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borishaifa [10]
2 years ago
9

P, Q and R are points in the same

Mathematics
1 answer:
Anna11 [10]2 years ago
6 0

Answer: 119°

Step-by-step explanation:

From the positive y-axis, all angles are measured clockwise

PR = PQ + QR = 5[150°] + 3[60°]

X = 5*sin150 + 3*sin60 = <u>5.1</u>

Y = 5*Cos150 + 3*Cos60 = <u>-2.83</u>

TanA = X/Y

A = -61° = 61° East of South = 119° Clockwise

Therefore, the bearing of R from P is 119°

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Find the area of the semicircle. diameter = 12
dimaraw [331]

Answer:

\huge\boxed{\sf Area\ of \ Semicircle = 56.55 \ units^2}

Step-by-step explanation:

Diameter = 12

Radius = 12/2 = 6

\sf Area\ of \ Semicircle =\frac{\pi r^2}{2} \\Area\ of \ Semicircle =\frac{\pi (6)^2}{2} \\Area \ of \ Semicircle = \frac{\pi (36)}{2}\\ Area \ of \ Semicircle = 18 \ pi

\sf Area\ of \ Semicircle = 56.55 \ units^2

7 0
3 years ago
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80% of an airline's flights depart on-time and 20% do not. Of those that depart on-time, 95% arrive on-time. Of those that depar
Dmitry_Shevchenko [17]

Answer:

0.78

Step-by-step explanation:

given that 80% of an airline's flights depart on-time and 20% do not.

Of those that depart on-time, 95% arrive on-time. Of those that depart late, 10% arrive on-time

Let A be the event that flight departs on time.

Now A and A' are mutually exclusive and exhaustive

Let B be the event the flight arrives on time

Using total probability calculation we have

the chance of someone taking a flight that will arrive on-time

= P(B)

=P(A)+P(A'B)\\= 0.80(0.95) +0.20(0.10)\\= 0.76+0.02\\=0.78

4 0
3 years ago
Which relationships have the same constant of proportionality between yyy and xxx as the equation 3y=27x3y=27x3, y, equals, 27,
Tanya [424]

Answer:

A, B and C

Step-by-step explanation:

In the equation: 3y=27x

Making y the subject of the equation, we have:

y=\frac{27}{3}x\\y=9x

The constant of proportionality between y and x  is 9.

We want to determine which relationships have the same constant of proportionality 9.

<u>Option A</u>

y=9x

The constant of proportionality is 9.

<u>Option B</u>

2y=18x

Divide both sides by 2 to obtain: y=9x

The constant of proportionality is 9.

<u>Option C</u>

x=3, y=1/3

Substitution into y=kx gives:

1/3=3k

k=9

The constant of proportionality is 9.

<u>Option D</u>

x=6, y=2/3

Substitution into y=kx gives:

2/3=6k

k=2/3*6=4

The constant of proportionality is 4.

<u>Option E</u>

When x=2, y=18

Substitution into y=kx gives:

18=2k

k=9

However, when x=4, y=27

Substitution into y=kx gives:

27=4k

k=6.75

This is not a proportional relation since the constant of proportionality is not equal.

The correct options are A, B and C

4 0
3 years ago
The sum of three consective nimbers is 54. What is the smallest of these numbers.
storchak [24]

Answer; 17, 18 and 19


Explanation:

Number = x , x + 1 , x + 2


x + x + 1 + x + 2 = 54

3x + 3 = 54

3x = 51

x = 17


x = 17

x + 1 = 18

x + 2 = 19


3 0
3 years ago
PLZ HELP ASAP!
rusak2 [61]

I would guess that 4.25 pounds is another way to say 4 1/4 pounds, but without being given the answer choices, I can only give you an educated guess.

3 0
4 years ago
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