work out the gradient of a line that passes through the coordinates (3,4) and (6,16)
Pls help fast , need for an assessment due today!
working out too please!!​

Simple linear regression is a statistical technique used to model the relationship between two variables by fitting a straight line to the data. It provides a way to predict or estimate the value of one variable (dependent variable) based on the value of another variable (independent variable).

In simple linear regression, the relationship between the independent variable (x) and the dependent variable (y) is represented by a straight line. The goal is to find the best-fitting line that minimizes the differences between the observed values of the dependent variable and the predicted values from the regression line.

A graph illustrating simple linear regression includes the scatterplot of the data points, the regression line, and the residuals. The scatterplot shows the individual data points with the independent variable on the x-axis and the dependent variable on the y-axis. The regression line is the line that best fits the data, minimizing the sum of the squared residuals.

Residuals are the vertical distances between the observed data points and the regression line. They represent the differences or errors between the actual values and the predicted values. By examining the residuals, we can assess how well the regression line fits the data. If the residuals are randomly scattered around zero, it suggests that the linear regression model is appropriate. If there is a pattern or systematic deviation in the residuals, it indicates that the model may not be capturing the underlying relationship accurately.

The regression line is constructed by minimizing the sum of the squared residuals, which is known as the least squares method. This ensures that the line represents the best linear approximation of the relationship between the variables.

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Answer:

36:9

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the age be xy or 10x + y.

Reverse the two digits of my age, divide by three, add 20, and the result is my age, convert this to equation:

We should consider both x and y are between 1 and 9 since both the age and its reverse are 2-digit numbers.

Possible options for x are:

and

So x can be 3 or 4.

So the age is 48.

The probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

The number of possible subcommittees that contain only undergraduate students can be calculated by choosing 3 members from the 4 undergraduate students. This can be done in

(4 choose 3) = 4 ways.

The total number of possible subcommittees of three students that can be formed from the 6 members of the committee can be calculated by choosing 3 members from the 6 students. This can be done in

(6 choose 3) = 20 ways.

Therefore, the probability that there will be no graduate students on the subcommittee is:

Number of subcommittees with only undergraduate students / Total number of possible subcommittees

= 4 / 20

= 1/5

= 0.2

So, the probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

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Step-by-step explanation:

If it looks like this: < with a line under it then it's called a less than or equal to sign.

If it looks like this: > with a line under it then it's a greater than or equal to sign

Answer:

420

Step-by-step explanation:

The monthly salary of Ward based on this annual salary is 5.53k

Annual salary = 66.4k

There are 12 months in a year

Monthly salary= Annual salary / 12

= 66.4k / 12

= 5.533333333333333

Approximately,

5.53k per month

Therefore, Ward receives monthly salary of 5.53k

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Mawi, inspired by the book "Beetles and Angels," experienced significant personal growth and transformation. In his dreams, he found himself both turning into a beetle and encountering angels, symbolizing his journey of self-discovery and spiritual enlightenment.

Additionally, Mawi read a book specifically about beetles and angels, which likely provided him with further inspiration and insight. Along his path, Mawi received support and guidance from various individuals who played pivotal roles in his development and progress.

Mawi's experience of dreaming about transforming into a beetle and encountering angels represents a metaphorical journey of self-realization. Just as beetles undergo metamorphosis, Mawi's dreams reflect his own transformation and growth as he navigates through challenges and strives for personal fulfillment. The presence of angels in his dreams suggests a spiritual dimension, indicating that Mawi's journey is not only physical and mental but also deeply connected to his values and beliefs.

The book Mawi read about beetles and angels likely provided him with valuable knowledge and insights. It could have served as a source of inspiration, offering him guidance on his own journey and helping him make sense of the symbolism in his dreams. By immersing himself in this literature, Mawi may have gained a deeper understanding of the potential for personal growth and spiritual exploration.

Crucially, Mawi's progress was not solely self-driven. Throughout his journey, he received support from various individuals who played important roles in his development. These people likely offered guidance, encouragement, and assistance, helping Mawi overcome obstacles and continue on his path of self-discovery. Their collective influence and involvement in Mawi's life further fueled his inspiration and contributed to his personal transformation.

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Not necessarily differentiability alone does not guarantee boundedness. Additional conditions, such as continuity, are needed to ensure boundedness.

It is true that if a function f is continuous on a closed bounded interval, then f is bounded on that interval. However, differentiability alone does not imply boundedness.

For example, consider the function f(x) = \(x^2\) on the interval [-1, 1]. This function is differentiable on the interval, but it is not bounded. As x approaches infinity, f(x) approaches infinity as well.

Another example is the function f(x) = 1/x on the interval [1, 2]. This function is also differentiable on the interval, but it is not bounded as x approaches 0 from the right.

Therefore, We can say that f does not guarantee boundedness.

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The probability that the wedding planner will have too many pollotarian meals is 0.998.

To calculate this, we can use the binomial probability formula. The binomial probability formula is used to calculate the probability of obtaining a certain number of successes in a certain number of trials. In this case, the number of trials is the total number of guests, and the number of successes is the number of guests who are pollotarian.

The formula is: P(x) =\(nCx * p^x * (1-p)^(n-x)\), where n is the number of trials, x is the number of successes, and p is the probability of success.In this case, n = 300, p = 0.03, and x = 9. Plugging these numbers into the formula, we get: P(x) = \(300C9 * 0.03^9 * (1-0.03)^(300-9)\) = 0.998.

Therefore, the probability that the wedding planner will have too many pollotarian meals is 0.998, or 99.8%.

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As a result, there are 180 students in the seventh grade.

A level οr prοgressiοn οn a scale, since abοut rank, success, excellence, wοrth, οr intensity: the highest grade οf paper. A stage οr phase in a cοurse and prοcess is a grοup οf peοple οr οbjects that have a same strength is relatively, quality, etc.

We can utilize percentage tο determine the tοtal quantity οf pupils in the class if 9 kids make up 5% οf a seventh-grade class. If we assume that there are x pupils inside the seventh grade οverall, we can calculate the prοpοrtiοn as fοllοws:

9 / x = 5 / 100

We may crοss-multiply and simplify tο find x's value:

9 × 100 = 5 × x

900 = 5x

x = 900 / 5

x = 180

In the seventh grade, there are 180 students.

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Answer: 6.8571 (Round as needed)

Hope this is correct

Step-by-step explanation:

This is a simple ratio problem

Using the similarity statement we can say 14:12, (ab:pq)

That is our ratio.

So we do 14/12 = 8/x, we solve this using algebra to get our answer.

Hope this is correct.

When performing a statistical analysis, we work with sample rather than the entire population because, we often lack manpower or resources to gather data. So option D is correct.

Statistical work is usually done with a sample. This is done because, if we try to include and collect data from the whole population, it will be very time consuming and need more manpower and resources. It will become a much tedious process.

So a sample which is representative of the whole population is needed. Selecting a sample size and determining the sample must follow certain criteria. They are population parameters we want to estimate, Cost of sampling, Variability of the population, how hard is it to collect data and how precise we want the final estimates to be. All these are taken into consideration and a sample that properly represent the population is determined without bias.

So, option D is the correct answer.

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Answer:

tig, get, tie, reg ger

Step-by-step explanation:

Answer:

\(x = - 1\)

\(y = 3\)

Step-by-step explanation:

\(y - 4x = 7(eqn \: 1)\)

\(2y + 4x = 2(eqn \: 2)\)

\(solving \: by \: eliminating \: one \: variable\)

\((y - 4x = 7)\)

\( + (2y + 4x = 2)\)

\(3y = 9\)

\(y = 3\)

\(y - 4x = 7\)

\(3 - 4x = 7\)

\( - 4x = 7 - 3\)

\( \frac{ - 4x}{ - 4} = \frac{4}{ - 4} \)

\(x = - 1\)

The solution to this system of linear equations will be (–1, 3). Then the correct option is D.

The solution of the equation means the value of the unknown or variable.

The equations are given below.

 y − 4x = 7   ...1

2y + 4x = 2  ...2

Add both equations, then we have

3y = 9

 y = 3

Put y = 3 in equation 1, then we have

3 − 4x = 7

     4x = –4

       x = –1

The solution to this system of linear equations will be (–1, 3).

Then the correct option is D.

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Answer:

15

Step-by-step explanation:

Answer:

Step-by-step explanation:

three units <3

If they run at the same speed, then William run 2 hour long.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given that Eliot and William went hiking. They went at the same speed. Let x mph be their speed.

Elliot:

Distance = 8 miles

Speed = x mph

Time  = 8/x hours

William:

Distance = 12 miles

Speed = x mph

Time= 12/x hours

then

8/x + 2/3 = 12/x

x = 6

So, William's hike was 12/6 = 2 hours long.

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The width of the plainfield is 56 yards, and the length is 216 yards.

Let's start by defining the variables we'll need to solve the problem. We'll use "P" to represent the perimeter of the plainfield, "l" to represent the length of the field, and "w" to represent the width of the field.

From the problem statement, we know that the perimeter of the plainfield is 544 yards, so we can write:

P = 544

The perimeter of a rectangle is given by the formula P = 2(l + w), so we can substitute our variables and get:

2(l + w) = 544

Simplifying this expression, we get:

l + w = 272

Now we need to use the information given about the relationship between the length and width of the field to write an equation that relates the two variables. We know that the length is 8 yards less than a quadruple of the width, so we can write:

l = 4w - 8

We can substitute this expression for "l" in the equation we derived earlier:

l + w = 272

(4w - 8) + w = 272

5w - 8 = 272

5w = 280

w = 56

So the width of the field is 56 yards. We can use the equation we derived earlier to find the length:

l = 4w - 8

l = 4(56) - 8

l = 216

So the length of the field is 216 yards.

Therefore, the width of the plainfield is 56 yards, and the length is 216 yards.

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Answer:

a=22.478

Step-by-step explanation:

Answer:

Angle DE = 11

Step-by-step explanation:

DE = DF

8x + 3 = 6x + 5

8x = 6x + 5 - 3

8x - 6x = 2

2x = 2

2x/2 = 2/2

x = 1

DE = 8x + 3

DE = 8(1) + 3

DE = 8 + 3

DE = 11

Hope this helps

Answer: 12 pints

Step-by-step explanation: if there are 8 pints in a gallon. We have 1 and 1/2 gallons

1 gal = 8 pints

1/2 gal = 4 pints

8 + 4 = 12 pints total

Answer:

12

Step-by-step explanation:

because there are 8 pints in a gallon so half a gallon is 4 pints 4+8=12

The estimated crop yield from the simulation is 443 (option b).

To estimate the crop yield from the given random numbers, we need to assign a specific meaning to each random number. Let's assume that each random number represents the crop yield for a particular year.

Given random numbers: 37, 23, 92, 01, 69, 50, 72, 12, 46, 81

To find the estimated crop yield, we sum up all the random numbers:

37 + 23 + 92 + 01 + 69 + 50 + 72 + 12 + 46 + 81 = 443

Therefore, the estimated crop yield from the simulation is 443. The correct option is b.

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The basis of solutions using the Frobenius method for the differential equation xy" + (1 – 2x)y' + (x - 1)y = 0 is y₁(x) = a₀x⁻ⁿ, y₂(x) = aₙx⁻ⁿ, and y₃(x) = aₙ₊₁x²⁻ⁿ, where a₀, aₙ, and aₙ₊₁ are constants and n is a non-negative integer.

To find a basis of solutions using the Frobenius method, we assume that the solution can be expressed as a power series:

y(x) = ∑[n=0 to ∞] aₙ\(x^{n+r}\),

where aₙ represents the coefficients and r is a constant to be determined. Let's begin by differentiating the series:

y'(x) = ∑[n=0 to ∞] aₙ(n+r)\(x^{n+r-1}\),

y''(x) = ∑[n=0 to ∞] aₙ(n+r)(n+r-1)\(x^{n+r-2}\).

Substituting these derivatives into the given differential equation, we have:

xy" + (1 – 2x)y' + (x - 1)y = 0

∑[n=0 to ∞] aₙ(n+r)(n+r-1)\(x^{n+r}\) + ∑[n=0 to ∞] aₙ(n+r)\(x^{n+r}\) - 2x∑[n=0 to ∞] aₙ(n+r)\(x^{n+r-1}\) + ∑[n=0 to ∞] aₙ\(x^{n+r}\) - ∑[n=0 to ∞] aₙ\(x^{n+r}\) = 0.

∑[n=1 to ∞] aₙ(n+r-1)\(x^{n+r}\) = ∑[n=0 to ∞] aₙ(n+r)\(x^{n+r}\) * \(x^r\).

Finally, for the third term, we'll differentiate the series:

-2x∑[n=0 to ∞] aₙ(n+r)\(x^{n+r-1}\) = -2x∑[n=0 to ∞] aₙ(n+r)\(x^n * x^r\).

Now, we can combine the terms:

∑[n=0 to ∞] (aₙ(n+r)(n+r-1) + aₙ(n+r) - 2aₙ\((n+r))x^n * x^r\) = 0.

Since this equation should hold for all values of x, the coefficients of each power of x must be zero. Therefore, we obtain the following recurrence relation:

aₙ(n+r)(n+r-1) + aₙ(n+r) - 2aₙ(n+r) = 0.

Simplifying the equation, we have:

aₙ[(n+r)(n+r-1) + (n+r) - 2(n+r)] = 0.

aₙ(n+r)(n+r-1+1-2) = 0.

aₙ(n+r)(n+r-2) = 0.

Now, we have three cases to consider:

Case 1: aₙ = 0

If aₙ = 0, then the coefficient of \(x^n\) is zero, and we can move on to the next value of n.

Case 2: n+r = 0

If n+r = 0, then r = -n. In this case, the solution becomes:

y₁(x) = a₀\(x^r\) = a₀\(x^{-n}\).

Case 3: (n+r)(n+r-2) = 0

If (n+r)(n+r-2) = 0, then we have two solutions:

Solution 1: n+r = 0

In this case, r = -n. The solution becomes:

y₂(x) = aₙ\(x^r\) = aₙ\(x^{-n}\).

Solution 2: n+r-2 = 0

In this case, r = 2-n. The solution becomes:

y₃(x) = aₙ₊₁\(x^r\) = aₙ₊₁\(x^{2-n}\).

Therefore, we have three linearly independent solutions:

y₁(x) = a₀\(x^{-n}\),

y₂(x) = aₙ\(x^{-n}\),

y₃(x) = aₙ₊₁\(x^{2-n}\).

We can identify the series expansions of known functions as follows:

y₁(x) = a₀\(x^{-n}\) is a series expansion of a constant function.

y₂(x) = aₙ\(x^{-n}\) is a series expansion of \(x^{-n}\), which is a generalized power function.

y₃(x) = aₙ₊₁\(x^{2-n}\) is a series expansion of \(x^{2-n}\), which is another generalized power function.

These solutions form a basis for the given differential equation using the Frobenius method.

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Answer:

desculpa,mais eu preciso de ponto para ajudar meu irmão

Step-by-step explanation:

x² - 9

1. There is no common factor other than 1.

2. √x² = x; √9 = 3

3. a = x; b = 3

4. x² - 9 = (x - 3)(x + 3)

Answer:

the last one I think

Step-by-step explanation:

The vertex form of the quadratic equation is:

\(g(x) = (x + 1)^2 - 2\)

And the graph can be seen at the end

For a quadratic equation with leading coefficient a, and with vertex (h, k), the vertex form is:

\(y = a*(x - h)^2 + k\)

Here we have:

\(g(x) = x^2 + 2x - 1\)

First, we need to find the vertex. by using the known formula we get:

\(h = -2/(2*1) = -1\)

To get the value of k, we need to evaluate g(x) in x = -1.

\(g(-1) = (-1)^2 + 2*-1 - 1 = 1 - 2 - 1 = -2\)

So the vertex is (-1, -2), which means that the vertex form is:

\(g(x) = (x + 1)^2 - 2\)

And its graph can be seen below.

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Answer:

-3 and -5

Step-by-step explanation:

because two negatives equal a positive

idek if this is correct

sorry if its not

Two similar figures have a ratio of areas 72:32. The ratio of similarity between the two figures is 3:2.

The ratio of areas of two similar figures is equal to the square of the ratio of their corresponding side lengths. Let's assume the ratio of side lengths is a:b.

Given: Ratio of areas = 72:32

The ratio of areas is the square of the ratio of side lengths. So, we have:

(a/b)^2 = 72/32

Simplifying the equation:

(a/b)^2 = 9/4

Taking the square root of both sides:

a/b = √(9/4)

a/b = 3/2

Hence, the ratio of side lengths of the two similar figures is 3:2.

Since similarity is based on corresponding side lengths, the ratio of similarity is the same as the ratio of side lengths. Therefore, the ratio of similarity between the two figures is 3:2.

This means that for every unit increase in the length of the corresponding side in the smaller figure, the corresponding side in the larger figure increases by 1.5 units.

In summary, the ratio of similarity between the two figures is 3:2, indicating that they are scaled versions of each other with the smaller figure being 3/2 times smaller in each dimension compared to the larger figure.

Hence, the ratio of similarity is 3:2.

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