Please help me with this AP Calculus question!!
1 answer:
9514 1404 393
Answer:
B. 3
Step-by-step explanation:
If all you want is a numerical result, sometimes a graphing calculator can provide that easily. The attachment shows it calculates the slope at x=4 to be 3.
dy/dx = 3 at x = 4
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The derivative of the expression can be found from the quotient formula:
d(u/v) = (du·v -u·dv)/v²
y' = ((x -2)(2x -7) -(x^2 -7x +2)(1))/(x -2)^2
= (2x^2 -11x +14 -x^2 +7x -2)/(x -2)^2
= (x^2 -4x +12)/(x -2)^2
= ((x -4)x +12)/(x -2)^2
Then for x=4, we have ...
y' = 12/4 = 3
dy/dx = 3 at x = 4
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Answer:
0.055 = 5.5% probability that exactly 5 employees were over 50.
Step-by-step explanation:
The employees are removed from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
In this question:
7 + 18 = 25 employees, which means that
7 over 50, which means that
10 dismissed, which means that
What is the probability that exactly 5 employees were over 50?
This is P(X = 5). So
0.055 = 5.5% probability that exactly 5 employees were over 50.