PLEASE HELP ASAP! Thanks!!!!! Explain:

Mathematics

1 answer:

Verdich [7]3 years ago

5 0

Answer:

(3, 3) and (15, 15)

Step-by-step explanation:

The points equidistant from the given point and the y-axis lie on the parabola that has (3,6) as its focus and the y-axis as its directrix. The equation for that can be simplified from ...

(x -3)^2 +(y -6)^2 = x^2

-6x +9 +y^2 -12y +36 = 0 . . . . . subtract x^2, eliminate parentheses

We can find the points that lie on the line y=x (equidistant from both axes) by substituting y for x or vice versa. Then we have the quadratic ...

x^2 -18x +45 = 0 . . . . substitute x for y and collect terms

(x -3)(x -15) = 0 . . . . factor it

x = 3 or 15

So, the points of interest are (x, y) = (3, 3) and (x, y) = (15, 15).

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The mean number of hours per day spent on the phone, according to a national survey, is four hours, with a standard deviation of

Reika [66]

Answer:

The new mean is 5.

The new standard deviation is also 2.

Step-by-step explanation:

Let the sample space of hours be as follows, S = {x₁, x₂, x₃...xₙ}

The mean of this sample is 4. That is, $\bar x=\frac{x_{1}+x_{2}+x_{3}+...+x_{n}}{n}=4$

The standard deviation of this sample is 2. That is, $s=\frac{1}{n-1}\sum (x_{i}-\bar x)^{2}=2$ .

Now it is stated that each of the sample values was increased by 1 hour.

The new sample is: S = {x₁ + 1, x₂ + 1, x₃ + 1...xₙ + 1}

Compute the mean of this sample as follows:

$\bar x_{N}=\frac{x_{1}+1+x_{2}+1+x_{3}+1+...+x_{n}+1}{n}\\=\frac{(x_{1}+x_{2}+x_{3}+...+x_{n})}{n}+\frac{(1+1+1+...n\ times)}{n}\\=\bar x+1\\=4+1\\=5$

The new mean is 5.

Compute the standard deviation of this sample as follows:

$s_{N}=\frac{1}{n-1}\sum (x_{i}-\bar x)^{2}\\=\frac{1}{n-1}\sum ((x_{i}+1)-(\bar x+1))^{2}\\=\frac{1}{n-1}\sum (x_{i}+1-\bar x-1)^{2}\\=\frac{1}{n-1}\sum (x_{i}-\bar x)^{2}\\=s$