consider a linear regression model where is a random vector with , , and no further assumptions are made about is an by deterministic matrix, and is invertible. is an unknown constant. let denote the least squares estimator of in this context. determine whether each of the the following statements is true or false. is the maximum likelihood estimator for .

the value of P(Z>-1.56) is 0.9406

The value of P(Z<0.26) is 0.6026

For a standard normal distribution,

the standard normal distribution is also known as the Z - distribution

it is a very special type of distribution in which the value of mean is zero and the value of standard deviation is one.

the formula of standard normal distribution is

[tex]f(x)=\frac{1}{\sigma\sqrt{2\pi } } e^{\frac{-1}{2}(\frac{x-\mu}{\sigma})^2 }[/tex]

(OR)

Z=[tex]\frac{x-\mu}{\sigma}[/tex]

where

[tex]\mu[/tex] is the value of mean

[tex]\sigma[/tex] is the value of standard deviation

f(x) is the probability density function

now,

the value of P(Z>-1.56) is

P(Z> -1.56) = 1 - P(Z< -1.56)

                  => 1 - 0.05938

                  => 0.94062  (By rounding to 4 decimal places we get)

                  => 0.9406

P(Z<0.26)    = 1 - P(Z<0.26)

                    => 0.60257 (By rounding to 4 decimal places we get )

                     => 0.6026

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13.3 is the interquartile range of the data set.

Given,

The midterm scores of an algebra class of 20 students;

69 84 52 93 81 74 89 85 88 63 87 64 67 72 74 55 82 91 68 77

We have to find the interquartile range using r.

Interquartile Range;-

The second and third quartiles, or the centre half of your data set, are contained in the interquartile range (IQR). The interquartile range provides the range of the middle half of a data set, whereas the range provides the spread of the entire data set.

Interquartile range = Q3 - Q1

Q1 is the lower quarter

Q3 is the upper quarter

Q2 is the median

Here,

Q2 = 63 + 87 / 2 = 150 / 2 = 75

Q1 = 81 + 74 / 2 = 77.5

Q3 = 74 + 55 / 2 = 64.5

Then,

Interquartile range = Q3 - Q1 = - (64 . 5 - 77.5) = 13.3

That is,

The interquartile range for the given data set is 13.3

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The surface area of a church window bounded above by a parabola and below by the arc of a circle is 2.750x^2, rounded to three decimal places.

Let x be the length of the window. The radius of the arc of a circle is x/2.

Surface area = [Area of parabola] + [Area of arc of a circle]

= (1/2)x^2 + (π/2)*(x/2)^2

= (1/2)x^2 + (π/4)x^2

= (π/4 + 1/2)x^2

= (1 + π/4)x^2

= 2.75x^2

Answer: 2.750

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By applying formulas of logistic growth we can find the answers as part (a) P(t) = 1800 / (1+3e^(-0.8t)) and part(b) 1.37 years

In a logistic growth the growth rate decreases with the passage of time until the growth reaches the maximum capacity at infinite time.

The formula is f(t) = L / (1+ ye^(-kt))

where L is the maximum value, k is the growth rate, y is a constant and t is time.

Part(a)

In this case, L = 1800, k = 0.8 yr-1

f(t) = 1800 / (1 + ye^(-0.8)t)

at t = 0 , f = 450,

450 = 1800/ (1+y)

solving this gives, y = 3

Thus the final answer is f(t) = 1800/ (1+ 3e^(-0.8t))

Part(b)

we need to find the time when f(t) = 900

900 = 1800/(1+3e^(-0.8t))

t = 1.37 years

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Step-by-step explanation:

p = a + 3

Three more a than p

The critical values for a 95% confidence interval using the chi-square distribution with 15 degrees of freedom are roughly 21.02 and 32.36.

The critical value for the 95% confidence interval using the 15 degrees of freedom chi-square distribution is the value that divides the distribution into two;

lower tail and upper tail. These values ​​are calculated such that the area under the curve of the chi-square distribution between the critical values ​​represents 95% of the total area under the curve.

To find critical values, you can use a chi-square table or a computer program that calculates critical values ​​for a given confidence level and degree of freedom.

In this case, the critical value for the 95% confidence interval with 15 degrees of freedom can be determined as follows:

Lower critical value:

The lower critical value is the value corresponding to the area under the chi-square distribution curve to the left of the value, equal to 2.5% (half of 5% not included in the confidence interval). Using a chi-square table or computer program, we can find that the lower critical value for the 95% confidence interval with 15 degrees of freedom is approximately 21.02. Upper critical value:

The upper critical value is the value corresponding to the area under the chi-square distribution curve to the right of the value, equal to 2.5% (half of 5% is not included in the confidence interval).

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The coefficient values will indicate the change in the dependent variable (hrswork) for a one-unit change in the independent variable (wage, educ, and nchild).

To examine this, we would use a regression analysis to look at the relationship between each of these variables and the hours worked per week. We would create a model with wage, educ, and nchild as the independent variables, and hrswork as the dependent variable. We can then analyze the coefficient of each of these variables to measure the effect they have on the hours worked per week. The coefficient values will indicate the change in the dependent variable (hrswork) for a one-unit change in the independent variable (wage, educ, and nchild).

1. Load the work hrs.rds dataset.

2. Examine the data to identify the independent and dependent variables. In this case, the independent variables are wage, educ, and nchild, and the dependent variable is hrswork.

3. Use a regression analysis to examine the relationship between the independent and dependent variables.

4. Create a model with wage, educ, and nchild as the independent variables, and hrswork as the dependent variable.

5. Analyze the coefficient of each of the independent variables to measure the effect they have on the dependent variable (hrswork).

6. Interpret the results to determine the effect of the independent variables on the dependent variable.

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The area of parallelogram with the vertices is √269 when vertices are P(1, 0, 2), Q(3, 3, 3), R(7, 5, 8), and S(5 , 2, 7).

Given that,

The vertices are P(1, 0, 2), Q(3, 3, 3), R(7, 5, 8), and S(5 , 2, 7).

We have to find the area of parallelogram with the vertices.

We know that,

PQ=Q-P=(3,3,3) -(1,0,2)=(2,3,1)

PR=R-P=(7,5,8) -(1,0,2)=(6,5,6)

Find area using cross product as

Area= |PQ x PR|

=|i (3(6)-1(5)) - j (2(6)-1(6)) + k (2(5)-3(6)) |

= |i (18 - 5) - j (12 -6) + k (10 -18) |

= |{13; 6; -8}|

=√(13²+6²+(-8)²)

=√269

Therefore, the area of parallelogram with the vertices is √269 when  vertices are P(1, 0, 2), Q(3, 3, 3), R(7, 5, 8), and S(5 , 2, 7).

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The required adjacent interior angle is the angle angles that lie later or former to the given angle.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,
Consider a triangle,
In triangle, there are three angles in triangle
Each of the angle is adjacent with the other two lying former and later in the sequence.

Thus, the required adjacent interior angle is the angle angles that lie later or former to the given angle.

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Answer: B; B. 0.2673>0.2562

Step-by-step explanation: So, let's focus on the decimals, we already know that 0.26 IS GREATER than 0.25. All the other expressions are showing the smaller number as greater, or equal to, I hoped this helped!

A linear recurrence relation is homogeneous if f(n) = 0. The order of the recurrence relation is determined by k. We say a recurrence relation is of order k if an = f(an−1,...,an−k).

Given: a)  an = 3an-1 + 4an-2 +5an-3

We note that the given recurrence relation is linear, because the right-hand side is a linear combination of previous terms. We note that the given recurrence relation is homogeneous, because the recurrence relation does not contain any constant terms. The degree of the recurrence relation is the largest value k for which are occurs in the recurrence relation.

k=3

Given: b) an = 2nan-1 + an-2

We note that the given recurrence relation is not linear, because the right-hand side is not a linear combination of previous terms (due to the

fact that 2n is not a constant). We note that the given recurrence relation is homogeneous, because the recurrence relation does not contain any constant terms.

Given: c) an = an-1 + an-4

Because the right-hand side is a linear combination of the prior terms, we observe that the provided recurrence relation is linear. Given that there are no constant terms in the recurrence relation, it is important to observe that it is homogenous. The biggest value k for which are k appears in the recurrence relation is the recurrence relation's degree.

Degree of linear homogeneous recurrence are k=3 .

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The required equation that following the pattern is n = 4s+1. So the option c is correct.

In the given question, we have to choose which equation below relates the number of squares, n, in a picture to the size number, s.

The given options are:

a) n = s+4

b) n = 4s

c) n = 4s+1

d) s = 4n

We find the pattern we firstly observe the given diagram closely.

As we can see that in first diagram have 5 blocks.

In second diagram have 9 blocks.

In third diagram have 13 blocks.

So, if the number of squares, represent by n, in a picture and the size number, represented by s, so the required equation that following the pattern is n = 4s+1. So the option c is correct.

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The coordinates of the endpoints of the segment T'V' are equal to: A. T'(-3, 6) and V'(0, 3).

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.

Next, we would have to dilate the coordinates of triangle TVW by using the following transformation rule with a scale factor of 3/4: (x, y)  →  (3x/4, 3y/4)

For coordinate T, we have;

Coordinate T = (-4, 8)  →  (3/4(-4), 3/4(8)) = Coordinate T' = (-3, 6).

For coordinate V, we have;

Coordinate V = (0, 4)  →  (3/4(0), 3/4(4)) = Coordinate V' = (0, 3).

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Answer:

A. T'(-3, 6) and V'(0, 3)

Step-by-step explanation:

Answer:

Step-by-step explanation:

disc=8²-4×1×15=64-60=4=2²>0

it is a  perfect square and >0

so it has one repeated rational number solution.

On solving the provided question, Mark the remaining distances with infinite and your chosen beginning node with a current distance of 0.

In a graph that may, for instance, represent a network of roads, Dijkstra's Method is an algorithm for determining the shortest routes between nodes. Computer scientist Edsger W. Dijkstra created it in 1956, and it was published three years later. Algorithms come in a wide variety.

Here is how the algorithm is described:

Mark the remaining distances with infinite and your chosen beginning node with a current distance of 0.Make current node C the non-visited node with the shortest current distance. You should double the distance between your current node C and each of its neighbors, N, by the weight of the edge that connects C and N. Make it the new current distance of N if it is less than the current distance of N. C is the current node; mark it as visited.

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The value for cotangent of ∠V is 55.6°.

What is pythagora's theorem?

Cotangent = adjacent / opposite

Pythagoras theorem,

WV² = XW² + VW²

9² = x² + (√57)²

x² = 81 - 57

= 24

x = √24

= 4.89

cot (v) =  √24 /  √57

v = cot⁻¹ (0.6488)

v = 55.6°

Hence, the value for cotangent of ∠V is 55.6°.

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The correct answer is D) As C increases, the margin becomes larger, which decreases bias but potentially increases variance.

In the Support Vector Classifier (SVC), the parameter C controls the trade-off between the model's complexity and the amount of training error that it is allowed to have. A larger value of C means that the model will be more complex, and therefore will have a larger margin.

This will decrease the bias of the model but may increase the variance.

On the other hand, a smaller value of C means that the model will be less complex and will have a smaller margin, which will increase the bias of the model but potentially decrease the variance.

So, in summary, as C increases, the margin becomes larger, which decreases bias but potentially increases variance.

Hence, the correct answer would be an option (D).

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Dy/dx = (dy/dt)/(dx/dt) denotes the slope of the tangent line of a parametric curve whose parametric equations are x = /(t) and y = g(t). Wherever dy/dt is zero and dx/dt is zero, a parametric curve has a horizontal tangent.

The x and y coordinates are defined as functions of t when parametric form is used to represent angles: Plot the entire circle by using the equations x = r cos t and y = r sin t. Polar equations are the name given to these parametric equations.

The given x=1+12+ dx=dt 0+12(1) =12

Parametric y Curve is as follows: ts-t dy 5t-1 dt z = ts+t dz dt 5t +1 (dz, dy, dz) = (12, 5t-1, St+1) dt 7 dt dt x = 13 =) When, 1+12 t = 13 12

(x(t), y(t), and z(t)) = (13,0,2) + + (12, 4, 6) x(t), y(t), and 2(t)) = (13+12t, ut, 2+ 6+) x(t) = 13+12t, y(t) = ut, 2(t).

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Full Question = Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

x = 1 + 12 t , y = t5 − t, z = t5 + t; (13, 0, 2)

x(t), y(t), z(t) =

The final equation that represent the given table is s=f+2. So the option c is correct.

In the given question, the pattern in this table continues.

We have to check which equation below relates the number of squares to the figure number.

a) s=4f+1

b) s=2f+3

c) s=f+2

d) f=2s+3

From the given table;

f(1) = 5, f(2) = 7, f(3) = 9, f(4) = 11, f(5) = 13

If we check closely the value of f(x), we can see that the difference between each number is of 2.

So if we want to write the function as

f(1) = 5,

f(2) = f(1)+2 = 7,

f(3) = f(2)+2 = 9,

f(4) = f(3)+2 = 11,

f(5) = f(4)+2 = 13

So the final equation that represent the given table is;

s=f+2

So the option c is correct.

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The measurement of the largest angle of the quadrilateral is 108°

Given,

Quadrilateral;

A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.

Here,

Three shortest sides of the quadrilateral are congruent.

Both diagonals are as long as the longest side.

That is,

Side 1 ≅ Side 2 ≅ Side 3

Side 4 = Diagonal 1 = Diagonal 2

Then,

The largest angles of the quadrilateral will be 108°

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Answer: B. 21.77%

Step-by-step explanation: See picture. I'm currently taking the test right now

Answer:

  (b)  21.77%

Step-by-step explanation:

Using the given tax rate table, you want to know the effective tax rate on a taxable income of $192,700.

The tax will be the sum of the taxes due in each of the brackets. This sum can be simplified to make the tax computation a little less work.

  tax = 0.10(10275) +0.12(41175 -10275) +0.22(89075 -41175) +0.24(17050 -89075) +0.32(192700 -170050)

  = 10275(0.10 -0.12) +41175(0.12 -0.22) +89075(0.22 -0.24) +170050(0.24 -0.32) +192700(0.32)

  = 192700(0.32) -(10275(0.02) +41175(0.10) +89075(0.02) +170050(0.08))

  = 192,700(0.32) -19708.50

  tax = 41955.50

The tax as a percentage of the taxable income is ...

  tax/income × 100% = 41955.50/192700 × 100% ≈ 21.77%

The effective tax rate is about 21.77%.

__

Additional comment

We can use this same idea to simplify the tax table all around. The various tax computations are shown in the second attachment. Interestingly, the tax due is the maximum of the computations for the different brackets. The graph shows the effective tax rate (%) as a function of income. The effective rate for $192,700 is marked.

Because the tax tables are written with discontinuities, there can be some confusion about the amount that fits in each bracket. For example, the tax on 10276 is not 10% of 10275 plus 12% of zero. Rather it is 10% of 10275 plus 12% of (10276 -10275), for a total of $1027.62.

<95141404393>

You are just couple of steps away from completing the proof.

So far you have concluded that two sides of triangles ZTX and WVY are congruent. You need to complete it for the third side and prove the triangles are congruent. Then use it to complete the proof.

Missing statement and reasons given below.

       Statement                                             Reason                        

a= -14.

[tex]5 + 2a = a - 9[/tex]

[tex]5 + 2a -5= a - 9-5\\ \\2a=a-14[/tex]

[tex]2a-a=a-14-a\\\\a=-14[/tex]

[tex]5 + 2(-14) = (-14) - 9\\ \\5-28=-23\\ \\-23=-23[/tex]

Both sides are equal to each other, hence a= -14 is the correct solution.

a= -14.

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Percentage change in company's sales is  11%

What is percentage?

In arithmetic, a proportion may be a range or magnitude relation expressed as a fraction of a hundred. it's usually denoted victimisation the percentage sign, "%", d. A proportion may be a dimensionless number; it's no unit of measuring.

Main body:

According to the question:

company's sales in year 1 = $330,000

company's sales in year 2 =$367,500

Change = $ 367500 – 330000 = $ 37,500

Percentage change = $ 37500 / $ 330000 = 0.11

Percentage change = 11%

Hence ,Percentage change in company's sales is  11%.

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the total pressure exerted on the sphere when it is at the bottom of the pond is 8∛2 ≈ 10.08

The volume of a hemisphere is given by the formula ...

 V = (2/3)πr³

Then the radius is ...

 r = ∛(3V/(2π))

 r = ∛(3·1071.79/(2·3.14)) ≈ ∛512.00 ≈ 8.00

The radius of Sarah's pond is 8 inches.

We can see from the above that the radius is proportional to the cube root of the volume. If Sarah wants to double the volume, she needs to multiply the radius by ∛2 ≈ 1.260.

The pressure will be 8∛2 ≈ 10.08

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Answer:

x is 3 and y is -3

Step-by-step explanation:

[tex]x + y = 0 \\ x + y - y = 0 - y \\ x = - y \\ \\ 8x + 9y = 3 \\ (8 \times - y) + 9y = 3 \\ - 8y + 9y = 3 \\ y = 3[/tex]

X = -3

Answer:

No, because [tex]5+6<12[/tex]

Step-by-step explanation:

The side lengths do not satisfy the triangle inequality.

Answer:

46°

Step-by-step explanation:

As m<UYX and m<W is corresponding angle because X is the midpoint of UV and Y is the midpoint of UW, therefore

m<W = 46°

I hope my answer helps you.

Answer:

m<W = 46 degrees

Step-by-step explanation:

UX = UV/2  ==> This is because X is the mid-point of UV, dividing UV by 2

                           to make UX

UY = UW/2 ==> Y is the mid-point of UW, dividing UW by 2 to make UY

XY = VW/2 ==> Since X is the midpoint of UV and Y is the midpoint of UW,

                          segment XY is exactly in the middle of point U and              

                          segment VW, so segment XY is half of segment VW.

Since all sides of the small triangle(ΔUXY) are exactly half of all sides in the big triangle(ΔUVW), The corresponding angles in each triangle are equal to each other:
Hence,  m<UYX = m<UWV

m<UWV ==> m<W = 46 degrees  ==> since m<UYX=46, m<W = 46 as well

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Mr. Keith's semimonthly salary is $16183.25.

What is rounded to the nearest cent?

If the number is five or higher and is to the right of the full cents, increase the cents by one. The cents should remain the same if the number is four or less.

For instance: $143.864. Consider the last digit, 4, since it is less than 5 and the cents should remain the same. Rounding up from $143.864 to $143.86.

Given that the annual salary of Mr. Keith is $64,733.

Semiannual means 4 times in yearly.

Thus divide whole salary by 4 to get semimonthly salary.

Therefore the semimonthly income is  $64,733/4 = $16183.25 (rounded to the nearest cent)

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