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elixir [45]
3 years ago
14

I need answer for page 2 plssss

Mathematics
1 answer:
Katena32 [7]3 years ago
8 0

Answer:

Question 4:  The minor arc is <em>AB </em><em>and has a measure of 115°.</em>

Question 5: 15\pi\: m

Question 6: The area of the figure is 70.6in^2

Question 7: -5.934\:  \text{radians.}

Question 8: -30^o

Step-by-step explanation:

Question 4:

<em>The minor arc of the circle that subtends the least degrees</em>, and for this circle it is AB and has a measure of 115°.

Question 5:

The length L of the arc of the circle with a radius R subtending \theta radians is

L = \theta R

The arc YPX measures 360° - 90° = 270, which is \dfrac{3}{2}\pi; therefore,

L = \dfrac{3}{2}\pi  *10

\boxed{L = 15\pi \:m }

Question 6:

We first need to find what percent of the circle the figure is.

165° is

\dfrac{165}{360} *100\% = 45.83\%

percent of 360°.

Therefore, the area of the figure must also be 45.83% of the area of the circle. The area of the circle is  

A = \pi (7)^2\\A = 153.94in^2

therefore, the are of the figure is

A_{seg} = 153.94*45.83\% \\\\\boxed{A_{seg} = 70.6in^2}

Question 7:

One radian is 57.296°; therefore, -340° in radians is

\dfrac{-340^o}{57.296^o}  = -5.934\:  \text{radians.}

Question 8:

One radian is 57.296°; therefore, \dfrac{-\pi }{6} radians in degrees is

\dfrac{-\pi }{6}*57.296^o = -30^o

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In a survey, 672 adults were asked what television programs they had recently watched. The following information was obtained: 2
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Answer:

a. the Big Game = 263

b. the Big Game but not the New Movie = 159

c. at least one program = 446

d. both programs = 104.

Step-by-step explanation:

Given that:

Total adults asked about TV programs, n(U) = 672

Total adults who watch New Movie, n(A) = 287

Let n(B) be the number of adults who watch Big Game.

Total adults who watch New Movie but not Big Game, n(A-B) = 183

As per formula:

n(A-B) = n(A) - n(A \cap B)

Where n(A \cap B) is the number of adults who watch New Movie and Big Game both.

n(A \cap B) = n(A) - n(A-B)

n(A \cap B) = 287 - 183 = 104

<u>Formula:</u>

n(U) = n(A \cup B) + n(A \cup B)'

n(A \cup B) is the number of adults who watch at least one program.

n(A \cup B)' is the number of adults who do not watch any program.

Given that n(A \cup B)' = 226

Putting values in the above formula:

672 = n(A \cup B) + 226

n(A \cup B) = 672 - 226 = 446

<u>Formula:</u>

n(A \cup B) = n(A) + n(B) - n(A \cap B)

446 = 287 + n(B) - 104

n(B) = 446 + 104 - 287

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The number of adults who watch the Big Game but not the New Movie, <em>n(B - A)</em>

<u>Formula:</u>

n(B - A) = n(B) - n(A \cap B)

n(B - A) = 263 - 104 = 159

So, the number of surveyed adults who watch:

a. the Big Game, n(A) = 263

b. the Big Game but not the New Movie, n(B - A) = 159

c. at least one program, n(A \cup B) = 446

d. both programs, n(A \cap B) = 104.

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Answer:

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Given that the vertices of the polygon in clockwise order from the top left corner are ABCD, we have the diagonals as AC and DB

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Therefore, given that the coordinates of the location of the midpoint of the diagonals AC and DB is the same, the diagonals bisect each other

Each diagonal passes through the midpoint of the other diagonal.

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