Answer:
a) what is the probability that Neither will of these products launch ?
= 0.30
b) At least one product will be launched ?
= 0.70
Step-by-step explanation:
From the above question, we have the following information:
P(A) = 0.45
P(B) = 0.60
P(A ∩ B) = P(A and B) launching = 0.35
Step 1
We find the Probability that A or B will launch
P (A ∪ B) = P(A) + P(B) - P(A ∩ B)
= 0.60 + 0.45 - 0.35
= 1.05 - 0.35
= 0.70
a) what is the probability that Neither will of these products launch ?
1 - Probability ( A or B will launch)
= 1 - 0.70
= 0.30
b)At least one product will be launched?
This is equivalent to the probability that A or B will be launched
P (A ∪ B) = P(A) + P(B) - P(A ∩ B)
= 0.60 + 0.45 - 0.35
= 1.05 - 0.35
= 0.70
Answer:

General Formulas and Concepts:
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Derivative Rule [Chain Rule]: ![\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28g%28x%29%29%5D%20%3Df%27%28g%28x%29%29%20%5Ccdot%20g%27%28x%29)
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>

<u>Step 2: Differentiate</u>
- Logarithmic Differentiation [Derivative Rule - Chain Rule]:

- Trigonometric Differentiation [Derivative Rule - Chain Rule]:

- Basic Power Rule:

- Rewrite [Trigonometric Identities]:

Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
The angle between the planes is the same as the angle between their normal vectors, which are
<em>n</em><em>₁</em> = ⟨1, 1, 1⟩
<em>n</em><em>₂</em> = ⟨4, 3, 1⟩
The angle <em>θ</em> between the vectors is such that
⟨1, 1, 1⟩ • ⟨4, 3, 1⟩ = ||⟨1, 1, 1⟩|| ||⟨4, 3, 1⟩|| cos(<em>θ</em>)
Solve for cos(<em>θ</em>) :
4 + 3 + 1 = √(1² + 1² + 1²) √(4² + 3² + 1²) cos(<em>θ</em>)
8 = √3 √26 cos(<em>θ</em>)
cos(<em>θ</em>) = 8/√78
Step-by-step explanation:
y = 8x² + 8x - 96
y = 8(x² + x - 12)
y = 8(x + 4)(x - 3)
When y = 0, 8(x + 4)(x - 3) = 0.
=> x = -4 or x = 3. (B)