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3 years ago

Mr. Davis bought solar lights for a pathway at his house. The lights cost $29.95 each and have an

1 answer:

3 0

He pays $223.65.

This is because from the equation you know that he pays 29.95+2.00 for one light therefore, if we use x to represent the amount of lights--

X(29.95+2.00)

is an equation you can use to solve for the amount Mr. Davis payed for his lights.

You might be interested in

Suppose that the population of the scores of all high school seniors who took the SAT Math (SAT-M) test this year follows a Norm

Vlad1618 [11]

Answer:

Confidence = $1-\alpha=1-0.01=0.99$

And then the confidence level would be given by 99%

Step-by-step explanation:

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Assuming the X follows a normal distribution

$X \sim N(\mu, \sigma)$

The distribution for the sample mean is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

$\bar x =512$ represent the sample mean

$\sigma=100$ represent the population standard deviation

n= 100 sample size selected.

The confidence interval is given by this formula:

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

The marginof error for this case is given by Me=25.76. And we know that the formula for the margin of error is given by:

$Me=z_{\alpha/2} \frac{\sigma}{\sqrt{n}}$

$25.76=z_{\alpha/2} \frac{100}{\sqrt{100}}$

And we can find the critical value $z_{\alpha/2}$ like this:

$z_{\alpha/2}=\frac{25.76(\sqrt{100})}{100}=2.576$

And we know that on the right tail of the z score =2.576 we have $\alpha/2$ of the total area. We can find the area on the right of the z score using this excel code:

"=1-NORM.DIST(2.576,0,1,TRUE)" or using a table of the normal standard distribution, and we got 0.004998= $\alpha/2$ , so then $\alpha=0.00498*2=0.009995 \approx 0.01$ , and then we can find the confidence like this:

Confidence = $1-\alpha=1-0.01=0.99$

And then the confidence level would be given by 99%

8 0

3 years ago

Find f(x) and g(x) so that the function can be described as y = f(g(x)).<br><br> y = 4/x^2+9

dlinn [17]

I'm assuming all of (x^2+9) is in the denominator. If that assumption is correct, then,

One possible answer is $f(x) = \frac{4}{x}, \ \ g(x) = x^2+9$

Another possible answer is $f(x) = \frac{4}{x+9}, \ \ g(x) = x^2$

There are many ways to do this. The idea is that when we have f( g(x) ), we basically replace every x in f(x) with g(x)

So in the first example above, we would have

$f(x) = \frac{4}{x}\\\\f( g(x) ) = \frac{4}{g(x)}\\\\f( g(x) ) = \frac{4}{x^2+9}$

In that third step, g(x) was replaced with x^2+9 since g(x) = x^2+9.

Similar steps will happen with the second example as well (when g(x) = x^2)

4 0

3 years ago

Fraction that less than 5/6 and has a denominator of 8

AnnyKZ [126]

A fraction that is less than 5/6 and has a denominator of 8 would be 4/8 because if you compare 4/8 and 5/6 4/8 is less than 5/6. (to compare this two fractions you need to make them have the same denominator so they would end up been 4/8=12/24
5/6=20/24
And 12/24 is smaller than 20/24
(Besides 4/8 is half and 5/6 is more than half

3 0

3 years ago

Calculate the length of the diagonal AB

Vesna [10]

Answer:

Please add a attachment.

Step-by-step explanation:

6 0

3 years ago

Write the Slope-Intercept and Point-Slope forms of the line passing through the point (-3, 2) and having a slope of -4/5

weeeeeb [17]

Answer:

slope-intercept: $y=\frac{-4}{5} x-\frac{2}{5}$

point-slope: $y-2=\frac{-4}{5} (x+3)$

Step-by-step explanation:

The slope-intercept form of a line is written as y = mx + b, where m is the slope and b is the y-intercept.

The point-slope form of a line is written as y - y1 = m(x - x1), where (x1, y1) is a given point and m is the slope.

Here, we see that the slope is -4/5, which means that m = -4/5. Since we're given a point (-3, 2), let's go ahead and just write the point-slope form already. (x1, y1) = (-3, 2) so x1 = -3 and y1 = 2. Then:

y - y1 = m(x - x1)

y - 2 = (-4/5) * (x + 3)

$y-2=\frac{-4}{5} (x+3)$

Now, we want to find the slope-intercept form, so we need to figure out the y-intercept. Well, first, let's plug in what we know:

y = mx + b

y = (-4/5)x + b

Any point on this line will satisfy the above equation. Since (-3, 2) is on this line, if we plug -3 in for x and 2 in for y, the equation should hold true, so we can solve for b:

y = (-4/5)x + b

2 = (-4/5) * (-3) + b

2 = 12/5 + b

b = -2/5

So, the y-intercept is -2/5. Then the slope-intercept form is:

$y=\frac{-4}{5} x-\frac{2}{5}$

Thus, our two equations are:

slope-intercept: $y=\frac{-4}{5} x-\frac{2}{5}$

point-slope: $y-2=\frac{-4}{5} (x+3)$

8 0

2 years ago