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3 years ago

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"the least squares method will minimize the sum of squares _______ when describing the equation that best fits the ordered pairs

."

1 answer:

Evgen [1.6K]3 years ago

3 0

The least squares method will minimize the sum of squares error when describing the equation that best fits the ordered pairs.

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How many acute angles did you measure in that figure?

olya-2409 [2.1K]

Answer:

4

Step-by-step explanation:

By having a clear glance at the picture , there are 4 acute angles. They are AMP , PMQ , BMQ & BMR

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3 years ago

Solve for x. Thank you

Lesechka [4]

Answer:

solve for what exactly, there is no equation here

Step-by-step explanation:

please there's no equation here

4 0

3 years ago

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Simplify this at its lowest terms also

alina1380 [7]

Answer:

you can add it up or multiply each number.

Step-by-step explanation that seem kinda hard.

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4 years ago

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It is known that the population variance equals 484. With a .95 probability, the sample size that needs to be taken if the desir

Ksju [112]

Answer:

We need a sample size of at least 75.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.025 = 0.975$ , so $z = 1.96$

Now, we find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

The standard deviation is the square root of the variance. So:

$\sigma = \sqrt{484} = 22$

With a .95 probability, the sample size that needs to be taken if the desired margin of error is 5 or less is

We need a sample size of at least n, in which n is found when M = 5. So

$M = z*\frac{\sigma}{\sqrt{n}}$

$5 = 1.96*\frac{22}{\sqrt{n}}$

$5\sqrt{n} = 43.12$

$\sqrt{n} = \frac{43.12}{5}$

$\sqrt{n} = 8.624$

$(\sqrt{n})^{2} = (8.624)^{2}$

$n = 74.4$

We need a sample size of at least 75.

6 0

4 years ago

Read 2 more answers

What is the solution to the system of linear equations?<br><br> −9x+4y=55<br><br> −11x+7y=82

LuckyWell [14K]

Here is my process with mathematical expression interpreter, LaTeX. Full process given below to obtain the values of variable "x" and "y" altogether, solutions to these system of linear equations.

$\begin{bmatrix}-9x & + & 4y & = & 55 & \bf{- - - \: Eq. \: 1} \\ \\ -11x & + & 7y & = & 82 & \bf{- - - \: Eq. \: 2} \end{bmatrix}$

Now here, we should isolate a variable, or take it as a separate form to find the equation, and furthermore substitute the value of variable "y" into the original isolation of "x", to obtain both the solutions for this linear system of equation. Perform this on equation number 1 (Eq. 1).

Subtract the variable attached value by "4y" on both the sides, in current expression.

$\mathbf{-9x + 4y - 4y = 55 - 4y}$

$\mathbf{-9x = 55 - 4y}$

Both the sides, perform a division of value "-9".

$\mathbf{\dfrac{-9x}{-9} = \dfrac{55}{-9} - \dfrac{4y}{-9}}$

$\mathbf{x = \dfrac{55 - 4y}{-9}}$

$\mathbf{x = - \dfrac{55 - 4y}{9}}$

Substitute or just plug the value of newly obtained expression for variable "x" into Equation, numbered as "2" (Eq. 2.) and isolate further for the variable "y", to obtain first solution for this linear equation.

$\mathbf{-11 \Bigg(- \dfrac{55 - 4y}{9} \Bigg) + 7y = 82}$

$\mathbf{\dfrac{(55 - 4y) \times 11}{9} + 7y = 82}$

Multiply both the sides by a value of "9".

$\mathbf{\dfrac{(55 - 4y) \times 11}{9} + 7y \times 9 = 82 \times 9}$

$\mathbf{11 (55 - 4y) + 63y = 738}$

$\mathbf{605 - 44y + 63y = 738}$

$\mathbf{605 + 19y = 738}$

Subtract both the sides by a value of "- 605".

$\mathbf{605 + 19y - 605 = 738 - 605}$

$\mathbf{19y = 133}$

Divide both the sides by "19".

$\mathbf{\dfrac{19y}{19} = \dfrac{133}{19}}$

$\boxed{\mathbf{y = 7}}$

Substitute this variable value of "y = 7" , into our original isolation for variable "x", the expression is to be substituted by that value to complete the solutions for the linear equations. That is:

$\mathbf{x = - \dfrac{55 - 4y}{9}; \quad y = 2}$

$\mathbf{\therefore \quad x = - \dfrac{55 - 4 \times 7}{9}}$

$\mathbf{\therefore \quad x = - \dfrac{55 - 28}{9}}$

$\mathbf{x = - \dfrac{27}{9}}$

$\boxed{\mathbf{x = - 3}}$

Finalised solutions for these linear system of equations for two components , is:

$\boxed{\mathbf{\underline{\therefore \quad Final \: Solutions \: for \: these \: System \: of \: Linear \: Equations: \: x = - 3, \: \: y = 7}}}$

Hope it helps.

5 0

3 years ago