Answer:
0.38% probability that the sample contains exactly two defective parts.
Step-by-step explanation:
For each part, there are only two possible outcomes. Either it is defective, or it is not. The probabilities for each part being defective are independent from each other. So we use the binomial probability distribution to solve this problem.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
In this problem we have that:
What is the probability that the sample contains exactly two defective parts?
This is
0.38% probability that the sample contains exactly two defective parts.
Answer:
(a)
(b)
(c) Simplifying first
General Formulas and Concepts:
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]:
Derivative Property [Addition/Subtraction]:
Derivative Rule [Basic Power Rule]:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Derivative Rule [Product Rule]:
Derivative Rule [Quotient Rule]:
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify.</em>
<em />
<u>Step 2: Differentiate Way 1</u>
- Derivative Rule [Quotient Rule]:
- Rewrite [Derivative Property - Addition/Subtraction]:
- Derivative Rule [Product Rule]:
- Rewrite [Derivative Rule - Multiplied Constant]:
- Derivative Rule [Basic Power Rule]:
- Simplify:
- Simplify:
- Simplify:
- Simplify:
- Rewrite:
∴ we find the derivative of the given function but it is a tedious method of computation.
<u>Step 3: Differentiate Way 2</u>
- [Function] Rewrite:
- [Function] Simplify:
- [Derivative] Rewrite [Derivative Property - Addition/Subtraction]:
- Rewrite [Derivative Property - Multiplied Constant]:
- Derivative Rule [Basic Power Rule]:
∴ we find the derivative of the given function <em>and </em>it is less complex and faster. We can conclude that simplifying first appears to be simpler for this problem.
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Learn more about differentiation: brainly.com/question/17830594
Learn more about calculus: brainly.com/question/23558817
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Answer:
the second car is 75 miles longer than the first car for 5 hours
Step-by-step explanation:
First we need to know the distance each one traveled in 5 hours
the first one travels 40 miles in one hour
1 h = 40 mi
1h * 5 = 40mi * 5
5h = 200 mi
the second one travels 55 miles in one hour
1 h = 55 mi
1h * 5 = 55mi * 5
5h = 275 mi
so the first one traveled 200 miles and the second 275 miles
if 275 we have 200 left, we will get how many more miles the second car made in 5 hours
275mi - 200mi = 75mi
Answer: 1/6
Step-by-step explanation: To find the probability of rolling a 4, let's use our ratio for the probability of an event which is shown below.
Number of favorable outcomes/total number of outcomes
Since only one side of a number cube has a 4 on it, the number of favorable outcomes for rolling a 4 is 1 and since there are six sides to a number cube and it's equally likely that the cube will land on any of these sides, the total number of outcomes is 6.
So the probability of rolling a 4 is 1/6 which is equivalent
to 0.167 or 16.7%.
That means it is't likely that you would roll a 4 for instance but it's just as likely as rolling any other number.