Kimberly makes a conjecture that the sum of two odd integers is always an even integer. Which choice is the best proof of her co
njecture?
1 answer:
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Answer:
A) -sqrt(3)/3
Step-by-step explanation:
If you know your unit circle (attached), 11pi/6 has the value of (sqrt(3)/2,-1/2), where the coords are (cosine, sine).
Tangent is sine/cosine:
(-1/2)/(sqrt(3)/2)
We can convert this to multiplication by miltiplying the reciprocal of sqrt(3)/2:
(-1/2)*(2/sqrt(3))
Multiplied out to:
-2/(2sqrt(3))
We have to rationalize this by multiplying the numerator and denominator by sqrt(3):
-2(sqrt(3))/2sqrt(3)(sqrt(3)
two of the same square roots multiplied together equals the number without the sqrt:
-2(sqrt(3))/2*3
we can factor out 2 from the numerator and denominator:
-sqrt(3)/3
Therefore, the answer is A
Answer:
Step-by-step explanation:
Given
The data for 25 undergraduates
Solving (a): Range and Standard deviation
The range is:
From the dataset:
So:
The standard deviation is:
First, calculate the mean
So, the standard deviation is:
Solving (b): The interval of the 95% of the observation.
Using the emperical rule, we have: