SVM & Kernel Methods Problem 1 (10 points) In this problem we would like to compare the solutions of hard and soft SVMs on a linearly seperable dataset. Let n > 1 be a fixed number. Is it true that there exists C > 0 such that for every sample S of n training examples with binary label, which are linearly separable, the hard-SVM and the soft-SVM (with parameter C) solutions will return exactly the same weight vector. Justify your answer. (Hint: consider n = 2, d = 1 and S = {(x1, yı), (x2, y2)}. Let a > 0 and consider x1 = a, yı = 1, X2 = –a, y2 = -1. Derive the optimal solution for hard and soft SVM and compare the results.)

[tex](2x^3)^2\cdot (3x)^4\implies (2^2 x^{3\cdot 2})\cdot (3^4x^4)\implies 4x^6\cdot 81x^4 \\\\\\ (4)(81)x^{6+4}\implies 324x^{10}[/tex]

Answer: There are 40 questions on Ethan's test.

Step-by-step explanation: To find what 32 is 80% of, you must first convert 80% to a decimal (.8).

Next, divide 32 by .8.

[tex]32/.8 = 40[/tex]

The polynomial can be written as a product of polynomials as (3xy³ - 5x²y⁴)(3xy³ + 5x²y⁴)

option C.

To rewrite the polynomial as the product of its form, we will factor the polynomial as shown below;

9x²y⁶ − 25x⁴y⁸ = x²y⁶(9 − 25x²y²)

The function (9 − 25x²y²), can factored using difference of two squares;

(9 − 25x²y²) = 3² − (5xy)²

3² − (5xy)² = (3 - 5xy)(3 + 5xy)

The final equation as the product of its factors is calculated as;

9x²y⁶ − 25x⁴y⁸ =  x²y⁶(3 - 5xy)(3 + 5xy)

= (3xy³ - 5x²y⁴)(3xy³ + 5x²y⁴)

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Answer:

78.8888888889 or just round to 79

Step-by-step explanation:

Your welcome. Can you please mark me brainliest please? :)

Answer:

78.8888888889

Step-by-step explanation:

Answer: the price of the item 8 years from today is approximately $1475.

Step-by-step explanation:

The given exponential function to model the future price of the item is:

P(t) = P(0) * (1.026)^t

Here, P(t) represents the price of the item t years from today, and P(0) is the current price of the item.

1. To find the current price, we need to find P(0):

P(0) = 1200 * (1.026)^0

Since any number raised to the power of 0 is 1:

P(0) = 1200 * 1

P(0) = $1200

So, the current price of the item is $1200.

2. To find the price 8 years from today, we need to find P(8):

P(8) = 1200 * (1.026)^8

Using a calculator:

P(8) ≈ 1200 * 1.229057

P(8) ≈ $1474.87

Rounded to the nearest dollar:

P(8) ≈ $1475

So, the price of the item 8 years from today is approximately $1475.

Since g(x) = x² - 6x - 16, a statement which is true include the following: C. The zeros are -2 and 8, because the factors of g are (x+2) and (x-

8).

In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;

y = ax² + bx + c

Where:

Next, we would solve the quadratic function by using the factorization method as follows;

g(x) = x² - 6x - 16

0 = x² - 6x - 16

0 = x² - 8x + 2x - 16

0 = x(x - 8) + 2(x - 8)

(x - 8)(x + 2)

x = 8 or x = -2.

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The number of rooms of the same size it willl vaccum in 3 hours is 10

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

Unit rate = 3/10 hour per room

Time = 3 hours

using the above as a guide, we have the following:

Number of rooms = Time/Unit rate

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

Number of rooms = 3/(3/10)

Evaluate the quotient

Number of rooms = 10

Hence, the number of rooms is 10

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The student's argument that y=x/9 does not represent a proportional relationship between x and y is false because there is constant factor which shows the proportional relationship.

A proportional relationship exists between two variables if they are related by a constant factor, meaning that multiplying one variable by a constant results in the other variable. However, this constant can also be obtained by dividing one variable by the other, as in the case of y=x/9.

To see why, we can rearrange the equation to x=9y, which shows that x is proportional to y with a constant factor of 9. Multiplying y by 9 results in x, just as dividing x by 9 results in y. Therefore, the relationship between x and y is still proportional, regardless of whether we multiply or divide to obtain the constant factor.

In general, we can say that a relationship between two variables is proportional if it can be written in the form y=kx, where k is a constant. It does not matter whether we use multiplication or division to express this constant, as long as it is the same for all values of x and y.

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The first semi-annual interest payment with a credit to in the amount of $109.556.15

Given that, a company issues $50,000 of 8%, 10-year bonds dated January 1 that pay interest semiannually on June 30 and December 31 each year.

We need to find the amount,

[tex]A = P(1+r/2)^{2t}[/tex]

[tex]A = 50,000(1+0.08/2)^{2(10)[/tex]

[tex]A = 50,000(1.04)^{20[/tex]

[tex]A = 109,556.15[/tex]

Hence, the first semi-annual interest payment with a credit to in the amount of $109.556.15

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Answer:

Step-by-step explanation:

To distribute the expression 18+(d+3)(d-3)(4), you can use the distributive property of multiplication, which states that a(b+c) = ab + ac.

Here's how you can apply the distributive property to the expression:

First, simplify the expression inside the parentheses by using the difference of squares formula: (d+3)(d-3) = d^2 - 3d + 3d -9

(d+3)(d-3) = d^2 - 9

So now the expression becomes:

18 + (d^2 - 9)(4)

Next, use the distributive property to multiply 4 by each term inside the parentheses:

18 + 4d^2 - 36

Simplify by combining like terms:

4d^2 - 18

So the final result is 4d^2 - 18

Answer:

6.7 = π(r^2)(33.5/12)

r = .874

75/(2 × .874) = 42.9 = 42 barrels

6.7 = (3.14)(r^2)(33.5/12)

r = .874

75/(2 × .874) = 42.9 = 42 barrels

Answer:

Step-by-step explanation:

ask ur teacher

0.034141137 o sobre 17/500

A. The domains and ranges of both functions are not restricted.

For f(x) = 5/8x + 1, any real number can be plugged in for x, so the domain is (-∞, ∞). Similarly, any real number can be obtained by evaluating the function, so the range is also (-∞, ∞).

For g(x) = 2/3x^3, any real number can be plugged in for x, so the domain is (-∞, ∞). As x is cubed, the range can be negative or positive infinity, or any real number in between, so the range is also (-∞, ∞).

Therefore, both functions have unrestricted domains and ranges.

The correct answer is A.

Answer: 1085

Step-by-step explanation:

Answer:

If you called at 11:45 pm and were on the phone for 1 hour 24 minutes, the call would have ended at 1:09 am.

The value of angle 1 given the value of angle 4 as 47° will be 133°

Parallel lines are two lines on a two-dimensional plane that, no matter how far they are extended, never collide. They always keep the same gap between them.

Parallel lines have the same slope, which means they have the same angle of inclination or steepness. In other words, they rise and fall at the same pace along their length.

The value will be:

= 180° - 47°

= 133°

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The price at the point of equilibrium is 105

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

The supply/demand graph

The price at the point of equilibrium is the price where the lines/curves of the supply and the demand functions intersect

Using the above and the graph as a guide, we have the following:

Price = 105 when demand = supply

Hence, the price at the point of equilibrium is 105

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Question

Using the above supply/demand graph, what is the price at the point of equilibrium? a. 105 b. 100 c. 95 d. 80

Answer:16x-4-2x+8=14x+4

Step-by-step explanation:

In order to solve this question you first want to multiply everything inside the bracket by the number outside.

4(4x-1)

so 4 times 4x which is 16x and 4 times -1 which is -4 so the first bracket is

(16x-4)

then do the same for the second bracket

-2(x-4)

so -2 times x would be -2x and -2 times -4 would be 8

for the final step collect the like terms and solve

so your answer would be

16x-2x which would be 14x and -4+8 which would be 4

so in conclusion the answer is

14x+4

Answer:

Step-by-step explanation:

a. Using the formula p(t) = 1 - e^(-kt), where k = 0.28:

Probability of mastering the dance's steps in 1 trial: p(1) = 1 - e^(-0.28*1) ≈ 0.243

Probability of mastering the dance's steps in 2 trials: p(2) = 1 - e^(-0.28*2) ≈ 0.446

Probability of mastering the dance's steps in 5 trials: p(5) = 1 - e^(-0.28*5) ≈ 0.846

Probability of mastering the dance's steps in 11 trials: p(11) = 1 - e^(-0.28*11) ≈ 0.981

Probability of mastering the dance's steps in 16 trials: p(16) = 1 - e^(-0.28*16) ≈ 0.997

Probability of mastering the dance's steps in 20 trials: p(20) = 1 - e^(-0.28*20) ≈ 0.999

b. The rate of change, p'(t), can be found by taking the derivative of the function p(t):

p'(t) = k * e^(-kt)

c. Here's a graph of the function p(t):

I apologize for the technical issue, but the graph doesnt load, so here's a description of the graph:

The graph of p(t) should be an increasing curve that starts at 0 and approaches 1 asymptotically. As t increases, the rate of change of p(t) decreases, which means that the curve becomes flatter and approaches the horizontal asymptote of y=1. The curve is concave down, meaning that its rate of change is decreasing. At t=0, the rate of change is k, which is the steepest point of the curve.

_______________________

graph of p(t) = 1 - e^(-0.28*t)

The x-axis represents the number of learning trials, and the y-axis represents the probability of mastering the dance's steps. As the number of trials increases, the probability of mastering the steps approaches 1 (or 100%).

Answer: 504 different ways.

Step-by-step explanation:

      This situation uses a permutation. We will use the given formula and simplify to solve. n is equal to the number of contestants and r is 3 since we are selecting and first-, second-, and third-place winner.

Given:

      [tex]\displaystyle P = \frac{n!}{(n-r)!}[/tex]

Substitute values:

      [tex]\displaystyle P = \frac{9!}{(9-3)!}[/tex]

Subtract:

      [tex]\displaystyle P = \frac{9!}{6!}[/tex]

Multiply:

      [tex]\displaystyle P = \frac{9*8*7*6*5*4*3*2*1}{6*5*4*3*2*1}[/tex]

Simplify using the knowledge that something divided by itself is 1:

      P = 9 * 8 * 7

Multiply:

      P = 504

      We can also think of it as 9 different people could win 1st, 8 different people could win 2nd, and 7 different people could win 3rd. 9 * 8 * 7 = 504. However, the steps above show why this works with the formula as well.

By calculating the median of the data, the meteorologist can claim that Portland tends to receive more rainfall than Seattle.

The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than. Hence, the median also represents the 50th percentile of a data-set.

The ordered data-sets for each city are given as follows:

The median is the middle element for each data-set, hence it is given as follows:

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Rounding to the closest hundredth, the final result is 12.16 mL, which is the amount of the drug that should be administered.

The patient's weight must first be converted from pounds to kilograms.

1 lb = 0.453592 kg

Therefore, 134 lb = 60.78 kg

The dose must then be determined depending on the patient's weight:

60.78 kg times 5 mg/kg equals 303.9 mg.

Now that we know the medication's concentration, we need to determine how much to deliver.

25 mg/mL x 125 mg/5 mL

The dosage for 303.9 mg is as follows:

303.9 mg x 25 mg/mL = 12.16 mL

The final result, rounded to the closest hundredth, is 12.16 mL.

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The change of base formula log 55 / log 3. The base we use to solve via change of base formula is Base 10. The value of x = 55.

The logarithmic expression given is

log₃ 55 = x

To solve for x using the change of base formula, we can use the formula

logₐ b = log c / log a

where a, b, and c are positive real numbers and a ≠ 1.

Using this formula, we can rewrite the given expression as

log x / log 3 = log 55 / log 3

We can simplify this expression by canceling out log 3 on both sides

log x = log 55

Now, we can use the definition of logarithms, which states that if log a b = c, then [tex]a^c[/tex] = b. Using this definition, we get

x = 55

Therefore, the solution is x = 55, rounded to the nearest hundredth of a decimal.

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The cost per ounce of the premium walnut is $0. 23

To determine the value of the cost, we need to note that proportion is simply described as the comparison of numbers such  that they are made equal to another.

From the information given, we have that;

54 ounces of premium walnuts costs $12.95

This is represented as;

54 ounces = $12. 95

Then 1 = x

cross multiply the values, we get;

x = $12.95/54

Divide the values, we get;

x = $0. 23

Hence, the value is $0. 23 per premium walnut

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The point of intersection between a Inverse Functions and its inverse occurs at (2, 2).

The point of intersection between a function and its inverse occurs when the input and output values are the same for both functions.

To find the point of intersection, we need to find the value of x where f(x) = f-1(x).

In this particular case, we can see from the graph that the point of intersection occurs at (2, 2).

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Differentiating y = x^3 ln 2x/e^x Sin x is: y' = x^2 [(3 ln 2x/e^x Sin x + 3/x) - 2 ln 2x/e^x Sin x cos x + cos x].

Differentiate y can be find using the product and chain rule.

Using the chain rule

v'(x) = [1/(2x/e^x)] * (2e^x - e^x*2x) / (2x/e^x)^2

v'(x) = [e^x(2-e^x)] / (2x)^2

Using the product rule

y' = 3x^2 ln(2x/e^x) sin(x) + x^3 [e^x(2-e^x)] / (2x)^2 sin(x) + x^3 ln(2x/e^x) cos(x)

Simplifying

y' = 3x^2 ln(2x/e^x) sin(x) + (x/2) [2-e^x] sin(x) + x^3 ln(2x/e^x) cos(x)

So,

derivative of y is:

y' = 3x^2 ln(2x/e^x) sin(x) + (x/2) [2-e^x] sin(x) + x^3 ln(2x/e^x) cos(x)

Therefore the differentiate of y is 3x^2 ln(2x/e^x) sin(x) + (x/2) [2-e^x] sin(x) + x^3 ln(2x/e^x) cos(x).

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