Please help me i'm struggling!

The optimal values of these parameters are:

a. β₁ = 0

b. β₂ = 0

The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:

SSE = 382 + 681 + 382 + 18β1β2

Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.

Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0

Now, we need to find the partial derivative of SSE with respect to β1.

∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0

Therefore, we obtain the optimal value of β2 as 0.

Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0

Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.

Thus, the optimal values of β1 and β2 are 0 and 0, respectively.

Therefore, the answers are: a. β₁ = 0 b. β₂ = 0

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Answer:

Step-by-step explanation:

You need to give all the fractions a common denominator so you can compare the numerators.

The least common multiple of 5, 8, 16, 4, 3 is 240.

⅖ = 96/240

⅞ = 210/240

15/16 = 225/240

¾ = 180/240

⅜ = 90/240

⅓ = 80/240

The only numerator between 96 and 210 is 180.

180/240 = ¾

⅖ < ¾ < ⅞

Answer:

10.9%

Step-by-step explanation:

You want to do the number of ways that can happen, which is \(_8C_2 = 28\) divided by the total number of possibilities which is \(2^8\) to get 10.9%

Answer:

5/9 or 55.5%

Step-by-step explanation:

there are 5 numbers divisible by 4, 12-20 inclusive:  4, 8, 12, 16, 20

there are 9 numbers from 12-20, inclusive

answer would be 5/9

1st quartile: 11

median: 38.50000

3rd quartile: 45

Measure descriptive statistics

1st quartile: 11

median: 38.50000

3rd quartile: 45

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I understand that the question you are looking for is :

2 Drag the tiles to the boxes to form correct pairs. Match the values associated with this data set to their correct descriptions.  {6, 47, 49, 15, 43, 41, 7, 36} first quartile 38.5  median 11  third quartile 10.5 the difference of the largest value and the median 45

Answer: C

Step-by-step explanation:

For our unknown value x, the opposite side = 10 and the adjacent side = 18, using this information you can use SOH CAH TOA.

TOA refers to opposite over adjacent, which would be

tan x = 10/18.

Hope this helps!

There were 360 students surveyed who liked exactly one of the three types of music means that out of the total number of students surveyed, 360 of them expressed a preference for only one of the three music types.

To find the number of students who liked exactly one of the three types of music, we need to subtract the students who liked two or three types of music from the total number of students who liked each individual type of music.

Let's define:

R = Number of students who like rock

C = Number of students who like country

J = Number of students who like jazz

Given the information from the survey:

R = 204

C = 164

J = 129

We also know the following intersections:

R ∩ C = 24

R ∩ J = 29

C ∩ J = 29

R ∩ C ∩ J = 9

To find the number of students who liked exactly one type of music, we can use the principle of inclusion-exclusion.

Number of students who liked exactly one type of music =

(R - (R ∩ C) - (R ∩ J) + (R ∩ C ∩ J)) +

(C - (R ∩ C) - (C ∩ J) + (R ∩ C ∩ J)) +

(J - (R ∩ J) - (C ∩ J) + (R ∩ C ∩ J))

Plugging in the given values:

Number of students who liked exactly one type of music =

(204 - 24 - 29 + 9) + (164 - 24 - 29 + 9) + (129 - 29 - 29 + 9)

= (160) + (120) + (80)

= 360

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a) The value of critical value t_α/2 needed to construct a 95% confidence interval is,

tα/2 = 2.002.

b)  If the sample size were n = 15, an additional assumption that would need to be made for the confidence interval to be valid is that the population follows a normal distribution.

a. To find the critical value tα/2 needed to construct a 95% confidence interval with a sample size of n = 61, we can use a t-distribution table or calculator with 60 degrees of freedom (df = n - 1) and α = 0.05.

From the table or calculator, we find that tα/2 = 2.002.

Therefore, we can construct the 95% confidence interval using the formula:

CI = x ± t_α/2  (S / √(n))

where x is the sample mean, S is the sample standard deviation, and sqrt(n) is the square root of the sample size.

b. If the sample size were n = 15, an additional assumption that would need to be made for the confidence interval to be valid is that the population follows a normal distribution.

When the sample size is small, the t-distribution is used to account for the increased uncertainty due to the small sample size.

However, the t-distribution approximates the normal distribution only when the sample size is large (typically n > 30).

When the sample size is small, the normality assumption is critical for the validity of the confidence interval.

If the population does not follow a normal distribution, alternative methods such as non-parametric tests may be needed.

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The 2 real solutions are rational and irrational solutions.

Quadratic Formula is the simplest method to find the roots of a quadratic equation. There are particular quadratic equations that cannot be easily factorized, and here we use this quadratic formula to find the roots in the quickest possible way.

Quadratic Formula: The roots of a quadratic equation ax² + bx + c = 0 are given by x = [-b ± √(b² - 4ac)]/2a.

The value b² - 4ac is called the discriminant of a quadratic equation and is represented as 'D'. The nature of the roots of the quadratic equation can be predicted based on the discriminant value.

If D > 0, the roots are real and distinct (two real solutions).

If D = 0, the roots are real and equal (one real solution).

If D < 0, the roots do not exist, or they are imaginary (two imaginary solutions).

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Two rays with a common endpoint form an angle. An angle is defined as a geometric figure formed by two rays that share a common endpoint. In other words, an angle is formed when two rays emanating from a common point, and this common point is known as the vertex.

The rays are the sides of the angle, and the angle is measured in degrees. Angles have different measures, ranging from 0 degrees to 360 degrees. The two rays that make up an angle are also called the sides or arms of the angle. The angle is measured in degrees, and the size of the angle depends on the distance between the two sides of the angle that meet at the vertex.

In geometry, an angle can be named in different ways, depending on the context in which it is being used. Angles are essential in mathematics, physics, and other scientific fields, where they are used to measure the rotation of an object, determine the direction of an object, and in other applications involving rays and lines. Two rays with a common endpoint form an angle.

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Question in English:

Tom has 2,021 gold coins. He divides them into piles containing consecutive numbers of pieces. if it has more than two piles, how much is in the highest pile?  

Plzzzzz give me Brainliest!!!!!  

The missing value in Diamond Problem 10 is 34.

The missing values in Diamond Problem 9 are 23.

The missing value in Diamond Problem 11 is X.

To complete the Diamond Problems, we need to follow the pattern shown on the right side of the question.

Diamond Problem 9:

-10 | 33

_|

برا | S

To find the missing values, we add the numbers in the opposite corners of the diamond:

برا + S = -10 + 33 = 23

Therefore, the missing values in Diamond Problem 9 are 23.

Diamond Problem 10:

12 | 3.4

|

10 | 15

To find the missing values, we multiply the numbers in the opposite corners of the diamond:

10 * 3.4 = 34

Therefore, the missing value in Diamond Problem 10 is 34.

Diamond Problem 11:

X | V₂

|

T | ?

To find the missing value, we add the numbers in the opposite corners of the diamond:

T + V₂ = X

Therefore, the missing value in Diamond Problem 11 is X.

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Given that a coin is biased such that a head is twice as likely to occur as a tail, the probability of getting a head is 2/3 and the probability of getting a tail is 1/3.

The expected number of tails when this coin is tossed twice can be calculated using the formula:
E(X) = ∑xp(x)
Where E(X) is the expected value, x is the number of tails, and p(x) is the probability of getting x tails.
There are three possible outcomes when the coin is tossed twice:
1) Two tails: The probability of this happening is (1/3) * (1/3) = 1/9

2) One tail and one head: The probability of this happening is 2 * (1/3) * (2/3) = 4/9
3) No tails (two heads): The probability of this happening is (2/3) * (2/3) = 4/9

So the expected number of tails is:
E(X) = (2 * 1/9) + (1 * 4/9) + (0 * 4/9) = 2/9 + 4/9 = 6/9 = 2/3
Therefore, the expected number of tails when this coin is tossed twice is 2/3.

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Answer:

huh i dont understand

Step-by-step explanation:

Using a calculator, we can calculate sin 84° right away by typing it there and the answer would be:

sin 84° = 0.9945218954

Since the question is asking us to round it to the nearest hundredth, meaning two places after the decimal, the answer will be 0.99.

Answer: See Explanation

Step-by-step explanation:

1st term = an= - 5n + 8 = -5(1) + 8

= -5 + 8

a1 = 3

2nd term = an= - 5n + 8 = -5(2) + 8

= -10 + 8

= -2

3rd term = an= - 5n + 8 = -5(3) + 8

= -15 + 8

= -7

4th term = an= - 5n + 8 = -5(4) + 8

= -20 + 8

= -12

5th term = an= - 5n + 8 = -5(5) + 8

= -25 + 8

= -17

Answer:

0.62 cents

Step-by-step explanation:

divide 5 and 3.10

hope this helps:)

The ability to order items in a sequence, such as longest to shortest, is known as Seriation.

Seriation is a cognitive skill that involves arranging objects, events, or ideas in a particular order or sequence. It is a crucial aspect of cognitive development and is typically acquired during early childhood. Seriation is the ability to mentally order objects along a quantitative dimension, such as size, weight, or length.

Seriation involves comparing and ordering items based on specific criteria. For example, if given a group of objects of different lengths, a child who has developed seriation skills will be able to arrange the objects in order from shortest to longest. Similarly, if given a group of numbers, a child who has developed seriation skills will be able to arrange them in order from smallest to largest.

Seriation is an important cognitive skill that is used in various areas of life, including academic, professional, and personal domains. It allows individuals to organize information and ideas in a logical and meaningful way, which can facilitate more efficient processing and understanding of complex concepts.

Overall, seriation is a fundamental cognitive skill that plays a crucial role in various aspects of life, including problem-solving, decision-making, and organization. It is an essential skill that supports the development of higher-order thinking skills, such as analysis, evaluation, and synthesis.

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The correct option is the fourth one, the slope and y-intercept are different.

Here we have the linear equation:

3x - 5y = 4

We know that it is dilated by a scale factor of 5/3, so let's find the dilation.

We can rewrite the linear equation as:

-5y = 4 - 3x

y =  (3/5)x - 4/5

Now let's apply the dilation:

y = (5/3)*[ (3/5)x - 4/5]

y = x - 4/3

Then we can see that the slope and the y-intercept are different, the correct option is 4.

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The linear approximation of f(x) = x²e^x at x=0 is simply 2x which is none of the options provided.

The linear approximation to f(x) = x²e^x is given by _____.

The formula for linear approximation is given by

f(x) ≈ f(a) + f'(a)(x - a) where a is a constant and f'(a) is the derivative of f at x = a.

We are given that f(x) = x²e^x. Therefore, f'(x) = (x + 2)e^x.

Let a = 0, then

f(0) = 0

and f'(0) = 0 + 2 = 2

The linear approximation is given by

f(x) ≈ f(0) + f'(0)x= 0 + 2x= 2x

Therefore, the linear approximation to f(x) = x²e^x is given by 2x.

So the answer is none of the options provided.

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The correct option is option D

The total number of Yogs used for a bonfire, if 5 new logs are added each hour​

the rectangular coordinates corresponding to the polar coordinates (5, π/6) are approximately (4.33, 2.5).

To convert polar coordinates to rectangular coordinates, you can use the following formulas:

Given polar coordinates (r, θ), where r represents the distance from the origin (or pole) to the point, and θ represents the angle between the positive x-axis and the line connecting the origin to the point:

Rectangular coordinate x = r * cos(θ)

Rectangular coordinate y = r * sin(θ)

Here's a step-by-step process for converting polar coordinates to rectangular coordinates:

1. Identify the given polar coordinates (r, θ).

2. Use the formula x = r * cos(θ) to calculate the rectangular coordinate x.

3. Use the formula y = r * sin(θ) to calculate the rectangular coordinate y.

4. The rectangular coordinates (x, y) represent the equivalent representation of the given polar coordinates.

For example, let's say we have polar coordinates (r, θ) = (5, π/6). To convert these to rectangular coordinates:

x = 5 * cos(π/6) = 5 * (√3/2) = 5√3/2 ≈ 4.33

y = 5 * sin(π/6) = 5 * (1/2) = 5/2 = 2.5

So, the rectangular coordinates corresponding to the polar coordinates (5, π/6) are approximately (4.33, 2.5).

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Answer

1. f - 3/4

2. 62 + h

Step-by-step explanation:

1. 1/4 of the fish are angelfish, all fish are one whole, one whole - 3/4's = 1/4

2. we dont have the value of H so we in turn have to figure out the equation and 62 + h is the only answer we can come to

Points J, K, and L are collinear. Point K is between J and L,

JL = 17y - 15, JK = 5y + 10, and KL = 9y + 2. Then the Value of JL = 17y - 15

In geometry, collinear points lie on the same straight line. Given three collinear points J, K, and L where K lies between J and L, we are tasked with finding the length of JL based on the expressions for JK and KL in terms of the variable 'y'.

1. Understanding the Problem: We are given that J, K, and L are collinear points, with K between J and L. The lengths of segments JK, KL, and JL are represented by the expressions 5y + 10, 9y + 2, and 17y - 15 respectively, where 'y' is a variable we need to solve for.

2. Using Segment Addition Postulate: According to the segment addition postulate, the sum of the lengths of two smaller segments is equal to the length of the larger segment they form. Applying this to our problem, we have: JK + KL = JL.

3. Substituting Lengths: Substituting the given expressions for JK and KL, we get: (5y + 10) + (9y + 2) = 17y - 15.

4. Solving for 'y': Now, let's solve for 'y'. Combine like terms on the left side: 14y + 12 = 17y - 15.

5. Isolating 'y': Subtract 14y from both sides: 12 = 3y - 15.

6. Further Isolation: Add 15 to both sides: 27 = 3y.

7. Final 'y' Value: Divide by 3: y = 9.

8. Finding JL: Now that we have the value of 'y', we can substitute it back into the expression for JL: JL = 17(9) - 15.

9. Calculating JL: Multiply: JL = 153 - 15 = 138.

Through the application of the segment addition postulate and algebraic manipulation, we determined that the length of segment JL is 138 units.

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Answer:it is the fist car

Step-by-step explanation:

Because im so fudgen smart

Answer: Ratio

Step-by-step explanation:

The time of day measured in military time can be considered a ratio variable because it has a clear definition of 0 and the differences between the values are meaningful. For example, the difference between 1800 and 1900 is the same as the difference between 1900 and 2000. In addition, the ratio of any two values can be calculated, such as the ratio of 1800 to 1900. This is not the case for the other levels of measurement, which do not have a clear definition of 0 or allow for the calculation of ratios.

The expression after simplifying with the first rule of radicals is 9√5.

A square is a two-dimensional figure that has four sides and all four sides are equal.

The area of a square is side²

We have,

Area of a square = side² _______(1)

Area = 405 square feet _______(2)

From (1) and (2) we get,

405 square feet = Side²

Side = √405 feet

[ 405 = 81 x 5 ]

Side = √(81 x 5)

[ 9² = 81 ]

Side = 9√5

Thus,

The side length is 9√5 feet.

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The graph of the function f(x) = 5\((x-3)^{5/3}\) have a vertical asymptote at x = 3.  The correct answer is option (b) concave up on (-∞, ∞), no points of inflection.

The graph of the function f(x) = 5\((x-3)^{5/3}\) can be described as follows:

a) Concavity: The concavity of the graph refers to the shape of the curve. To determine the concavity, we need to analyze the second derivative of the function. Taking the derivative of f(x) twice, we get:

f'(x) = 5 * (5/3) * \((x - 3)^{(2/3)}\)

f''(x) = (25/9) *\((x - 3)^(-1/3)\)

The second derivative f''(x) is defined for all x except x = 3, where the denominator becomes zero. Therefore, we have a vertical asymptote at x = 3.

b) Points of Inflection: Points of inflection occur where the concavity changes. To find the points of inflection, we need to identify where the second derivative changes sign. Since f''(x) is always positive, there are no points of inflection in this case.

Based on the above analysis, the correct answer is option b) concave up on (-∞, ∞), no points of inflection. The graph is concave upward throughout the entire domain, and there are no points where the concavity changes (no points of inflection).

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