What is the ratio of feet to inches on a measuring tape

The ratio of the circumference of two circles is 3:2.What is the ratio of their area

Nezavi [6.7K]

The ratio of their area is 9/4

<h2>Explanation:</h2>

We use ratios to compares values. In this exercise, we are comparing the circumference of two circles, which is:

$3:2$

and we want to know what is the ratio of their area. Recall that the circumference of a circle is given by:

$C=2\pi r \\ \\ \\ Where: \\ \\ C:Circumference \\ \\ r:Radius \ of \ the \ circle$

If we define:

$C_{1}: \ Circumference \ of \ circle \ 1 \\ \\ C_{2}: \ Circumference \ of \ circle \ 2 \\ \\ r_{1}: \ Radius \ of \ circle \ 1 \\ \\ r_{2}: \ Radius \ of \ circle \ 2$

Then, the ratio of the circumference of two circles is 3:2 is:

$\frac{C_{1}}{C_{2}}=\frac{2\pi r_{1}}{2\pi r_{2}}=\frac{3}{2} \\ \\ \therefore \frac{r_{1}}{r_{2}}=\frac{3}{2}$

The area of a circle is given by:

$A=\pi r^2 \\ \\ A:Area \\ \\ r:Radius$

So the ratio of their area can be found as:

$\frac{A_{1}}{A_{2}}=\frac{\pi r_{1}^2}{\pi r_{2}^2} \\ \\ \\ A_{1}:Area \ of \ circle \ 1 \\ \\ A_{2}:Area \ of \ circle \ 2$

So:

$\frac{A_{1}}{A_{2}}=\frac{r_{1}^2}{r_{2}^2}=\left( \frac{r_{1}}{r_{2}} \right)^2 \\ \\ \frac{A_{1}}{A_{2}}=\left(\frac{3}{2}\right)^2 \\ \\ \boxed{\frac{A_{1}}{A_{2}}=\frac{9}{4}}$

<h2>Learn more:</h2>

Unit rate: brainly.com/question/13771948#

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5 0

3 years ago

Variance and standard deviation

kirza4 [7]

Answer: 8.3

Step-by-step explanation:

To find the variance, you want to find the mean of the data.

$\frac{3+3+8+1+9+6}{6} =5$

Now that we have the mean, we find the difference between each data point and the mean.

3-5=-2

8-5=3

1-5=-4

9-5=4

6-5=1

With the difference, you square each and find the average.

(-2)²=4

3²=9

(-4)²=16

4²=16

1²=1

$\frac{4+4+9+16+16+1}{6} =\frac{25}{3}$

The variance is 8.3.

3 0

3 years ago

Help me find the slope please guys<br> Im struggling

tatuchka [14]

Answer:

negative 1

Step-by-step explanation:

$\frac{y2 - y1}{x2 - x1} = m$

the 2 points: (-2,0), (-3,1)

(1-0)/(-3+2)

=-1

m=-1

brainliest please

7 0

3 years ago

Run a multiple regression where the dependent variable is ratings and the independent variables are star and fact. Use data from

Vanyuwa [196]

Answer:

See explaination

Step-by-step explanation:

See attachment for diagram

The r value is 0.373 (low). This implies a weak correlation between the dependent and independent variables for this sample.

The overall p- value for the regression model is 0.0017. This implies that at least one of the two independent variables (x1 or x2) in the model is significant predictor of the dependent variable y.

p- values for the both "Fact" and "Star" are < 0.05. This means both the independent variables are significant predictors of the "Rating" at 95% confidence level. The variable "Fact" is significant at 99% level of confidence also. This means the rating viewers award to a movie depends upon both the storyline (fact or Fiction) and the presence or absence of stars.

Expected rating for a fact based movie with no stars = 1.7991(1) + 1.2586(0) + 12.5685 = 14.37

Expected rating for a fiction based movie with a star = 1.7991(0) + 1.2586(1) + 12.5685 = 13.83

So, one may expect a fact based movie without any stars to get better ratings than a fiction based movie with one star.

7 0

3 years ago

A parabola can be represented by the equation x2 = 2y. What are the coordinates of the focus and the equation of the directrix?

SOVA2 [1]

The standard equation for a parabola that opens upward parallel to the y-axis is x2=4ay, where a = distance from the vertex to focus. Vertex is at origin(0,0)
4a=2
a=2/4
a=1/2 or 0.5
the coordinate of the focus is (0, 1/2)
the equation of the directrix is y=-1/2

5 0

3 years ago

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