding 5 each time, and for the cube equal to 156 that is uh I don't really know, try the 50th one, because 5x50 is 155

Step-by-step explanation:

I am so sorry if I'm wrong.

The formula of the set is generally written as follows.

The term set in math is defined as an organized collection of objects and can be represented in set-builder form or roster form.

Here we need to find the formula that can be used in set.

The general formula of the set can be written as follows:

=> n ( P ∪ Q ) = n(P) + n(Q) – n ( P ∩ Q)

where

n(P U Q) refers the number of elements present in one of the sets P or Q.

n(P ⋂ Q) refers the number of elements present in both the sets P & Q.

Where as If P ∩ Q = ∅, then the value is calculated as,

=> n ( P ∪ Q ) = n(P) + n(Q)

Here we have also want to know that sets P and Q are equal only if all the elements they contain intersect, and none of them have any unique elements which are not present in the other set.

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the value of the discriminant of the given equation is -20.

The discriminant of a quadratic equation is a value derived from the coefficients of the equation that can be used to determine the number and type of solutions of the equation. The discriminant of a quadratic equation in the form ax2 + bx + c is calculated by the formula b2 - 4ac. In this case, the equation is 2x2 + 4x + 3. Plugging the coefficients into the formula, we get (4)2 - 4(2)(3) = -20. Therefore, the value of the discriminant of the given equation is -20.

(4)2 - 4(2)(3) = 16 - 24 = -8

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Answer: 34cm

Step-by-step explanation:

4cm + 3cm = 7cm

9cm - 7cm = 2cm

The missing value is 2cm

Leading the perimeter to be 34cm

The angle 78.125° is rewritten as 78 degrees 7 minutes and 30 seconds.

Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

The angle is given below.

⇒ 78.125°

Convert the decimal part into minutes and seconds. Then we have

⇒ 78° + 0.125 x 60

⇒ 78°7.5'

⇒ 78°7' + 0.5 x 60

⇒ 78°7'30''

The angle 78.125° is rewritten as 78 degrees 7 minutes and 30 seconds.

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Answer: She can buy a total of 33 packets and have 25 cents leftover.

Step-by-step explanation:

Answer:

she will have $1 left

Step-by-step explanation:

265÷8=33.125 or 33 1/8

she will have $1 left

Since there is a proportional relationship between a volume measured in cups and the same volume measured in tablespoons, the value of y in the ordered pair (1, y) is 16.

Mathematically, a proportional relationship or direct variation can be represented by the following equation:

y = kx

Where:

In order to have a proportional relationship and equivalent ratios, the variables x and y must have the same constant of proportionality. Next, we would determine the constant of proportionality (k) based on the given parameters:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 48/3

Constant of proportionality (k) = 16.

Therefore, a linear equation that relates the volume measured in tablespoons (y) and volume measured in cups (x) is given by;

y = kx

y = 16x

When x = 1 cups, the value of y is given by;

y = 16(1)

y = 16 tablespoons.

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The 4 step plan in math:

Math problem solving can be a daunting task, but it doesn't have to be. By following a simple four-step plan, anyone can approach and solve math problems in an organized and efficient manner. The four steps to successful math problem solving are identifying the problem, gathering information, planning a solution, and solving the problem.

Identifying the problem is the first step to successful math problem solving. This step involves breaking down the problem into its individual parts and understanding what needs to be solved. It is important to be thorough and get a good grasp of the problem before moving on to the next step.

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Answer:

Step-by-step explanation:

7.89 is about 8 so we can multiply 215*8 to get 1720 dollars

Answer:

$1696.35

Step-by-step explanation:

$7.89 × 215 = $1696.35

A man who has hemophilia and a woman who is a carrier has:

A hemophilia carrier is what?

Both an X chromosome from the mother and an X chromosome from the father are passed down to a daughter. Let's say the gene for typical blood coagulation is present on her mother's X chromosome. Let's say her father's X chromosome carries the hemophilia gene.

Since the normal blood clotting gene from the mother is dominant, the daughter won't get hemophilia. The hemophilia gene's instructions cannot be transmitted because of this.

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The two steps for calculating the mean:

Add up all the values in the data set.

Divide this number by the number of values.

The mean of a dataset is the sum of all values divided by the total number of values. It’s the most commonly used measure of central tendency and is often referred to as the “average.”

There are two steps for calculating the mean [tex](\bar{x})[/tex]:

(1) Add up all the values in the data set.

Sum of all the observations of given data denoted by [tex]\sum x[/tex]

(2) Divide this number by the number of values.

The total number of values of given data denoted by 'n'

Sample mean:

[tex]$$\overline{x}= \frac{\sum x}{n} $$[/tex]

Example: Find the mean step by step?

42, 13, 31, 87, 24, 58, 76, 69

Solution:

Step 1: Find the sum of the values by adding them all up.

[tex]\sum x=[/tex] 42 + 13 + 31 + 87 + 24 + 58 + 76 + 69 = 400

Step 2: Divide the sum by the number of values

In the formula, n is the number of values in your data set. Our data set has 8 values.

[tex]$$\overline{x}= \frac{\sum x}{n} $$[/tex]

[tex]$$\overline{x}=\frac{400}{8}[/tex]

[tex]$$\overline{x}[/tex] = 50

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Answer: okay so you add all of the numbers in the data set and then divide by how many numbers there were in the set.

Step-by-step explanation:

Answer:

From above graph

(A) The domain can be best described using

Interval notation

The domain is

-infinity , infinity

(a) The range cambe best described wing

Interval notation

The range is [4, infinity )

To obtain xA³ + 3xA² + 3x + 5 we msut add xA³ + xA² - 2x - 1 to

2xA² + 5x + 6.

A polynomial is an algebraic expression.

A polynomial of degree n in variable x can be written as,

a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.

Given, A polynomial 2xA² + 5x + 6.

Now, We know we can do arithmetic operations on like terms.

So to obtain xA³ + 3xA² + 3x + 5 we must subract 2xA² + 5x + 6.

Therefore, ( xA³ + 3xA² + 3x + 5) - (2xA² + 5x + 6).

= xA³ + xA² - 2x - 1 should be added to obtain xA³ + 3xA² + 3x + 5.

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Answer:

D. 3

Step-by-step explanation:

Initially, the vertex is at [tex](6,6)[/tex]. After the transformation, the vertex moves to [tex](3,13)[/tex].

So, [tex]h=3[/tex].