Given the following function, state the domain.

A function is shown below.

alexandr402 [8]

Answer:

the answer is 4

Step-by-step explanation:

if y=21 the we substitute in the main equation

21=8x-11

8x=32

x=4

3 0

2 years ago

Which point is on the circle centered at the origin with a radius of 5 units? Distance formula: StartRoot (x 2 minus x 1) square

Sergeeva-Olga [200]

Answer:

Option A) $(2,\sqrt{21})$

Step-by-step explanation:

The following information is missing in the question:

A. $(2,\sqrt{21})$

B. $(2,\sqrt{23})$

C. (2, 1)

D. (2, 3)

We are given the following in the question:

A circle centered at origin and radius 5 units.

We have to find the equation of a point that lies on the circle.

Let (x,y) lie on the circle.

Distance formula:

$d = \sqrt{(y_2-y_1)^2+(x_2-x_1)^2}$

Putting

$(x_2,y_2) = (x,y)\\(x_1.y_1) = (0,0)\\d = 5$

We get,

$5 = \sqrt{(y-0)^2 + (x-0)^2}\\\sqrt{x^2+y^2}=5\\x^2+y^2 = 25$

is the required equation of point on the circle centered at the origin with a radius of 5 units.

The point $(2,\sqrt{21})$ satisfies the given equation.

Verification:

$(2)^2 + (\sqrt{21})^2\\=4 + 21\\=25$

Thus, $(2,\sqrt{21})$ lies on the circle centered at the origin with a radius of 5 units.

7 0

4 years ago

Read 2 more answers

At Burnt Mesa Pueblo, archaeological studies have used the method of tree-ring dating in an effort to determine when prehistoric

Marina CMI [18]

Answer:

a) The range is (1199, 1267)

b) The range is (1165, 1301)

c) The range is (1131, 1335)

Step-by-step explanation:

Previous concepts

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".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

$X \sim N(1233,34)$

Where $\mu=1233$ and $\sigma=34$

The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ). Broken down, the empirical rule shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).

Part a

For this case we can use the statement from the empirical rule "68% of the data falls within the first standard deviation (µ ± σ)", and we can find the limits like this:

$\mu -\sigma= 1233-34=1199$

$\mu +\sigma=1233+34=1267$

The range is (1199, 1267)

Part b

For this case we can use the statement from the empirical rule "95% of the data within the first two standard deviations (µ ± 2σ)", and we can find the limits like this:

$\mu -2\sigma= 1233-(2*34)=1165$

$\mu +2\sigma=1233+(2*34)=1301$

The range is (1165, 1301)

Part c

For this case we can use the statement from the empirical rule "99.7% of the data within the first three standard deviations (µ ± 3σ)" and that represent almost all the data, and we can find the limits like this:

$\mu -3\sigma= 1233-(3*34)=1131$