1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
vampirchik [111]
3 years ago
5

In the circle shown below, ∠BAC is a central angle, and r is the length of AB.

Mathematics
1 answer:
Bas_tet [7]3 years ago
8 0

Answer:

Ф = the measure of ∠BAC in radians

Step-by-step explanation:

∵ ∠BAC is a central angle

∴ The are of the sector will depended on the length of the radius <em>r </em>and the measure of the central angle <em>Ф</em>

If the measure of Ф in degrees

∴ The area of the sector = Ф°/360° (π r²)

If the measure of Ф in radians

∴ The area of the sector = 1/2 r² Ф

When to change from degree to radian you do that

Ф radian = Ф°/180 × π

∴ Ф/360 π r² = 1/2 <u>(Ф/180 π)</u> r² ⇒ ∵ underline is Ф radian

∴ Area sector = 1/2 r² Ф ⇒ Ф in radians

You might be interested in
Maya is cleaning out her closet and is shocked when she realizes that she has 55 shirts. She decides to donate 40% of them. ​
ipn [44]

Maya is cleaning out her closet and is shocked when she realizes that she has 55 shirts. She decides to donate 40% of them. How many more shirts does she have for her ?

Answer:

The number of T-shirt that Maya will have after donating 40% is 22 shirts

Explanation:

Given:( as per the above data provided)

Total number of T-shirts = 55

Percentage of T-shirts she wish to donate = 40%

To find:

Remaining number of T-shirt left after donating?

Formula to be used:

Remaining T shirt = (Total number of T-shirt /100) X The Percentage of T-shirt she wish to donate

Steps:

Substituting all the above provided values in the formula we get,

              = (55/100)*40

              = 22 shirts.

Thus the number of T-shirts left with her is 22.

3 0
3 years ago
In a home theater system, the probability that the video components need repair within 1 year is 0.02, the probability that the
earnstyle [38]

Answer:

(a) The probability that at least one of these components will need repair within 1 year is 0.0278.

(b) The probability that exactly one of these component will need repair within 1 year is 0.0277.

Step-by-step explanation:

Denote the events as follows:

<em>A</em> = video components need repair within 1 year

<em>B</em> = electronic components need repair within 1 year

<em>C</em> = audio components need repair within 1 year

The information provided is:

P (A) = 0.02

P (B) = 0.007

P (C) = 0.001

The events <em>A</em>, <em>B</em> and <em>C</em> are independent.

(a)

Compute the probability that at least one of these components will need repair within 1 year as follows:

P (At least 1 component needs repair)

= 1 - P (No component needs repair)

=1-P(A^{c}\cap B^{c}\cap C^{c})\\=1-[P(A^{c})\times P(B^{c})\times P(C^{c})]\\=1-[(1-0.02)\times (1-0.007)\times (1-0.001)]\\=1-0.97216686\\=0.02783314\\\approx 0.0278

Thus, the probability that at least one of these components will need repair within 1 year is 0.0278.

(b)

Compute the probability that exactly one of these component will need repair within 1 year as follows:

P (Exactly 1 component needs repair)

= P (A or B or C)

=P(A\cap B^{c}\cap C^{c})+P(A^{c}\cap B\cap C^{c})+P(A^{c}\cap B^{c}\cap C)\\=[0.02\times (1-0.007)\times (1-0.001)]+[(1-0.02)\times 0.007\times (1-0.001)]\\+[(1-0.02)\times (1-0.007)\times 0.001]\\=0.02766642\\\approx 0.0277

Thus, the probability that exactly one of these component will need repair within 1 year is 0.0277.

7 0
3 years ago
A person who weighs 100 pounds on earth weighs 16.6 lb on the moon. What is the independent variable? Explain why
Leviafan [203]
Independent variable (IV): something the scientist can change.

Thus, in this case, the IV can be the weight of the person.
5 0
3 years ago
Vidriana rolled a number cube 96 times. Her results are shown in the table, what is the experimental probability of rolling an e
hichkok12 [17]

Answer:

50/96

Step-by-step explanation:

I assume the table is:

\left[\begin{array}{cc}Result&Total\\1&15\\2&13\\3&16\\4&17\\5&15\\6&20\end{array}\right]

Even numbers are 2, 4, and 6.  The total number of times she rolled an even number is 13 + 17 + 20 = 50.

So the probability is 50/96.

7 0
3 years ago
PLEASE HELP!!!!!! The length of a rectangle is three times its width. If the perimeter of the rectangle is 56 cm, find its area.
Alexus [3.1K]

Step-by-step explanation:

l = length

w = width

l = 3w

perimeter p = 2l + 2w = 56

using the identity of the first equation

p = 2(3w) + 2w = 56

6w + 2w = 56

8w = 56

w = 7 cm

l = 3w = 3×7 = 21 cm

so, the area is

l×w = 21×7 = 147 cm²

8 0
2 years ago
Other questions:
  • Simplify.
    14·2 answers
  • 3 distance questions:
    8·1 answer
  • Can Anyone help me out?
    8·2 answers
  • 18.There is no battery in this simulation. Move the magnet with the N pole toward the loops (coils) connected to the light bulb
    7·1 answer
  • Critical thinking is important for evaluating which parts of advertisements are true and can be believed.
    11·2 answers
  • What is the solution to this equation?<br> 4x = 32
    6·2 answers
  • Which transformation can be used to prove Similarity and why?
    6·1 answer
  • Macie na to 1 godz daje naj szybko pls
    6·1 answer
  • Which postulate can be used to prove the two triangles are congruent?
    10·1 answer
  • Solve.<br> X = -7<br> 4x - 4y = 12<br> (x,y)
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!