Question
Newton's Law of Universal Gravitation: The gravitation attraction, f , between two objects of masses x and y is proportional to the product of the masses and inversely proportional to the square of the distance, d , between the objects.

Write an equation for the constant of variation, k, in terms of f, x, y, and d.

Complete the equation in the space below (do not enter “k=“)

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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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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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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Answer:

Step-by-step explanation:

1)

She takes medicine at the moment 0

24(1/2)^0

24 · 1

24 mg

2)

24 (1/2)^1

24 (1/2)

12 mg

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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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 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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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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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 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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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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One example of a problem involving multiplication of fractions that can be made easier using the associative property is as follows:

Given the expression (2/3) * (4/5) * (6/7), we can use the associative property to rearrange the terms and simplify the expression. Specifically, the associative property states that the order in which we perform operations does not change the result. In this case, we can rearrange the terms as follows:

(2/3) * (4/5) * (6/7) = (4/5) * (2/3) * (6/7)

Then, we can simplify the expression using the commutative property of multiplication (which states that the order of the terms does not affect the result of the multiplication):

(4/5) * (2/3) * (6/7) = (2/3) * (4/5) * (6/7)

Finally, we can simplify the expression by multiplying the fractions:(2/3) * (4/5) * (6/7) = (12/21).

Using the associative property allows us to rearrange the terms and simplify the expression, making the problem easier to solve.

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 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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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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As per the concept of probability, the probability of getting head is 99.5%.

The term probability in statistics is known as the possible way of getting the particular event.

Here we have given that

And we need to find the probability of getting  head.

Here we know that the number of coins is 10.

So, the sample space for the 10 coins is calculated as,

Here we already know that for each of the 10 coin tosses, we have either a head (H) or a tail (T).

so, the total number of probability of 10 coins is 210 strings in the sample space.

Here we know that the only option of all tails doesn't have head in it.

So, the number tosses that have head in it is calculated as,

=> 210 - 1

=> 209

Therefore, the probability is calculated as,

=> P = 209/210

=> P = 0.995

Therefore, the probability in percentage is 99.5%

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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 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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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.

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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:

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

Step-by-step explanation:

The side lengths do not satisfy the triangle inequality.

The City A and Abilene are nearest to each other

The Austin and Abilene are farthest apart from each other

Here the two angles of the triangle = 59 degrees and 64 degrees

The sum of the angles in a triangle is 180 degrees

Then the third angle will be

59 + 64 + x = 180

123 + x = 180

x = 180 - 123

x = 57 degrees

The third city name is not visible so consider it as city A

Part a

Here the smallest angle is 57 degrees

Opposite side of the angle will be the smallest distance

That is the distance between city A and Abilene

Part b

Here the largest angle is 64 degrees

The opposite side of the angle will be largest distance

That is the distance between Austin and Abilene

Therefore, the City A and Abilene are nearest to each other and Austin and Abilene are farthest apart from each other

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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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Answer: Thus, the present age of Queens University College is 45 years, and the present age of GAGE University College is 15 years.

Step-by-step explanation: Let Q be the present age of Queens University College and G be the present age of GAGE University College.

Since the present age of Queens University College is three times that of GAGE University College, we can write the equation Q = 3G.

After 5 years, the difference of their ages will be 30 years, so we can write the equation Q + 5 = G + 30.

Substituting the first equation into the second equation, we get 3G + 5 = G + 30.

Solving for G, we find that G = 15.

Substituting this value into the equation Q = 3G, we find that Q = 3 * 15 = 45.

Thus, the present age of Queens University College is 45 years, and the present age of GAGE University College is 15 years.

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!

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

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                        

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.

By using the mean formula, the mean grade across all four classes was 83.25%.

The mean is a measure of central tendency that represents the average value of a set of data

The formula for calculating the mean:

Mean = (x1 + x2 + x3 + ... + xn) / n

Where:

x1, x2, x3, ..., xn are the individual values in the set

n is the total number of values in the set

Mean = (74 + 82 + 86 + 91) / 4

Mean = 333 / 4

Mean = 83.25

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