On interval 0 ≤ x < 2π, where are the x-intercepts of y = cos(2x)?
2 answers:
The answer is choice D because we plug in something like x = pi/4 and it leads to
y = cos(2x)
y = cos(2*pi/4)
y = cos(pi/2)
y = 0
Use the unit circle to see why cos(pi/2) = 0.
Since we get y = 0 as a result, this shows x = pi/4 is one of the x intercepts.
You'll also get y = 0 if you plug in x = 3pi/4, x = 5pi/4, and x = 7pi/4. All of these values are on the interval
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A) The mean would be 1.842 and the standard deviation would be 1.339.
b) It would not be unusually low.
Explanation
a) This can be modeled as a binomial distribution, since there are two outcomes (7 or not 7), the events are independent (getting a 7 on one spin does not influence the chance of a 7 on the next spin) and there are a fixed number of trials (70). In a binomial distribution, the mean is given by n*p, where n is the number of trials and p is the probability.
μ=n*p=70*(1/38) = 1.842.
The standard deviation of a binomial distribution is given by
σ=√(n*p*(1-p))=√(70(1/38)(37/38)=1.339.
b) To determine if this is unusually low, we find the probability:
Since this is not below 0.05, we do not consider this unusual.
b) It would not be unusually low.
Explanation
a) This can be modeled as a binomial distribution, since there are two outcomes (7 or not 7), the events are independent (getting a 7 on one spin does not influence the chance of a 7 on the next spin) and there are a fixed number of trials (70). In a binomial distribution, the mean is given by n*p, where n is the number of trials and p is the probability.
μ=n*p=70*(1/38) = 1.842.
The standard deviation of a binomial distribution is given by
σ=√(n*p*(1-p))=√(70(1/38)(37/38)=1.339.
b) To determine if this is unusually low, we find the probability:
Since this is not below 0.05, we do not consider this unusual.