Mathematics : asked on gianna61
 02.11.2021

If 52 ,52,d are angle of the triangle d=

. 5

Faq

Mathematics
Step-by-step answer
P Answered by PhD

the Standard deviation for the angles is 0.00766°

Step-by-step explanation:

We first covert the angles to standard angle format.

For A) 42° 52' 09'' we have;

42 + (52/60) + (9/3600)

= 42 + 0.866 + 0.00305 = 42.8685°

Repeating the same procedure for the other angles we have

B) 42. 88605°

C) 42.87377°

D) 42.87461°

E) 42.87211°

F) 42.88438°

Mean of the angles becomes

x' = (42.8685+42.88605+42.87377+42.87461+42.87211+42.88448)/6

x' = 42.87657°

x - x' = 0.00807, 0.00948, 0.0028, 0.00196, 0.00446, 0.00781

NB: x - x' values is the mean angle minus the individual angle. We ignore the minus signs

(x - x') ^2 = 0.000065, 0.0000898, 0.0000784, 0.0000384, 0.0000198, 0.0000609

Variance = ( 0.000065+0.0000898+0.0000784+0.0000384+0.0000198+0.0000609)/6

= 0.000358/6 = 0.0000587.

Standard deviation = square root of variance

SD = 0.0000587^0.5 = 0.00766°

Mathematics
Step-by-step answer
P Answered by PhD

A. ∡R=43°, ∡T=85°, ∡X=43°, ∡Z=85°

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. The types of triangles are scalene triangle, equilateral triangle, right angled triangle and obtuse triangle.

Cosine rule states that given a triangle with sides a, b, c and their corresponding angles opposite to the sides as A, B, C. Then:

a^2=b^2+c^2-2bc*cos(A)

In triangle XYZ, we can find XZ using cosine rule:

XZ^2=XY^2+YZ^2-2(XY)(YZ)cosY\\\\subtituting:\\\\XZ^2=15^2+8^2-2(15)(8)cos(52)\\\\XZ^2=141.24\\\\XZ=11.88\\\\Using\ sine\ rule:\\\\\frac{XZ}{sin(Y)}=\frac{XY}{sin(Z)}\\\\\frac{11.88}{sin(52)}=\frac{15}{sin(Z)}\\\\sin(Z)=15*sin(52) /11.88\\\\sin(Z)=0.9946\\\\Z=sin^{-1}(0.9946)\\\\Z=85^0

∠X + ∠Y + ∠Z = 180° (sum of angles in a triangle)

∠X + 52 + 85 = 180

∠X + 137 = 180

∠X = 43°

∠X = 3w - 35

3w - 35 = 43

3w = 78

w = 26

In triangle RST, using sine rule:

∠R = w + 17

∠R = 26 + 17

∠R = 43°

∠R + ∠S + ∠T = 180° (sum of angles in a triangle)

43 + 52 + ∠T = 180

∠T + 95 = 180

∠T = 85°

Mathematics
Step-by-step answer
P Answered by PhD
X = 180 - (67 + 52)

because all 3 of them angles form a linemeaning all 3 angles, when added = 180
Mathematics
Step-by-step answer
P Answered by PhD
X = 180 - (67 + 52)

because all 3 of them angles form a linemeaning all 3 angles, when added = 180
Mathematics
Step-by-step answer
P Answered by PhD

the Standard deviation for the angles is 0.00766°

Step-by-step explanation:

We first covert the angles to standard angle format.

For A) 42° 52' 09'' we have;

42 + (52/60) + (9/3600)

= 42 + 0.866 + 0.00305 = 42.8685°

Repeating the same procedure for the other angles we have

B) 42. 88605°

C) 42.87377°

D) 42.87461°

E) 42.87211°

F) 42.88438°

Mean of the angles becomes

x' = (42.8685+42.88605+42.87377+42.87461+42.87211+42.88448)/6

x' = 42.87657°

x - x' = 0.00807, 0.00948, 0.0028, 0.00196, 0.00446, 0.00781

NB: x - x' values is the mean angle minus the individual angle. We ignore the minus signs

(x - x') ^2 = 0.000065, 0.0000898, 0.0000784, 0.0000384, 0.0000198, 0.0000609

Variance = ( 0.000065+0.0000898+0.0000784+0.0000384+0.0000198+0.0000609)/6

= 0.000358/6 = 0.0000587.

Standard deviation = square root of variance

SD = 0.0000587^0.5 = 0.00766°

Mathematics
Step-by-step answer
P Answered by PhD

Part 2) What's the perimeter of a regular heptagon if one side measures 3 inches?

we know that

The number of sides in a regular heptagon is equal to 7

so

The perimeter is equal to

P=7*a

where

a is the length side

in this problem

a=3\ in

substitute

P=7*3 =21\ in

therefore

the answer Part 2) is the option

B. 21 in.

Part 3) A polygon that has all sides the same measure and all angles the same measure is called what?

we know that

When all angles are equal and all sides are equal, is a polygon that is equiangular and equilateral, so, is called a regular polygon

therefore

the answer part 3) is the option

C. Regular polygon

Part 4) The gazebo in the park is an octagon. Each side of the gazebo is 4 feet long. What is the perimeter of the gazebo?

we know that

The number of sides in a octagon is equal to 8

so

The perimeter is equal to

P=8*a

where

a is the length side

in this problem

a=4\ ft

substitute

P=8*4 =32\ ft

therefore

the answer Part 4) is the option

D. 32 feet

Part 5) Which of the following best describes a plane?

we know that

--The edge of a desk is a piece of a straight or curved line.

-- A curve in a road is a piece of a curved line.

-- The intersection of two walls is a piece of a straight line

therefore

the answer Part 5) is the option

A. The surface of a flat table

Part 6) Two angles are supplementary. The first angle measures 40°. What's the measurement of the second angle?

we know that

Two angles are supplementary if the sum of their angles is equal to 180 degrees

so

Let

x------> the measure of the second angle

40+x=180\\  x=180-40\\  x=140\ degrees

therefore

the answer Part 6) is the option

C. 140°

Part 7) In order for a button to fit through its buttonhole, the hole needs to be the size of the button's diameter. What size buttonhole is needed for a button with a circumference of 9.42 centimeters?

we know that

The circumference is equal to

C= \pi D

where

D is the diameter

solve for D

D=\frac{C}{\pi}

D=\frac{9.42}{\pi}

D= 3\ cm

therefore

the answer Part 7) is the option

C. 3 centimeters

Part 8) The Pentagon in Washington DC is immense in size, with each outside wall 921 feet in length. What is the perimeter of the Pentagon?

we know that

The number of sides in a pentagon is equal to 5

so

The perimeter is equal to

P=5*a

where

a is the length side

in this problem

a=921\ ft

substitute

P=5*921 =4,605\ ft

therefore

the answer Part 8) is the option

D. 4,605 ft.

Mathematics
Step-by-step answer
P Answered by PhD

Part 2) What's the perimeter of a regular heptagon if one side measures 3 inches?

we know that

The number of sides in a regular heptagon is equal to 7

so

The perimeter is equal to

P=7*a

where

a is the length side

in this problem

a=3\ in

substitute

P=7*3 =21\ in

therefore

the answer Part 2) is the option

B. 21 in.

Part 3) A polygon that has all sides the same measure and all angles the same measure is called what?

we know that

When all angles are equal and all sides are equal, is a polygon that is equiangular and equilateral, so, is called a regular polygon

therefore

the answer part 3) is the option

C. Regular polygon

Part 4) The gazebo in the park is an octagon. Each side of the gazebo is 4 feet long. What is the perimeter of the gazebo?

we know that

The number of sides in a octagon is equal to 8

so

The perimeter is equal to

P=8*a

where

a is the length side

in this problem

a=4\ ft

substitute

P=8*4 =32\ ft

therefore

the answer Part 4) is the option

D. 32 feet

Part 5) Which of the following best describes a plane?

we know that

--The edge of a desk is a piece of a straight or curved line.

-- A curve in a road is a piece of a curved line.

-- The intersection of two walls is a piece of a straight line

therefore

the answer Part 5) is the option

A. The surface of a flat table

Part 6) Two angles are supplementary. The first angle measures 40°. What's the measurement of the second angle?

we know that

Two angles are supplementary if the sum of their angles is equal to 180 degrees

so

Let

x------> the measure of the second angle

40+x=180\\  x=180-40\\  x=140\ degrees

therefore

the answer Part 6) is the option

C. 140°

Part 7) In order for a button to fit through its buttonhole, the hole needs to be the size of the button's diameter. What size buttonhole is needed for a button with a circumference of 9.42 centimeters?

we know that

The circumference is equal to

C= \pi D

where

D is the diameter

solve for D

D=\frac{C}{\pi}

D=\frac{9.42}{\pi}

D= 3\ cm

therefore

the answer Part 7) is the option

C. 3 centimeters

Part 8) The Pentagon in Washington DC is immense in size, with each outside wall 921 feet in length. What is the perimeter of the Pentagon?

we know that

The number of sides in a pentagon is equal to 5

so

The perimeter is equal to

P=5*a

where

a is the length side

in this problem

a=921\ ft

substitute

P=5*921 =4,605\ ft

therefore

the answer Part 8) is the option

D. 4,605 ft.

Physics
Step-by-step answer
P Answered by PhD

A

Explanation:

Snell's law states:

n₁ sin θ₁ = n₂ sin θ₂

where n is the index of refraction and θ is the angle of incidence (relative to the normal).

The index of refraction of air is approximately 1.  So:

1 sin 30° = 1.52 sin θ

θ ≈ 19°

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