Answer:
0.05
Step-by-step explanation:
this is because the total probability always adds up to 1
Answer:
Step-by-step explanation:
A. y-Intercept of ƒ(x)
ƒ(x) = x² - 4x + 3
f(0) = 0² - 4(0) + 3 = 0 – 0 + 3 = 3
The y-intercept of ƒ(x) is (0, 3).
If g(x) opens downwards and has a maximum at y = 3, it's y-intercept is less than (0, 3).
Statement A is TRUE.
B. y-Intercept of g(x)
Statement B is FALSE.
C. Minimum of ƒ(x)
ƒ(x) = x² - 4x + 3
a = 1; b = -4; c = 3
The vertex form of a parabola is
y = a(x - h)² + k
where (h, k) is the vertex of the parabola.
h = -b/(2a) and k = f(h)
h = -b/2a = -(-4)/(2×1 = 2
k = f(2) = 2² - 4×2 + 3 =4 – 8 +3 = -1
The minimum of ƒ(x) is -1. The minimum of ƒ(x) is at (2, -1).
Statement C is FALSE.
D. Minimum of g(x)
g(x) is a downward-opening parabola. It has no minimum.
Statement D is FALSE
The table is attached in the figure.
g(x) = f(4x) ⇒⇒⇒ differentiating both sides with respect to x
∴ g'(x) = ⇒⇒⇒⇒⇒⇒ chain role
To find g '(0.1)
Substitute with x = 0.1
from table:
f'(0.1) = 1 ⇒ from the table
∴ g'(0.1) = 4 * [ f'(0.1) ] = 4 * 1 = 4
Answer:
Yes, Based on this data, baldness and being over 45 are independent events, because P(bald | over 45) = P(bald).
Step-by-step explanation:
The given data is as following:
Under 45 Over 45 Total
Bald : 24 16 40
Not Bald : 36 24 60
Total : 60 40 100
<u>We should know that:</u>
The events A and B are independent when If P(A∩B) = P(A) * Pr(B)
Using conditional probabilities this property can be written as:
P(A|B) = P(A∩B)/P(B) = P(A) * Pr(B)/ P(B) = P(A)
So, we will check baldness and being over 45 independent events.
From the given data:
1. P(man is bald) = 40/100 = 0.4
3. P(bald | over 45) = 16/40 = 0.4
So, P(man is bald) = P(bald | over 45) = 0.4
<u>So, The events are independent. </u>