Help please will mark brainliest if correct

4x^2+4y^2=64<br> what are the domain and range

marissa [1.9K]

Use a graphing tool and you'll see a circle form. This circle has a center of (0,0) and radius of 4. Side note: this equation is equivalent to x^2+y^2 = 16 after you divide everything by 4

Looking at the graph, the smallest x can be is -4. The largest x can be is 4. So the domain in interval notation is $[-4,4]$

Similarly the range in interval notation is also <span> $[-4,4]$ because the lowest you can go is y = -4. The highest you can go is y = 4</span>

8 0

3 years ago

"Select the equation of the least squares line for the data: (34.0, 1.30), (32.5, 3.25), (35.0, .65), (31.0, 6.50), (30.0, 5.85)

yulyashka [42]

Answer:

$y=-1.055 x +37.643$

And the best option would be:

a. ŷ= 37.643-1.0543x

Step-by-step explanation:

We assume that the data is this one:

x: 34.0, 32.5, 35.0, 31.0, 30.0, 27.5, 29.0

y: 1.30, 3.25, 0.65, 6.50, 5.85, 8.45, 6.50

Find the least-squares line appropriate for this data.

For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

So we can find the sums like this:

$\sum_{i=1}^n x_i = 34.0+ 32.5+ 35.0+ 31.0+ 30.0+ 27.5+ 29.0
=219$

$\sum_{i=1}^n y_i =1.3+3.25+0.65+6.5+5.85+8.45+6.5=32.5$

$\sum_{i=1}^n x^2_i = 34.0^2+ 32.5^2+ 35.0^2+ 31.0^2+ 30.0^2+ 27.5^2+ 29.0^2
=6895.5$

$\sum_{i=1}^n y^2_i =1.3^2+3.25^2+0.65^2+6.5^2+5.85^2+8.45^2+6.5^2=202.8$

$\sum_{i=1}^n x_i y_i =34*1.3 + 32.5*3.25+ 35*0.65+ 31*6.5+30*5.585 +27.5*8.45 +29*6.5=970.45$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=6895.5-\frac{219^2}{7}=43.929$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=970.45-\frac{219*32.5}{7}=-46.336$

And the slope would be:

$m=-\frac{46.336}{43.929}=-1.055$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{219}{7}=31.286$

$\bar y= \frac{\sum y_i}{n}=\frac{32.5}{7}=4.643$

And we can find the intercept using this:

$b=\bar y -m \bar x=4.643-(-1.055*31.286)=37.643$

So the line would be given by:

$y=-1.055 x +37.643$

And the best option would be:

a. ŷ= 37.643-1.0543x

5 0

4 years ago

<img src="https://tex.z-dn.net/?f=4g%20-%207c%20%2B%203g" id="TexFormula1" title="4g - 7c + 3g" alt="4g - 7c + 3g" align="absmid

pashok25 [27]

Step-by-step explanation:

4g-7c+3g

7g-7c i hope this helps

4 0

3 years ago

IF ANYBODY IS GOOD WITH CIRCLES HELP! HELP I NEED HELP WITH CIRCUMFERENCE!! What is the radius of a circle with circumference of

Dmitrij [34]

Answer:

7.96 cm or rounded, it is C. 8

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

What is the correct set of data for the stemplot? The stemplot below represents the number of bite-size snacks grabbed by 10 stu

STatiana [176]

Answer:

C. 15, 16, 16, 17, 19, 20, 21, 23, 32, 42.

Step-by-step explanation:

Using the key: 2|4 = 24, the following are the set of data represented by the stem-and-leaf plot showing:

Row one, 1| 5 6 6 7 9:

This means there are 5 data set for the first row which are:

15, 16, 16, 17, 19

Row two, 2|0 1 3:

There are 3 data here, which are:

20, 21, 23

Row 3, 3|2: = 32

Row 4, 4|2: = 42

The correct set of data are 15, 16, 16, 17, 19, 20, 21, 23, 32, 42.

Correct option is C.

6 0

3 years ago