-7x+x-y-3+3 what is the answer Click and drag like terms onto each other to simplify fully.

Researchers are interested in the effect of a certain nutrient on the growth rate of plant seeding. Use a hydroponics grow proce

Rashid [163]

Answer:

The 95% confidence interval for the mean would be given by (56.604;68.596)

The 99% confidence interval for the mean would be given by (53.196;72.004)

Step-by-step explanation:

1) Previous concepts

When we compute a confidence interval for the mean, we are interested on the parameter population mean, and we use the info from the sample to estimate this parameter.

2) Basic operations

The sample mean can be calculated with the following formula

$\sum_{i=1}^n \frac{x_i}{n}$

Using excel we can use this function to calculate the mean:

=AVERAGE(54.2,59.8,61.8,63.3,65.1,71.4)

The value obtained is $\bar X=62.6$

In order to find the sample deviation we can use this formula

$s=\sqrt{\sum_{i=1}^n \frac{(x_i-\bar X)^2}{n-1}}$

And using excel we can use this function to calculate the sample standard deviation:

=STDEV.S(54.2,59.8,61.8,63.3,65.1,71.4)

The value obtained is $s=5.713$

The sample size for this case is n=6, n<30 so then is better use the t distribution to calculate the margin of error. First we need to calculate the degrees of freedom, on this case $df=n-1=6-1=5$

The formula for the confidence interval would be given by:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

3) Part a

If we want a 95% or 0.95 of confidence, then the value for the signficance is $\alpha=1-0.95=0.05$ , and $\alpha/2=0.025$ , and $1-\frac{\alpha}{2}=0.975$ so we can find the critical t value with the following formula in excel:

=T.INV(0.975,5)

And we got $t_{\alpha/2}= 2.571$

And we can replace into equation (1) and we got:

$62.6 \pm 2.571\frac{5.713}{\sqrt{6}}$

And using excel with the following formulas we got:

=62.6-2.571*(5.713/SQRT(6)) = 56.604

=62.6+2.571*(5.713/SQRT(6)) = 68.596

So the 95% confidence interval for the mean would be given by (56.604;68.596)

4) Part b

If we want a 99% or 0.99 of confidence, then the value for the signficance is $\alpha=1-0.99=0.01$ , and $\alpha/2=0.005$ , and $1-\frac{\alpha}{2}=0.995$ so we can find the critical t value with the following formula in excel:

=T.INV(0.995,5)

And we got $t_{\alpha/2}= 4.032$

And we can replace into equation (1) and we got:

$62.6 \pm 4.032\frac{5.713}{\sqrt{6}}$

And using excel with the following formulas we got:

=62.6-4.032*(5.713/SQRT(6)) = 53.196

=62.6+4.032*(5.713/SQRT(6)) = 72.004

So the 99% confidence interval for the mean would be given by (53.196;72.004)

8 0

2 years ago

HELP HELP HELP

Solnce55 [7]

Answer:

Step-by-step explanation:

2. Given a point with integral coordinates (a, b):

Vertical line that contains (a, b):

So here it's not to hard, all you have to understand, is what a vertical line is. If you were to draw a vertical line, you would notice that the x-values remain constant, and the only thing that changes is the y-value. So you're going to have an equation as such: x=a, where a is some constant value, and y is literally anything. So in this case b doesn't matter. The only thing that matters is that x=a. Which is the equation. As long as x is equal to a, it should pass through (a, b)

Horizontal line that contains (a, b):

So this is very similar to the vertical line, as one of the values is constant, although the variable that's constant is different. If you were to draw a horizontal line, you would notice the x is changing, but the y-value isn't. This means the y is going to equal to constant value, which may look something like: y=b, which is the equation in this case, since as long as y=b, then the x should at some point equal a on the horizontal line

Why is it impossible to write the equation of a vertical line in slope-intercept form:

As mentioned before, in a vertical line, the only thing that varies is the y-value, so if you wrote a vertical line as such: y=mx+b, then the x-value would have to vary. But if we were to put restrictions on the equation so that x can only equal some constant value, that means y would only be one point, but if you draw a vertical line, you would know that the y-value is all real numbers (unless of course you put some range restriction), but even then it's going to be more than one number. The other thing is to write an equation in slope-intercept form, you need to know the slope. which is defined as $\frac{y_2-y_1}{x_2-x_1}$ . and by definition a vertical line only varies in y-values and not x. The value of x is defined in the constant equation: x=a. So the slope would be defined as: $\frac{y_2-y_1}{a-a} = \frac{y_2-y_1}{0} = \text{undeefined}$ ("I typed undefined wrong intentionally since it won't let me type it for some reason"). anyways the point is you can divide by 0. So main takeaways: the x-value can't vary, the formula has to output all real numbers for the y-value (unless some range restriction), the slope will have 0 as the denominator since x doesn't vary meaning x_2 - x_1 will = 0, because x_2 = x_1 (because x doesn't vary)

Given an equation in point slope form, explain how to determine the coordinate of the y-intercept:

There are two ways to do this. The point slope form is expressed as such: y-a = m(x-b). But the m can be distributed so the equation becomes y-a = mx-mb and then add "a" to both equations to get y=mx -mb+a, in this case (0, -mb+a) will be the y-intercept, because if you plug in x as 0, mx will become 0 and it will leave these two values. You could also just of course plug in 0 as x in the point slope intercept form: y-a = m(x-b) and then solve for y. This gives the same result as it simplified to y-a = m(-b) which becomes y-a=-mb which then becomes y=-mb+a.

5 0

1 year ago

HELP PLEASE!! Which one is correct? =/ or = ?

Delicious77 [7]

The answer is = since each equation equals 32
6•6=36
2•2=4
36-4=32
And then the next equation
6+2=8
4(8)=32

3 0

10 months ago

Read 2 more answers

A company manufactures and sells x meras per month The monthly revnuee function is given by R(x)=200x-0.02x+1000 a) What is the

Anvisha [2.4K]

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4 0