Write two different ratios equal to 6:30
2 answers:
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Answer:
(a)
(b) 0.7910
(c) 0.0401
(d) 0.6464
Step-by-step explanation:
Let <em>X</em> = amount of time that people spend at Grover Hot Springs.
The random variable <em>X</em> is normally distributed with a mean of 73 minutes and a standard deviation of 16 minutes.
(a)
The distribution of the random variable <em>X</em> is:
(b)
Compute the probability that a randomly selected person at the hot springs stays longer than 60 minutes as follows:
*Use a <em>z</em>-table for the probability.
Thus, the probability that a randomly selected person at the hot springs stays longer than an hour is 0.7910.
(c)
Compute the probability that a randomly selected person at the hot springs stays less than 45 minutes as follows:
*Use a <em>z</em>-table for the probability.
Thus, the probability that a randomly selected person at the hot springs stays less than 45 minutes is 0.0401.
(d)
Compute the probability that a randomly person spends between 60 and 90 minutes at the hot springs as follows:
*Use a <em>z</em>-table for the probability.
Thus, the probability that a randomly person spends between 60 and 90 minutes at the hot springs is 0.6464
Answer:
tan(2x)=-24/7
Step-by-step explanation:
Since tan(x)=sin(x)/cos(x)
We are going to need sin(x) any time, so lets find it right away.
To do this, remember that. sin(x)^2 + cos(x)^2=1
so.
This leads to.
We have obtained two solutions, -3/5 and 3/5.
We need to pick one, since not all of them are correct for our scenario, in this case, we've been told that x belongs to the range [180, 270], in this range, sin(x)<0.
So in our previous solution, we have that sin(x)= -3/5
Now, to find tang(2x), we need to apply the definition
Tang(2x)=sin(2x)/cos(2x).
Lets remember that
sin(2x)=2*sin(x)*cos(x)
cos(2x)=cos(x)^2 - sin(x)^2.
Lets evaluate our given result.
sin(2x)=2*(-3/5)*(4/5)=-24/25
cos(2x)=(-4/5)^2 - (3/5)^2=7/25
Hence
tan(2x)= -(24/25) / (7/25)=-24/7