Answer:
a) P(X≥6) = 0.9614
b) P(7≤ X ≤9) = 0.628
c) P(X≤5) = 0.0386
Step-by-step explanation:
This can be solved using the binomial distribution formula:
P(X=x) = ⁿCₓ pˣ qⁿ⁻ˣ
Where p = probability of success
q = probability of failure = 1-p
n = number of trials
x = number of successful trials
We have p = 70% = 0.7
n = 12
a) Find the probability that the number who disapprove of smoking pot daily is no less than 6 i.e. P(X≥6). This can be calculated as:
P(X≥6) = 1 - P(X<6)
= 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)]
= 1 - [¹²C₀ (0.7)⁰(0.3)¹² + ¹²C₁ (0.7)¹(0.3)¹¹ + ¹²C₂ (0.7)²(0.3)¹⁰ + ¹²C₃ (0.7)³(0.3)⁹ + ¹²C₄ (0.7)⁴(0.3)⁸ + ¹²C₅ (0.7)⁵(0.3)⁷]
= 1 - (0.000000531 + 0.0000148 + 0.0001909 + 0.00148 + 0.00779 + 0.02911)
= 1 - 0.0386
P(X≥6) = 0.9614
b) P(7≤ X ≤9) = P(X=7) + P(X=8) + P(X=9)
= ¹²C₇ (0.7)⁷(0.3)¹²⁻⁷ + ¹²C₈ (0.7)⁸(0.3)¹²⁻⁸ + ¹²C₉ (0.7)⁹(0.3)¹²⁻⁹
= 0.158 + 0.231 + 0.239
P(7≤ X ≤9) = 0.628
c) P(X≤5) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)
= ¹²C₀ (0.7)⁰(0.3)¹² + ¹²C₁ (0.7)¹(0.3)¹¹ + ¹²C₂ (0.7)²(0.3)¹⁰ + ¹²C₃ (0.7)³(0.3)⁹ + ¹²C₄ (0.7)⁴(0.3)⁸ + ¹²C₅ (0.7)⁵(0.3)⁷
P(X≤5) = 0.0386
For 6: 12, 18, 24, 30, 36
For 9: 18, 27, 36, 45, 54
For 7: 14, 21, 28, 35, 42
<u><em>Answer:</em></u>
CG
<u><em>Explanation:</em></u>
A plane is defined using three points.
The intersection between two planes is a line
<u>Now, we are given the planes:</u>
<span>ACG and BCG
</span>
By observing the names of the two planes, we can note that the two points C and G are common.
This means that line CG is present in both planes which means that the two planes intersect forming this line.
Hope this helps :)
N+14 that’s it! Pls mark as brainliest
Answer:
210.25 or 210.3495409 depending on how your teacher does it
Step-by-step explanation:
Looking for circumference of the circle when it asks for perimeter
Formula for Circumference C = π x r <em>3 (cubed)</em>
The diameter is 10 so you take half of ten or 10 ÷ 2 = 5
5 x 5 x 5 = 125 (r squared equation)
125 x π = 392.6990817
Some classes ans stuff use 3.14 for pi so i'll show it that way too
125 x 3.14 = 392.5
(equation with π)
392.6990817 ÷ 2 = 196.3495409
196.3495409 + 14 = 210.3495409
(equation with 3.14)
392.5 ÷ 2 = 196.25
14 + 196.25 = 210.25
