Charles rolled a number cube labeled from 1 to 6. What is the probability that he will roll a number greater than 2? in a fracti
2 answers:
Answer:
or 2/3
Step-by-step explanation:
<u>Key skills needed: Probability, Casework, Fractions</u>
1) He rolled a number cube (or a dice) and it has 6 numbers: 1,2,3,4,5,6
2) We want to find the probability a number will be greater than 2
The numbers that are greater than 2 are ---> 3,4,5 and 6
That is 4 numbers.
3) 4 out of 6 of the numbers work. This means the probability is 4/6
4) 4/6 then can be simplified into 2/3 (take out 2 from both the numerator and the denominator)
The answer is 2/3
<em>Hope you understood and have a nice day!! :D</em>
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Answer:
(B)
General Formulas and Concepts:
<u>Calculus</u>
Limits
Derivatives
- The definition of a derivative is the slope of the tangent line.
Derivative Notation
Instantaneous Rates
- Tangent Line:
Step-by-step explanation:
Since we are trying to find a <em>rate</em> at which W(t) changes, we must find the <em>derivative</em> at <em>t</em> = 3.
We are given 2 close answer choices that would have the same <em>numerical</em> answer but different <em>meanings</em>:
- (A)
- (B)
If we look at answer choice (A), we see that our units would simply just be volume. It would not have the units of a rate of change. Yes, it may be the closest numerically correct answer, but it does not tell us the <em>rate</em> at which the volume would be changing and it is not a derivative.
If we look at answer choice (B), we see that our units would be cm³/s, and that is most certainly a rate of change. Answer choice (B) is also a <em>derivative</em> at <em>t</em> = 3, and a derivative tells us what <em>rate</em> something is changing.
∴ Answer choice (B) will give us the best estimate for the value of the instantaneous rate of change of W(t) when <em>t</em> = 3.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Book: College Calculus 10e