What is the area of this composite figure

A spinner with 3 sectors is shown in the figure below. The measures of the central angles of the red, white, and blue sectors, i

RideAnS [48]

Given that a spinner with 3 sectors. The measures of the central angles of the red, white, and blue sectors, in that order, are in the ratio 2:3:4.

So we can write:

Measure of the central angle of the red sector = 2x

Measure of the central angle of the white sector = 3x

Measure of the central angle of the blue sector = 4x

We know that sum of central angle of the circle is 360 degree so the sum of above three angles will also be 360 degree

2x+3x+4x=360

9x=360

x=40

Then measure of the central angle of the red sector = 2x=2*40= 80 degree

Measure of the central angle of the white sector = 3x=3*40=120 degree

Measure of the central angle of the blue sector = 4x=4*40=160 degree

We have to find the probability for red sector so first we need to find are of the red sector which is given by formula :

$Area = \frac{\pi r^2 \theta}{360}$ , where r is the radius of the spinner.

$Area = \frac{\pi r^2 *80}{360}$

$Area = \frac{2 \pi r^2}{9}$

Area of the spinner is circular so that is given by

Area of spinner $= \pi r^2$

Now the probability that the arrow stops in the red sector is given by ratio or area of red sector and the area of spinner

Probability $= \frac{\frac{2}{9}\pi r^2}{\pi r^2}$

Probability $= \frac{\frac{2}{9}}{1}$

Probability $= \frac{2}{9}$

Hence required probability is 2/9.

5 0

3 years ago

If school starts at 8:30 a.m. and ends at 3:20 p.m., how long is the school day?

12345 [234]

School day is 6 hours and 50 minutes long.

7 0

3 years ago

A child wanders slowly down a circular staircase from the top of a tower. With x,y,zx,y,z in feet and the origin at the base of

babymother [125]

Answer:

a) The tower is 90 feet tall

b) She reaches the bottom at t = 18 minutes.

c) Her speed at time t is 5 \sqrt[]{5} ft/minute

d) Her acceleration at time t is 10 ft/minute^2

Step-by-step explanation:

Consider the path described by the child as going down the tower to have the following parametrization $\gamma(t) = (10\cos t, 10 \sin t, 90-5t)$

a) Assuming that the child is at the top of the tower when she starts going down, we have that at the initial time (t=0) we will have the value of the height of the tower. That is z = 90-5*0 = 90 ft.

b) The child reaches the bottom as soon as z =0. We want to find the value of t that does that. Then we have 0 = 90-5t, which gives us t = 18 minutes.

c) Given the parametrization we are given, the velocity of the child at time t is given by $\frac{d\gamma}{dt}= (\frac{d}{dt}(10\cos t), \frac{d}{dt} (10 \sin t ), \frac{d}{dt}(90-5t)) = (-10 \sin t, 10 \cos t, -5)$ . The speed is defined as the norm of the velocity vector,

so, the speed at time t is given by $v = \sqrt[]{(-10 \sin t)^2+(10 \cos t)^2+(-5)^2} = \sqrt[]{100(\sin^2 t + \cos^2 t)+25} = \sqrt[]{125}= 5 \sqrt[]{5}$

d) ON the same fashion we want to know the norm of the second derivative of $\gamma$ .

We have that $\gamma ^{''}(t) =(-10\cost t, -10 \sin t , 0)$ so the acceleration is given by $\sqrt[]{100(\cos^2 t+ \sin^2 t )} = 10$

6 0

3 years ago

The length of a rectangle is 4 cm more than its width. The area of the rectangle is 96

Yakvenalex [24]

Answer:

12is the answer

Step-by-step explanation:

let the width be 2c

length*width =96

4*2c=96

8c=96

c=96/8

c=12

4 0

3 years ago

What is the least common denominator of 3/4 and 15/16

Rudiy27

The least common denominator of 3/4 and 15/16 is 16.

<h3>What is Least Common Denominator?</h3>

When two or more fractions are given, the least common denominator is the smallest number of all common multiples of the denominators.
To find the least common denominator, list the multiples of both denominators until you find the smallest multiple shared by both.
Because 28 is the first shared multiple of 4 and 7, it must be the least common denominator of these two fractions.

So, LCD od 3/4 and 15/16:

3/4 × 4/4 = 12/16
15/16 × 1/1 = 15/16

Now, the denominator of both the fractions is the same which is 16.

Therefore, the least common denominator of 3/4 and 15/16 is 16.

Know more about Least Common Denominator here:

brainly.com/question/19249494

#SPJ9

8 0

1 year ago