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1 year ago

8

consider this confidence interval interpretation: we are 95% confident the mean sodium content for all beef hot dogs is between

353.2 and 449.1 mg. what needs to be done to fix this statement?

1 answer:

ArbitrLikvidat [17]1 year ago

3 0

"We are 95% confident that the mean sodium content for all beef hot dogs is between 353.2 and 449.1 mg." is the correct statement.

The true parameter must be properly and contextually stated.

We are researching confidence intervals for population means rather than for particular observations. The parameter is, to put it in plain English, the average sodium content of all beef hot dogs. The phrase "We are 95% confident" would be a better translation.

Thus the correct statement is as mentioned above.

To know more about population you may visit the link which is mentioned below:

brainly.com/question/27779235

#SPJ4

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Bailey sold pumpkin pies for two days. on Monday, she sold 13 pies and on Tuesday she sold 23 pies. If she used 3/4 cup of pumpk

MArishka [77]

Answer:

27

Step-by-step explanation:

13 + 23 = 36 x 3/4 = 27

8 0

3 years ago

EXAMPLE 5 Find the maximum value of the function f(x, y, z) = x + 2y + 11z on the curve of intersection of the plane x − y + z =

Taya2010 [7]

Answer:

$\displaystyle x= -\frac{10}{\sqrt{269}}\\\\\displaystyle y= \frac{13}{\sqrt{269}}\\\\\displaystyle z = \frac{23\sqrt{269}+269}{269}$

<em>Maximum value of f=2.41</em>

Step-by-step explanation:

<u>Lagrange Multipliers</u>

It's a method to optimize (maximize or minimize) functions of more than one variable subject to equality restrictions.

Given a function of three variables f(x,y,z) and a restriction in the form of an equality g(x,y,z)=0, then we are interested in finding the values of x,y,z where both gradients are parallel, i.e.

$\bigtriangledown f=\lambda \bigtriangledown g$

for some scalar $\lambda$ called the Lagrange multiplier.

For more than one restriction, say g(x,y,z)=0 and h(x,y,z)=0, the Lagrange condition is

$\bigtriangledown f=\lambda \bigtriangledown g+\mu \bigtriangledown h$

The gradient of f is

$\bigtriangledown f=$

Considering each variable as independent we have three equations right from the Lagrange condition, plus one for each restriction, to form a 5x5 system of equations in $x,y,z,\lambda,\mu$ .

We have

$f(x, y, z) = x + 2y + 11z\\g(x, y, z) = x - y + z -1=0\\h(x, y, z) = x^2 + y^2 -1= 0$

Let's compute the partial derivatives

$f_x=1\ ,f_y=2\ ,f_z=11\ \\g_x=1\ ,g_y=-1\ ,g_z=1\\h_x=2x\ ,h_y=2y\ ,h_z=0$

The Lagrange condition leads to

$1=\lambda (1)+\mu (2x)\\2=\lambda (-1)+\mu (2y)\\11=\lambda (1)+\mu (0)$

Operating and simplifying

$1=\lambda+2x\mu\\2=-\lambda +2y\mu \\\lambda=11$

Replacing the value of $\lambda$ in the two first equations, we get

$1=11+2x\mu\\2=-11 +2y\mu$

From the first equation

$\displaystyle 2\mu=\frac{-10}{x}$

Replacing into the second

$\displaystyle 13=y\frac{-10}{x}$

Or, equivalently

$13x=-10y$

Squaring

$169x^2=100y^2$

To solve, we use the restriction h

$x^2 + y^2 = 1$

Multiplying by 100

$100x^2 + 100y^2 = 100$

Replacing the above condition

$100x^2 + 169x^2 = 100$

Solving for x

$\displaystyle x=\pm \frac{10}{\sqrt{269}}$

We compute the values of y by solving

$13x=-10y$

$\displaystyle y=-\frac{13x}{10}$

For

$\displaystyle x= \frac{10}{\sqrt{269}}$

$\displaystyle y= -\frac{13}{\sqrt{269}}$

And for

$\displaystyle x= -\frac{10}{\sqrt{269}}$

$\displaystyle y= \frac{13}{\sqrt{269}}$

Finally, we get z using the other restriction

$x - y + z = 1$

Or:

$z = 1-x+y$

The first solution yields to

$\displaystyle z = 1-\frac{10}{\sqrt{269}}-\frac{13}{\sqrt{269}}$

$\displaystyle z = \frac{-23\sqrt{269}+269}{269}$

And the second solution gives us

$\displaystyle z = 1+\frac{10}{\sqrt{269}}+\frac{13}{\sqrt{269}}$

$\displaystyle z = \frac{23\sqrt{269}+269}{269}$

Complete first solution:

$\displaystyle x= \frac{10}{\sqrt{269}}\\\\\displaystyle y= -\frac{13}{\sqrt{269}}\\\\\displaystyle z = \frac{-23\sqrt{269}+269}{269}$

Replacing into f, we get

f(x,y,z)=-0.4

Complete second solution:

$\displaystyle x= -\frac{10}{\sqrt{269}}\\\\\displaystyle y= \frac{13}{\sqrt{269}}\\\\\displaystyle z = \frac{23\sqrt{269}+269}{269}$

Replacing into f, we get

f(x,y,z)=2.4

The second solution maximizes f to 2.4

5 0

3 years ago

What is 8.04 × 101?<br> 0.804<br> 8.04<br> 8.4<br> 80.4

Lerok [7]

8.04 * 100= 804

You move the decimal point two times to the right

8.04*101=812.04

6 0

3 years ago

Read 2 more answers

(The equation of line L is Y=3X+2) what is the slope of a line parallel to L?

AleksandrR [38]

Explanation:

The parallel lines have the same slopes
<span><span>tanα</span>=<span>tanβ</span></span>

<span>The coefficient of x gives the slope of line</span>

<span>Slope=3</span>

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</span>

7 0

3 years ago

Find the equation of the line shown. Enter yoir answwr in slope intercept form

nlexa [21]

Answer:

y = x

Step-by-step explanation:

The equation for slope is y = mx +b. If you look at the line you see that it passes through the origin, this is your y-intercept, 0. If you look at two points at the line and use the rise over run method, you get the slope to be 1. If you substituent these values into the equation you get, y = x.

Hope this helps!

-Luna

8 0

3 years ago