Please help with question

Let $DEF$ be an equilateral triangle with side length $3.$ At random, a point $G$ is chosen inside the triangle. Compute the pro

umka21 [38]

$|\Omega|=(\text{the area of the triangle})=\dfrac{a^2\sqrt3}{4}=\dfrac{3^2\sqrt3}{4}=\dfrac{9\sqrt3}{4}\\|A|=(\text{the area of the sector})=\dfrac{\alpha\pi r^2}{360}=\dfrac{60\pi \cdot 1^2}{360}=\dfrac{\pi}{6}\\\\\\P(A)=\dfrac{\dfrac{\pi}{6}}{\dfrac{9\sqrt3}{4}}\\\\P(A)=\dfrac{\pi}{6}\cdot\dfrac{4}{9\sqrt3}\\\\P(A)=\dfrac{2\pi}{27\sqrt3}\\\\P(A)=\dfrac{2\pi\sqrt3}{27\cdot3}\\\\P(A)=\dfrac{2\pi\sqrt3}{81}\approx13.4\%$

8 0

4 years ago

Read 2 more answers

The ratio of the ages of Mandy and Sandy is 2:5. After 8 years, their ages will be in the ratio 1:2. What is the difference betw

swat32

A ratio shows us the number of times a number contains another number. Caitlin is right.

<h3>What is a Ratio?</h3>

A ratio shows us the number of times a number contains another number.

The ratio of the ages of Mandy and Sandy is 2:5. Therefore, the ratio will be,

M/S = 2/5

M = 2S/5

After 8 years, their ages will be in the ratio 1:2, therefore,

(M+8)/(S+8) = 1/2

2M + 16 = S + 8

2M - S = -16 + 8

Substitute the value of M,

2(2S/5) - S = -8

-0.2S = -8

S = 40

Now, if we substitute the value of S in the first ratio,

M/S = 2/5

M/40 = 2/5

M = 16

Now, if we take the difference in their ages the difference will be 24(40-16).

Since the difference is 24, we can conclude that Caitlin is right.

Hence, Caitlin is right.

Learn more about Ratios:

brainly.com/question/1504221

#SPJ1

4 0

2 years ago

You are trying out for the school play. The probability that you are chosen to

Luda [366]

Answer:

Option D is the correct option.

solution,

Probability that you are given to lead role:

$\frac{probability \: you \: are \: chosen \: to \: be \: in \: team\: }{probability \: that \: you \: are \: chosen \: to \: lead}$

$= \frac{0.1}{0.5} \\ = 0.2$

hope this helps...

Good luck on your assignment..

6 0

3 years ago

1+2+3+4+5+6+7+8+9+012

sweet [91]

Using calculator
Answer=57

5 0

3 years ago

Read 2 more answers

la un joc pe calculator, trei copii au castigat inpreuna 780 de puncte. Al doilea copil a castigat de 3 ori mai multe puncte dec

ratelena [41]

Answer:

The number of points won by the first child was 37 points

The number of points won by the second child was 119 points

The number of points won by the third child was 624 points

Step-by-step explanation:

<u><em>The question in English is</em></u>

In a computer game, three children won together 780 points. The second child gained 3 times more points than the first and 8 more points, the third child gained four times more points than the first two in one place. How many points did each child earn

Let

x ----> number of points won by the first child

y ----> number of points won by the second child

z ----> number of points won by the third child

we know that

three children won together 780 points

so

$x+y+z=780$ ----> equation A