Answer:
(a)
and
are indeed mutually-exclusive.
(b)
, whereas
.
(c)
.
(d)
, whereas 
Step-by-step explanation:
<h3>(a)</h3>
means that it is impossible for events
and
to happen at the same time. Therefore, event
and
are mutually-exclusive.
<h3>(b)</h3>
By the definition of conditional probability:
.
Rearrange to obtain:
.
Similarly:
.
<h3>(c)</h3>
Note that:
.
In other words,
and
are collectively-exhaustive. Since
and
are collectively-exhaustive and mutually-exclusive at the same time:
.
<h3>(d)</h3>
By Bayes' Theorem:
.
Similarly:
.
For the scale factor, use the dimensions from similar sides:
Using 18 from the original image you would use 6 from the scaled image.
18 /6 = 3
This means the scaled image is 3 times smaller than the original. Because the scaled image is smaller divide 1 by the scale factor to get 1/3.
Q2:
The scale factor is 1 inch = 12 miles.
Multiply the total inches by 12:
6.5 x 12 = 78 miles.
Answer:
Option A & D are correct Option.
Step-by-step explanation:
We are given with following :
Area of Base = 15 in.²
Height of Prism = 3 in.
Length of edge of base = 5 in.
Volume of Prism = Area of Base × Height = 15 × 3 = 45 in.³
Therefore, Option A & D are correct Option.
The area of the kitchen counter is 21 square ft.
<u>Step-by-step explanation:</u>
Area of the sink = 2 x 3
= 6 square ft.
Area of the kitchen counter = 9 x 3 -(6)
=27 - 6
= 21 square ft.
The area of the kitchen counter is 21 square ft.
The length of the major arc LNM is 
<h3><u>Length of an arc</u></h3>
From the question,
We are to determine the value of the length of the major arc LNM
The length of the major arc LNM can be calculated using the formula

Where r is the radius
First, we will determine the value of the reflex ∠LKM
Reflex ∠LKM + ∠LKM = 360° (<em>Sum of angles at a point</em>)
From the given information,
∠LKM = 70°
Then,
Reflex ∠LKM + 70° = 360°
Reflex ∠LKM = 360° - 70°
Reflex ∠LKM = 290°
Also, from the question
r = 3 cm
Now, putting the parameters into the formula, we get

Then,


Hence, the length of the major arc LNM is 
Learn more on calculating length of an arc here: brainly.com/question/2005046