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DaniilM [7]
2 years ago
11

The ________ of an event A is the collection of all outcomes in the sample space that are not in A.

Mathematics
1 answer:
IRISSAK [1]2 years ago
8 0

Answer:

The complement of an event A is the collection of all outcomes in the sample space that are not in A.

Step-by-step explanation:

We have to fill the sentence in the given question:

Complement of an event:

  • Let A be an event, then complement of an event is defined as the the event with outcome not in A.
  • It is represented as A'
  • We can write P(A') = 1- P(A)
  • P(A) + P(A') = 1

Thus, we can fill the bank as

The complement of an event A is the collection of all outcomes in the sample space that are not in A.

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An aeroplane X whose average speed is 50°km/hr leaves kano airport at 7.00am and travels for 2 hours on a bearing 050°. It then
Zigmanuir [339]

Answer:

(a)123 km/hr

(b)39 degrees

Step-by-step explanation:

Plane X with an average speed of 50km/hr travels for 2 hours from P (Kano Airport) to point Q in the diagram.

Distance = Speed X Time

Therefore: PQ =50km/hr X 2 hr =100 km

It moves from Point Q at 9.00 am and arrives at the airstrip A by 11.30am.

Distance, QA=50km/hr X 2.5 hr =125 km

Using alternate angles in the diagram:

\angle Q=110^\circ

(a)First, we calculate the distance traveled, PA by plane Y.

Using Cosine rule

q^2=p^2+a^2-2pa\cos Q\\q^2=100^2+125^2-2(100)(125)\cos 110^\circ\\q^2=34175.50\\q=184.87$ km

SInce aeroplane Y leaves kano airport at 10.00am and arrives at 11.30am

Time taken =1.5 hour

Therefore:

Average Speed of Y

=184.87 \div 1.5\\=123.25$ km/hr\\\approx 123$ km/hr (correct to three significant figures)

(b)Flight Direction of Y

Using Law of Sines

\dfrac{p}{\sin P} =\dfrac{q}{\sin Q}\\\dfrac{125}{\sin P} =\dfrac{184.87}{\sin 110}\\123 \times \sin P=125 \times \sin 110\\\sin P=(125 \times \sin 110) \div 184.87\\P=\arcsin [(125 \times \sin 110) \div 184.87]\\P=39^\circ $ (to the nearest degree)

The direction of flight Y to the nearest degree is 39 degrees.

7 0
3 years ago
What is .466666 as a fraction?
katovenus [111]
As a fraction it is 466666/1000000
6 0
2 years ago
Read 2 more answers
An angle measures 64 degrees more than the measure of its complementary angle. What is the measure of each angle?
fiasKO [112]

Answer:

13 and 77 degrees

Step-by-step explanation:

Complementary = 90 degrees

Set an angle to x

x+(x+64)=90

2x+64=90

2x=26

x=13

angle measures: 13, 77 degrees

7 0
2 years ago
The volume of a rectangular box with a square base remains constant at 500 cm3 as the area of the base increases at a rate of 6
Andre45 [30]

Answer:

the rate at which the height of the box is decreasing is -0.0593 cm/s

Step-by-step explanation:

Given the data in the question;

Constant Volume of a rectangular box with a square base = 500 cm³

area of the base increases at a rate of 6 cm²/sec

so change in the area of the base with respect to time dA/dt = 6 cm²/sec

each side of the base is 15 cm long

so Area of the base = 15 cm × 15 cm = 225 cm²

the rate at which the height of the box is decreasing = ?

Now,

V = Ah

dv/dt = 0 ⇒ Adh/dt + hdA/DT = 0

⇒ dh/dt = -hdA/dt / A

we substitute

dh/dt = [ -( 500 / 225 ) × 6 ] / 225

dh/dt = [ -(2.22222 × 6)  ] / 225

dh/dt = [ -13.3333 ] / 225

dh/dt = -0.0593 cm/s

Therefore, the rate at which the height of the box is decreasing is -0.0593 cm/s

7 0
2 years ago
What is the solution to the system: 9x+3y=24 2y+4x=8
egoroff_w [7]

Answer:

x = 4, y = -4

Step-by-step explanation:

9x + 3y = 24

3x + y = 8                       divide both sides by 3

y = 8 - 3x                        subtract 3x from both sides

2y + 4x = 8

2(8 - 3x) + 4x = 8             replace y with 8 - 3x

16 - 6x + 4x = 8                distributive property

-6x + 4x = 8 - 16               subtract 16 from both sides

-2x = -8                            divide both sides by -2

x = 4

y = 8 - 3x

y = 8 - 3(4)                        replace x with 4

y = 8 - 12

y = -4

8 0
2 years ago
Read 2 more answers
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