Describe a real-life representation of the following.



12/49 =0.24

From the given pairs of ordered pairs {(-1, 3), (2, 6), (3, 9), (4, 12), (5, 20)} it is a function.

The core concept of mathematics calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x.

As per the set of ordered pairs given in the question,

1.

{(-1, 3), (2, 6), (3, 9), (4, 12), (5, 20)}

It is a function because every input has a single output.

2.

{(-7, 3), (-7, 6), (-7, 12), (-7, 18)}

It is not a function because 7 corresponds to two different images like 3, 6, 12, and 18.

3.

{(9, -3), (4, -2), (1, -1), (0, 0), (1, -3)}

It is not a function because 1 corresponds to two different images, like -1 and 3.

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As per the estimated percentage, the test statistic is 0.6167 or 61.67%

The term percentage is defined as the number or ratio that can be expressed as a fraction of 100.

Here we have given that in Arkansas than Virginia. the sample results show that, rounded to two decimal places, the estimated percentage of Arkansas residents who were born there is %. the sample results also show that, rounded to two decimal places, the estimated percentage of Virginia residents who were born there is %.

And we need to find the test statistics.

While we looking into the given situation we have identified the following values,

=> H0 : p = 0.577

=> Ha : p ≠ 0.577

Now, we have estimate the proportion of stay-at-home residents in Arkansas is calculated as,

Here the Proportion of stay-at-home residents in Arkansas is written as,

=> p = 74/120 = 0.6167

Therefore, the test statistics is 0.6167.

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The 90% confidence interval for the population mean is given as follows:

(18.75, 22.51).

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are presented as follows:

The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 16 - 1 = 15 df, is t = 1.7531.

From the sample given in this problem, the parameters are as follows:

[tex]\overline{x} = 20.63, s = 4.3, n = 16[/tex]

Then the lower bound of the interval is given as follows:

20.63 - 1.7531 x 4.3/4 = 18.75.

The upper bound of the interval is of:

20.63 + 1.7531 x 4.3/4 = 22.51.

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The graph of the linear inequation [tex]y \leq \frac{1}{2}x -5[/tex] has been described below

What is linear inequation?

Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by

[tex]> , < , \geq, \leq[/tex]

A one degree inequation is known as linear inequation.

The given linear inequation is

[tex]y \leq \frac{1}{2}x -5[/tex]

Here equality is maintained. So the line is a solid line

Now, (0, 0) does not satisfy the inequality.

So the solution is below the line

When graphing the inequality above, we will draw a solid line and the solution lies below the line

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Answer:

Divide the numerator and denominator by 45.

Step-by-step explanation:

7650/341055

Divide the numerator and denominator by 5.

1530/68211

Divide the numerator and denominator by 3.

510/22737

Divide the numerator and denominator by 3.

170/7579

Finding the t statistic is necessary to check the normality of a five-class observed frequency distribution.

The t-value gauges the magnitude of the difference in relation to the range of your sample's data. Or to put it another way, T is just the calculated difference shown in units of standard error. The evidence is stronger against the null hypothesis the larger the value of T.

In general, t-values that are more than +2 or less than -2 are acceptable. We are more confident in the coefficient's ability to predict outcomes the higher the t-value. Low t-values are a sign of the predictability of that coefficient's coefficient being unreliable.

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The value of the equation is [tex]A = (\sqrt{63x}^{(11yz)^1^0}[/tex]

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is given by

Root of 63x to the power of 11 yz to the power of 10

The value of root of 63x = [tex]\sqrt{63x}[/tex]

Now , the value of root of 63x to the power of 11 yz is

The value of root of 63x to the power of 11 yz = [tex](\sqrt{63x}^{(11yz)[/tex]

And ,

The value of root of 63x to the power of 11 yz to the power of 10 is

Value of root of 63x to the power of 11 yz to the power of 10 is [tex](\sqrt{63x}^{(11yz)^1^0}[/tex]

Therefore , the value of A is [tex](\sqrt{63x}^{(11yz)^1^0}[/tex]

Hence , The value of the equation is [tex]A = (\sqrt{63x}^{(11yz)^1^0}[/tex]

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Answer:

B

Step-by-step explanation:

Subtract $1.95 from $12 to account for the flat rate that Jason must pay, then divide that by 0.55, or the per mile charge. The answer, or the highest amount of miles he can go with $12, is 18.27272727. The answer that best represents the number of miles he can go is B because he can go up to 18 miles, including 18 miles, hence the closed circle.

Answer:

14.128

Step-by-step explanation:

you need to extract the 872g which is 0.872kg

from the 15 and that is 14.128kg

The indirect proof that defines triangle RVS is not equilateral is explained below.

How triangle look like?

In math, A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices and also a polygon.

Here we need to find the indirect proof for the triangle RVS which is not equilateral.

Here we know that, We need to write an indirect proof in paragraph proof.

For, the given statement, △RVT and SVT are equilateral; 

And △RVS is not equilateral.

Then the explanation for this one is written as,

Let us assume temporarily that △RST is equilateral.

And we have given that △RVT and SVT are equilateral, then the sides of △RVT, SVT, and RST are congruent.

Therefore, RV≅VSRS which follows that △RVS is equilateral.

In contradicts the given that △RVS is not equilateral, then the temporary assumption must be false. It follows that △RST is not equilateral.

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The solution of the system of the equations, y = 1/3x + 3 and y = 2x - 4, as shown in the graph below is: (4.2, 4.4).

A system involving two equations has a solution, which are the coordinates of the point on a graph where the two equations intersect.

Given the equation, y = 1/3x + 3, which is represented by the red line in the graph below, when y = 2x - 4 (represented as the blue line) is added, a system is formed which will make both lines intersect at the point that has the coordinates (4.2, 4.4).

Therefore, the solution of the system y = 1/3x + 3 and y = 2x - 4 is (4.2, 4.4).

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Answer:

The exact value of x so that the greatest possible amount of light is emitted is 8.96ft.

What is the perimeter of a semicircle?

The perimeter of a semicircle is half that of a circle, that is [tex]\pi r[/tex], where r is the radius of the circle.

Step-by-step explanation:

Given the width of the rectangle is x, let the height of the rectangle be y.

The radius of the semicircle is x/2.

The perimeter of the window is equal to [tex]2y+x+\pi \frac{x}{2} =32[/tex].

The area of the window is [tex]xy+\frac{1}{2}(\pi )(\frac{x}{2})^2=xy+\frac{\pi x^2}{8}[/tex].

We can insert into the formula for the area to obtain the area in terms of only x by solving the equation for the perimeter of y in terms of x.

[tex]2y=32-(1+\frac{\pi }{2} )x=32-(\frac{2+\pi }{2} )x\\y=16-(\frac{2+\pi }{4} )x[/tex].

Now the area of the window in terms of only x is:

Area=[tex]16x-(\frac{2+\pi }{4} )x^2+\frac{\pi x^2}{8}[/tex].

Since it is given in the question that maximum light should be admiitted, we will differentiate the Area and set it to 0.

[tex]16-2(\frac{2+\pi }{4} )x+\frac{\pi x}{4}=0\\ 16=x(1+\frac{\pi }{4})\\ x=\frac{16}{1+\frac{\pi }{4}} \\x=8.96ft[/tex].

Therefore the exact value of x is 8.96ft.

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[tex]-2 + 6.45z - 6 + (-3.25z)[/tex]

Combine Like Terms:

[tex](6.45z+-3.25z)+(-2+-6)[/tex]

[tex]\fbox{3.2z - 8}[/tex]

Answer:  4

Step-by-step explanation

3^2×=6561

then think 3 raise to power what is 6561

the answer is 8

3^2×=3^8

three cancel three

2×=8

divide both sides by 2

then ×=4

In this case, the coefficient of determination is 0.5297, which means that 53% of the sample variation in Final grades is explained by the sample regression equation.

The data file contains the midterm and final scores of 32 students in a statistics course. To estimate a student's final score as a function of their midterm score, we used a regression analysis. The regression equation was Final = 27.5818 + 0.6774 Midterm. This equation can be used to predict the final score of a student based on their midterm score. The standard error of the estimate was 14.947. This indicates the accuracy of the estimated final score. The coefficient of determination was 0.5297, which means that 53% of the sample variation in final grades is explained by the regression equation. This tells us that the regression equation is a relatively good predictor of a student's final score.

Given:

Midterm Score = x

Final Score = y

Regression Equation: y = 27.5818 + 0.6774x

Standard Error of the Estimate = 14.947

Coefficient of Determination = 0.5297

Calculating Final Score:

y = 27.5818 + 0.6774x

y = 27.5818 + 0.6774(x)

y = 27.5818 + 0.6774(x)

y = 27.5818 + 0.6774(x)

y = 27.5818 + 0.6774x

Final Score = 27.5818 + 0.6774(Midterm Score)

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It is said that the rural landscape has been replaced by the urban landscape because rural landscapes have been transformed into urban ones.

We have to:

At present, more and more rural spaces become urban, which is why it is indicated that the urban landscape is replacing the rural one.

¡Hope this helped!

Answer:

now

Step-by-step explanation:

d= √(X2 _ X1) +(Y2 - Y1). = (5 -2 )+ (-4- 1)=

The solution is Option D.

The value of x from the triangle is x = 31

What are similar triangles?

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be ABC

The measure of side AB = 14.5

The measure of side BC = 15.5

Let the second triangle be XYZ

The measure of side XY = 29

The measure of side YZ = x

Now , if the triangle ABC is similar to triangle XYZ , then the corresponding sides of the triangles will be equal in ratio

So , the equation will be

XY / AB = YZ / BC

Substituting the values in the equation , we get

29 / 14.5 = x / 15.5

On simplifying the equation , we get

x/15.5 = 2

Multiply by 15.5 on both sides of the equation , we get

x = 2 x 15.5

x = 31

Therefore , the value of x is 31

Hence , the value of x of side YZ is 31

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Option B  [tex]n_{1} = 27 ,n_{2} = 29[/tex]  are the two sample sizes cannot be true.

HYPOTHESIS TEST

Given that:

The degree of freedom for the test of two independent population means is 56.

Degrees of freedom for two independent populations are well known.

[tex]n_{1} + n_{2} - 2[/tex]

[tex]n_{1} + n_{2} - 2[/tex] = 56

[tex]n_{1} + n_{2}[/tex] = 54

Total sample sizes = 54

Option B (   [tex]n_{1} = 27 ,n_{2} = 29[/tex] ) cannot be true.

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callback restricted is a function that is passed as an argument to another function

It tests whether the condition returned by the callback function holds for at least one item in array.

What is an array?

It should be noted that an array means a data structure that can store a fixed size collection of elements.

In this case, the true statement of the array is that it tests whether the condition returned by the callback function holds for at least one item in array.

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The value of f(g(2)) from the given functions f(x) and g(x) is 3.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are f(x)=2x²+1 and g(x)=3x-5.

We need to find f(g(2)).

Put x=2 in the function g(x)=3x-5, we get

g(2)=3×2-5

= 6-5

= 1

So, g(2)=1

Put x=1 in the function f(x)=2x²+1, we get

f(g(2))=2(1)²+1

= 2+1

=3

Therefore, the value of f(g(2)) is 3.

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The amount allowed for housing and expenses is $2023.73.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Gross pay = $2759

Deduction:

7.65%

= 7.65/100 x 2759

= $211.06

12%

= 12/100 x 2759

= $331.08

7%

= 7/100 x 2759

= $193.13

The remaining amount.

= 2759 - 211.06 - 331.08 - 193.13

= $2023.73

Thus,

The amount allowed is $2023.73.

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The length of the vector v is approximately 4.24. A vector is a mathematical object that has both magnitude and direction

Vectors are commonly used in physics, engineering, and other fields to represent quantities that have both magnitude and direction, such as velocity, acceleration, and force. They are also important in linear algebra, where they can be used to represent lines and planes in space, and to solve systems of linear equations.

The vector v can be expressed in component form as v = <2-5, 10-7> = <-3, 3>.

To express the vector v as a linear combination of the unit vectors i and j, we can write it as v = (-3)i + 3j.

To find the length of the vector, we can use the Pythagorean theorem:

length of v = sqrt((-3)^2 + 3^2) = sqrt(9 + 9) = sqrt(18) = 3*sqrt(2) = 4.24

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Answer:

b and c

Step-by-step explanation:

For the given equation the value of n is equal to option D.

n = (s/180) + 2.

As given in the question,

Given equation is equal to  :

s = (n-2)180

Now take all the terms on one side and term n on other side of the equation we have,

Divide both the side by 180 we get,

s/ 180 =  [(n-2)180]/180

s/180 = n -2

Add 2 both the side of the equation we get,

(s/180 ) + 2 = n -2 + 2

(s/180 ) + 2 = n

so here the value is equal to

n = (s/180) +2.

Therefore, the value of n in the equation is equal to option D.

n = (s/180) + 2.

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Answer:

99 inches

Step-by-step explanation:

1 foot=12 inches

8x12=96

96+3=99

The probability that the person is a woman is 40%.

P(Glasses) = P(M ∩ G) + P(W ∩ G)

P(Glasses) = 0.45 × 0.40 + 0.55 × 0.20

P(Glasses) = 0.27

P(Woman) = P(W ∩ G) / P(Glasses)

P(Woman) = 0.55 × 0.20 / 0.27

P(Woman) = 0.44

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By taking minimum perimeter the value of length and width will both be [tex]\sqrt{5A}[/tex].

Perimeter is basically the sum of all sides of a figure.

The perimeter of a rectangle is 2l + 2w where l = length and w = width of rectangle.

Since the perimeter needed in this question is minimum, the figure must be a square and not a rectangle. For a square, area = a^2

5A = a^2

a = l = w = [tex]\sqrt{5A}[/tex]

Hence, both the length and width are equal to [tex]\sqrt{5A}[/tex].

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a. P = [tex]\left[\begin{array}{ccc}\frac{2}{3} &\frac{1}{3} &0 \\\\\frac{2}{9} &\frac{5}{9} &\frac{2}{9}\\ \\0&\frac{2}{3} &\frac{1}{3} \end{array}\right][/tex]

b. P[[tex]x_{3} = 2[/tex]] = 0.18

c. p = 0.8353

d   [tex]\pi _{1} = \frac{1}{2} \\\\\pi _{2} = \frac{1}{6} \\\\\pi _{0} = \frac{2}{6}[/tex]

Given that:

{[tex]x_{n}[/tex] ; n > 0} is a Markov chain

[tex]x_{n}[/tex] denotes no of black balls in Urn A after [tex]n^{th}[/tex] round of exchange.

Clearly know that no of black balls in Urn A cannot exceed.

Hence, state space is {0, 1,2}

Transition probabilities can be

(a) [tex]P_{00}[/tex] = P [white ball is selected from A & white ball is selected from B]

          = P [white ball from A] × P [white ball from B]

           = [tex]\frac{2}{3}[/tex]

   [tex]P_{01}[/tex] = P [white ball from A & black ball from B ]

         = [tex]\frac{1}{3}[/tex]

   [tex]P_{10}[/tex] = P [black ball from A & white ball from B]

         = [tex]\frac{2}{9}[/tex]

   [tex]P_{11}[/tex] = P [black ball from A &  black ball from B]

              or P [white from A & white from B]

          [tex]= \frac{1}{3} * \frac{1}{3} + \frac{2}{3} *\frac{2}{3}\\ \\ = \frac{1}{9} + \frac{4}{9}\\ \\= \frac{5}{9}[/tex]

    [tex]P_{12}[/tex] =  P [white from A & white from B]

          = [tex]\frac{2}{9}[/tex]

    [tex]P_{21}[/tex] =  P [black ball from A & white ball from B]

          = [tex]\frac{2}{3}[/tex]

     [tex]P_{22}[/tex] =   P [white from A & white from B]

           = [tex]\frac{1}{3}[/tex]

Transition probability matrix P = [tex]\left[\begin{array}{ccc}\frac{2}{3} &\frac{1}{3} &0 \\\\\frac{2}{9} &\frac{5}{9} &\frac{2}{9}\\ \\0&\frac{2}{3} &\frac{1}{3} \end{array}\right][/tex]

(b) The probability that after 3 exchanges, there are exactly 2 black balls in Urn A.

P[[tex]x_{3} = 2[/tex]]

given initial distribution

[tex]p [x_{0} = 0] = 0 , p [x_{0} = 1] = 1 , p [x_{0} = 2] = 0[/tex]

p[tex][x_{3} = 2] =[/tex] ∑ i = 0 to 2 P [tex][x_{3} = 2 , x_{0} =i ][/tex]

              = ∑ i = 0 to 2 P [tex][x_{3} = 2 , x_{0} =i ][/tex]  . P[tex][ x_{0} = i][/tex]

              =  ∑ i = 0 to 2 P [tex]i^{2^3}[/tex] P[tex][ x_{0} = i][/tex]

Transition probability matrix can be calculated by increasing power of P matrix to 3 i.e [tex]P^{3}[/tex]

P[[tex]x_{3} = 2[/tex]] = 0.18

(c) The probability that by the time we have done 3 exchanges, there has never been 2 black balls in Urn A.

[tex]P[x_{3} \neq 2 , x_{2} \neq 2, x_{1} \neq 2 | x_{0} = 1 ][/tex]

p = 0.8353

(d) Long run proportions of state 0,1,2.

[tex]\pi _{0} = \frac{2}{3} \pi _{0} + \frac{2}{3} \pi _{1}[/tex]

[tex]\pi _{1} = \frac{1}{3} \pi _{0} + \frac{5}{9} \pi _{1} + \frac{2}{3} \pi _{2}[/tex]

[tex]\pi _{2} = \frac{2}{9} \pi _{1} + \frac{1}{3} \pi _{2}[/tex]

[tex]\pi _{0} + \pi _{1} + \pi _{2} = 1[/tex]

[tex]\pi _{0} = \frac{2}{3} \pi _{1} \\[/tex]

[tex]\pi _{2} = \frac{1}{3} \pi _{1}[/tex]

[tex]\pi _{1} [\frac{1}{3} + \frac{2}{3} + 1 ] = 1[/tex]

[tex]\pi _{1} = \frac{1}{2} \\\\\pi _{2} = \frac{1}{6} \\\\\pi _{0} = \frac{2}{6}[/tex]

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Answer:

2x+9<25 or u just can say c