In a study to determine whether miles driven is a good predictor of trade-in value, 11 cars of the same age, make, model, and condition were randomly selected. The following scatterplot shows trade-in value and mileage for those cars. Five of the points are labeled A, B, C, D, and E, respectively.
E $6,500+ А $6,000 B $5,500+ $5,000+ $4,500+ Value $4,000 + + 50 60 70 80 90 100 Miles Driven (thousands) Which of the five labeled points is the most influential with respect to a regression of trade-in value versus miles driven?

Answer:

[tex]f(x)=x^2(x-a)^2(x-b)^4(x-c)[/tex]

Step-by-step explanation:

There is a double root at [tex]x=0[/tex], which corresponds to [tex]x[/tex] raised to an even power.

There are also 2 more double roots and one more single root. This corresponds to two factors raised to an even power and one factoe raised to an odd power.

The only option that satisfies this is Option 1.

The graphical representation of the polynomial function is given by the relation f ( x ) = x² ( x - a )²( x - b )⁴ ( x - c )

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Identify the even and odd multiplicities of the polynomial functions' zeros.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities

Given data ,

Let the polynomial equation be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = x² ( x - a )²( x - b )⁴ ( x - c )

The factors (x - a), (x - b), and (x - c) indicate that the function has roots at x = a, x = b, and x = c. These roots are of multiplicity 2, 4, and 1 respectively, which means that they are repeated in the factors (x - a)², (x - b)⁴, and (x - c), respectively.

The factor x² indicates that the graph of the function opens upward, since the leading coefficient is positive.

Overall, the graph of this function will have eight "humps" or "bumps" corresponding to its eight roots, and the heights and shapes of these bumps will depend on the values of a, b, and c.

Hence , the graph of the function is plotted

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In mathematics, Stirling's approximation (or Stirling's formula) is a factorial approximation. A good approximation that gives accurate results even for small values ​​of n. It is named after James Stirling and was first given by Abraham de Moivre, although relevant but less accurate.

Factorial is one of thein mathematics. It is also an important mathematical concept ubiquitous concepts used in data science. Factors are used to model probability distributions in Poisson processes. The probability mass function of the Poisson distribution has a factorial formula in the denominator. You can't find the probability of a Poisson random variable without a way to compute the factorial.

Factorials are also related to combinatorics. For example, hmm! is the number of permutations of n unique objects. From the point of view of statistical mechanics, entropy is defined as a combinatorial problem. Entropy also has its own definition in information theory. Comparing the two alternative definitions, they are identical.

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After analyzing the given data we will get to know that all the options mentioned above are true.

A = BUC, B is a singleton set, and A = CU2 if A is the set of all prime numbers, B is the set of all even prime numbers, and C is the set of all odd prime numbers. Therefore, option D - All of the specified - is the answer to this question.

We've got

The entire set of prime numbers is A.

A = {2, 3, 5, 7, 11, 13}

B is a collection of even prime numbers.

B = {2}

C is a collection of all odd prime numbers.

C = {3, 5, 7, 11, 13,}

We are aware that the only even prime number is two. As a result, Set B is a singleton set because it only has one element.

Additionally, if we combine sets B and C, we will obtain set A, which contains all prime numbers.

Thus, we obtain A = B U C.

Since B = 2 is a singleton set, if we have A = B U C, we can also say A = C U 2.

Therefore, each of the aforementioned choices is appropriate.

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Answer:

there was 30 people at her birthday party

The number of capybaras that you will get after 14 days is given as follows:

3 capybaras.

Initially, the number of capybaras that you have is given as follows:

2 capybaras.

The pattern is then given as follows:

The time composed by 14 days is of 2 weeks, then the procedure will finish on the Monday 2 weeks from now.

The number of capybaras in that Monday than can be calculated step by step as follows:

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The transfer function for the given integrator circuit in terms of frequency,f and imaginary unit,j is expressed as [tex]T(f)=-j0.00628f[/tex]

The figure of the integrator is shown at bottom of the answer.

The transfer function of an integrator can be expressed in form of impedances of the circuit elements connected to the op-amp.

Assume the impedance at the input side be [tex]Z_1[/tex] and impedance of the feedback be [tex]Z_2[/tex]

We can observe that at input, in consists of capacitor with capacitance,C [tex]= 0.1\mu F=10^{-7}F[/tex]

and at the feedback loop, the circuit element is a resistor with resistance,R [tex]= 10k\Omega = 10^4 \Omega[/tex]

Now,

the transfer function for an integrator can be written as ,

[tex]T(f) = -\frac{Z_2}{Z_1}[/tex]

We know that,

impedance of capacitor is [tex]Z_1=\frac{1}{j\omega C}=\frac{1}{j2\pi f C}[/tex]

impedance of resistor is [tex]Z_2=R[/tex]

Now,

[tex]T(f)=-\frac{R}{\frac{1}{j2\pi fC}}\\\\T(f)=-R*j2\pi f C\\\\T(f)=-j10^4*2\pi f 10^{-7}\\\\T(f)=-j0.00628f[/tex]

Hence, the transfer function is [tex]T(f)=-j0.00628f[/tex]

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Answer:

I don't know the answer of this questions

Answer:

30/4+5•3-9

= 7.5+15-9

= 22.5-9

= 13.5

Step-by-step explanation:

Answer: The answer is 3

Step-by-step explanation: I’m smart.

x= 3.

[tex]19 - 4x = 2x + 1[/tex]

[tex]19 - 4x-19 = 2x + 1-19\\ \\-4x=2x-18[/tex]

[tex]-4x-2x=2x-18-2x\\ \\-6x=-18[/tex]

[tex]\frac{-6x}{-6} =\frac{-18}{-6} \\ \\x=3[/tex]

[tex]19 - 4(3) = 2(3) + 1\\ \\19-12=6+1\\ \\7=7[/tex]

That's correct. Therefore, x= 3 is the correct answer!

The classification of the triangle according to its side lengths and vertices would be scalene triangle.

To classify the triangle, you first need to find the lengths of the sides of the triangle. You can do this by finding the distance between the vertices given.

To find the vertices, the formula is:

= √ ( ( x₂ - x₁ ) ² + ( y ₂ - y ₁) ² )

The length of AB is therefore 3.61 units

The length of BC is 8.54 units

The length of AC is 10 units.

None of the side lengths of this triangle are the same so it is a scalene triangle.

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The value of the standard deviation does not change and remains the same.

Given, a retired statistic professor has recorded final exam results for decades. the mean final exam score for the population of a student is 82.4 with a standard deviation of 6.5.

The mean μ = 82.4

The standard deviation σ = √[ ((x - μ)2 + (y - μ)2 + (z - μ)2)/3 ]

we have to find the variance,

We now add a constant k to each data value and calculate the new mean μ'.

μ' = ((x + k) + (y + k) + (z + k)) / 3 = (x + y + z) / 3 + 3k/3 = μ + k

We now calculate the new mean standard deviation σ'.

σ' = √[ ((x + k - μ')2 +(y + k - μ')2+(z + k - μ')2)/3 ]

Note that x + k - μ' = x + k - μ - k = x - μ

also y + k - μ' = y + k - μ - k = y - μ and z + k - μ' = z + k - μ - k = z - μ

Therefore σ' = √[ ((x - μ)2 +(y - μ)2+(z - μ)2)/3 ] = σ

If we add the same constant k to all data values included in a data set, we obtain a new data set whose mean is the mean of the original data set PLUS k. The standard deviation does not change.

Hence, the standard deviation does not change.

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The relationship between x and y is and the constant of variation is 24.

What is inversely proportional?

One kind of proportionality relationship is inverse proportion. If two quantities are inversely related, one will increase while the other will decrease. Building a wall would be an example of an inverse proportion in action.

Given that x and y are inversely proportion.

Assume that the relationship between x and y is

y = k/x where k is constant of variation.

Putting x = 3 and y = 8 in y = k/x :

8 = k/3

Multiply both sides by 3:

k = 8 × 3

k = 24

Putting x = 4 and y = 6 in y = k/x :

6 = k/4

Multiply both sides by 4:

k = 6 × 4

k = 24

The relationship is y = 24/x and the constant of variation is 24.

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Answer:

x and y are not inversely proportional.

Image:

The ounces of butter that are needed to make a pound of jelly is  3 ounce  .

In the question ,

it is given that ,

Samuel is using 1/5 of an ounce of butter to make 1/15 of a pound of jelly.

let the number of ounces of butter needed to make a pound of jelly be "x" .

So , the equation for the situation can be represented as

( 1/5 ounce butter)/(1/15 pound jelly) = x/( 1 pound jelly)

So ,after cross multiplication ,

we get ,

15/5 = x/1

So , x = 3  .

Therefore , the ounces of butter needed is 3 ounce .

The given question is incomplete , the complete question is

Samuel used 1/5 of an ounce of butter to make 1/15 of a pound of jelly. How many ounces of butter are needed to make a pound of jelly ?

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The equivalent measure of the angle when converted from radians to degrees is 128.57 degrees

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

Angle = \large \frac{5\pi}{7}radians to degrees.

This angle can be properly expressed

So, we have the following representation

Angle = 5π/7 radians

Also, the angle can be further expressed

So, we have the following representation

Angle = 5/7 π radians

As a general rule of angle conversion, we have

π radians = 180 degrees

Substitute the known values in the above equation, so, we have the following representation

Angle = 5/7 * 180 degrees

Evaluate the products

Angle = 128.57 degrees

Hence, the measure of the angle in degrees is 128.57 degrees

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Answer the angle when converted from radians to degrees is 128.57 degrees

Angle = 5π/7 radians

Angle = 5/7 π radians

π radians = 180 degrees

Angle = 5/7 * 180 degrees

Evaluate the products

Angle = 128.57 degrees

Based on the information , the store that gives the best deal is Store A .

Inn the question ,

it is given that ,

the original price for the shoes that Samuel is buying is = $80 .

the discount offered by Store A is = 25% ,

So , the effective price is = 80 - 0.25 of original price  

Substituting the values  ,

we get ,

= 80 - 20

= $60

the discount offered by Store B is = $10

So , the effective price is = 80 - 10 = $70 .

So , the price of shoe is less in store A in comparison to store B .

Therefore , the best deal is given by Store A .

The given question is incomplete , the complete question is

Samuel is buying a pair of boots with an original price of $80. Store A is offering a 25% discount off the original price of all boots. Store B is offering a $10 discount off the original price of all boots .

Based on this information, which store gave the best deal ?

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The radius of the sphere with the given point and the center is √238.

Here we have to find the radius of the sphere.

Given data:

The point on the surface of a sphere is (-4, -6, 10) and the point on the center is (2, 3, -1).

The formula for the radius:

r² = (x2 - x1)² + (y2 - y1)² + (z2 - z1)²

where (x1, y1, z1) = point on the center

(x2, y2, z2) = point on the sphere

Now putting the values we have

r² = (-4-2)² + ( -6-3)² + ( 10 +1)²

  =( -6)² +(- 9)²  + (11)²

  = 36 + 81 + 121

  = 238

r = √238.

Therefore the radius is √ 238.

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Triangle ABC and triangle XYZ are congruent thus ∆ABC and XYZ are similar

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects.

if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

line DY bisects AC and line ZE bisects line AB.

Therefore line AD is congruent to line AE and line CD is congruent to line EB.

therefore AB = CD and similar XY = YZ

therefore ∆ABC and ∆XYZ are similar

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Answer:

7pi/9

Step-by-step explanation:

subtract 360 from 500 as many times as you can

number left should be converted to radians

500 - 360 = 140

140 * (pi/180) =

140Pi/180 =

simplify by dividing by 20 top & bottom

7Pi/9

varsitytutors

The equation of the line parallel to y = 6 and passing through (-1, 8) is y = 8.

The slope or gradient of a line is a number that describes both the direction and the steepness of the line.

Given that, an equation of the line that passes through (-1, 8) and is parallel to the line y = 6.

Slope of the parallel lines are equal to each other, therefore, solving for c,

8 = -1x0 + c

c = 8

Hence, The equation of the line parallel to y = 6 and passing through (-1, 8) is y = 8.

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Answer:

25. y = 36

26. w = -4

Explanation:

25.

74 + 74 = 148

360 - 148 = 212

212 ÷ 2 = 106

106 = 2y + 34

106 - 34 = 2y

72 = 2y

72 ÷ 2 = (2y) ÷ 2

y = 36

26.

72 = 2w + 80

72 - 80 = 2w

-8 = 2w

-8 ÷ 2 = (2w) ÷ 2

w = -4

From given data we can conclude that there is no influence of age on how many hours a person spends doing/reading/answering emails in a week.

In this question, the given data has 2 categories of age and the number of hours per week someone spends on email.

Let H0(null hypothesis): age has any influence on how many hours a person spends doing/reading/answering emails in a week.

Ha = age has no influence on how many hours a person spends doing/reading/answering emails in a week.

36 and under   over 36       x - y          (x - y)²

      28                  0              28             784

       4                   2               2                 4

       2                   0               2                 4

      25                  1              24               576

      15                  5              10               200

       3                   2                1                  1

      15                  4               11               121

      20                  8               12               144

      10                  5                5                  25

       1                  10               -9                 81

                            Total :        86             1940

Using the formula for t-score:

t = (∑D / N)/[√(∑D² - (∑D)²/N)/(N-1)N]

where

∑D = sum of differences

∑D² = sum of squared differences

(∑D)² = square of sum of differences

t = (86 / 10)/[√(1940 - 7396/10)/(10-1)10]

t = 8.6/√((1940 - 739.6)/90)

t = 8.6 /√(1200.4/90)

t = 8.6 /√13.34

t = 2.35

The p-value with degree of freedom = 9 and alpha-level = 0.05 is 0.021653

Since calculated value is greater than the p-value, we reject the null hypothesis.

Therefore, age has no influence on how many hours a person spends doing/reading/answering emails in a week.

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Answer:

2

Step-by-step explanation:

Answer:

34

× 12

---------

8

60

40

+ 300

----------

= 408

Answer: True.

Because the trapezoid is isosceles, the base angles are congruent by default.

Given isosceles trapezoid ABCD

Sides AB and DC are congruent

By the SAS postulate, triangles ABC and DCB are congruent

Therefore, segment AC is congruent to segment DB

a) The length of segment A'B' is given as follows: 4 units.

b) The length of segment B'B is given as follows: 4 units.

The two similar triangles in this problem are given as follows:

ABC and A'B'C'.

Then side lengths of ABC are given as follows:

12, 9 and 2 + x.

The equivalent side lengths on triangle A'B'C' are given as follows:

y, 3 and 2.

When the triangles are similar, the side lengths are proportional, hence the following equation is built:

12/y = 9/3 = 2+x/2.

Then the length of segment A'B' is obtained as follows:

12/y = 9/3

12/y = 3

3y = 12

y = 12/3

y = 4.

The length of segment B'B is x, hence it is obtained as follows:

9/3 = 2+x/2.

2 + x = 6

x = 4 units.

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a. When vector is added to vector , the resultant is vector such that its magnitude and direction is proportional to the resultant magnitude and direction of the component vectors.

b. ∅ = (Rx/Ry)

Vectors are used to represent physical quantities in terms of magnitude and direction. Vectors can be added using the parallelogram method or the triangle addition method. The magnitude and direction of the resulting vector are generally proportional to the magnitude and direction of the component vectors.

I have every vector in 2D that has both vertical and horizontal components.

There are vectors say:  A = xi + yj

                              and, B =zi + wj

For example, adding two vectors gives the result

R = (x +z)i + (y + w) j.

The - component has y +w as z and the y component as w. The sum has the horizontal component as x + z and the vertical component as y + w. So we get the y component of the resulting vector R = A+ y component of B

The direction of the angle is found as

tan∅ = Rx/Ry

     ∅ = (Rx/Ry)

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Howard Steele needs to invest  $117,817.77 today so that he may withdraw $12,000 each year for the next 20 years

Simple interest is often a predetermined percentage of the principal amount borrowed or lent paid or received over a specific time period.

Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

We know the equation, [tex]P = \frac{A\times(1-(1+r)^{-n}}{r}[/tex] the annuity, and the present value of money, P, can be connected.

P = 12000, r = 0.08 and n = 20.

∴ [tex]12000 = \frac{A\times(1-(1.08)^{-20}}{0.08}[/tex].

A = $117,817.77.

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