There are 5 red marbles, 8 blue marbles, and 12 green marbles in a bag. What is the theoretical probability of randomly drawing
2 answers:
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Answer:
C.
General Formulas and Concepts:
<u>Calculus</u>
- Mean Value Theorem (MVT) - If f is continuous on interval [a, b], then there is a c∈[a, b] such that
- MVT is also Average Value
Step-by-step explanation:
<u>Step 1: Define</u>
f'(c) = 20
Interval [1, b]
<u>Step 2: Check/Identify</u>
Function [1, b] is continuous.
Derivative [1, b] is continuous.
∴ There exists a c∈[1, b] such that
<u>Step 3: Mean Value Theorem</u>
- Substitute:
- Rewrite:
And we have our final answer!
Answer: 1)
2)
Step-by-step explanation:
1) Let the function that shows the thickness of the paper after n folds,
---------(1)
Since, According to the question,
Initially the thickness of the paper = 0.6
That is, at n = 0, t(0) = 0.6
By equation (1),
Hence the function that shows the given situation,
-----------(2)
Again when we fold the paper the thickness of the paper will be doubled.
Thus, at n = 1, t(1) = 1.2
By equation (2),
Thus, the complete function is,
2) Let the function that is passing through the points (-2, 2/5) and (-1,2),
---------(1)
For f(x) = 2, x = -1
By equation (1),
---------(2)
Also, For f(x) = 2/5, x = -2
Again, By equation (1),
By substituting this value in equation (2),
We get, a = 10
Hence, from equation (1), the function that is passing through the points (-2, 2/5) and (-1,2),