Let

denote the event that an HD is defective, and

the event that a particular HD was produced at facility

.
You are asked to compute



From the definition of conditional probabilities, the first two will require that you first find

. Once you have this, part (c) is trivial.
I'll demonstrate the computation for part (a). Part (b) is nearly identical.
(a)

Presumably, the facility responsible for producing a given HD is independent of whether the HD is defective or not, so

.
Use the law of total probability to determine the value of the denominator:

We know each of the component probabilities because they are given explicitly: 0.015, 0.02, 0.01, and 0.03, respectively. So

and thus

(b) Similarly,

(c)
When I see the words "instantaneous rate of change", I have to assume that you're in some stage of pre-calculus in your math class.
The instantaneous rate of change of a function is just its first derivative.
We have the function
V(r) = 3 π r²
and we need its first derivative with respect to ' r '. That shouldn't be
too hard, because the ' 3 π ' is nothing but constants.
Watch me while I do it slowly for you:
-- The derivative of ' r² ' with respect to ' r ' is ' 2r '.
-- The derivative of V(r) with respect to ' r ' is (3 π) times the derivative of ' r² '.
-- The derivative of V(r) with respect to ' r ' is (3 π) times (2r) = <u>6 π r</u> .
The value of the derivative when r=3 is (6 π 3) = 18π = about <em>56.5 feet³/foot .</em>
ANSWER
58°
EXPLANATION
The relationship between the measure of the bigger arc and the smaller arc and the angle created by the secant and the tangent is

Multiply through by 2
This implies that

We simplify to get:

Solve for x.



Answer:Here you can enter any number with as many or as few decimal places as you want, and we will round it to the nearest one decimal place. Please enter your
Step-by-step explanation:
33. -8 belongs to:
- Set of real numbers; all rational and irrational numbers
- Set of integers; positive and negative whole numbers
34. 14 belongs to:
- Set of natural numbers; all positive whole numbers
- Set of real numbers; all rational and irrational numbers
35. 9.23 belongs to:
- Set of real numbers; all rational and irrational numbers
36.
belongs to:
- Set of real numbers; all rational and irrational numbers
37. Zero (0) belongs to:
- Set of Integers; all positive and negative whole numbers
- Set of real numbers; all rational and irrational numbers
38. -1 belongs to:
- Set of integers; all positive and negative whole numbers
- Set of real numbers; all rational and irrational numbers
39. 1/2 belongs to:
- Set of real numbers; all rational and irrational numbers
40. 0.3 where 3 is recurring belongs to:
- Set of real numbers; all rational and irrational numbers