Answer:
For this case assuming that the random variable is X

And replacing n = 24 we got:

And we notate the distribution we got: 
Step-by-step explanation:
Previous concepts
The t distribution (Student’s t-distribution) is a "probability distribution that is used to estimate population parameters when the sample size is small (n<30) or when the population variance is unknown".
The shape of the t distribution is determined by its degrees of freedom and when the degrees of freedom increase the t distirbution becomes a normal distribution approximately.
The degrees of freedom represent "the number of independent observations in a set of data. For example if we estimate a mean score from a single sample, the number of independent observations would be equal to the sample size minus one."
Solution to the problem
For this case assuming that the random variable is X

And replacing n = 24 we got:

And we notate the distribution we got: 
Answer:
t = 1.57 sec
distance, d = 98.65 mm
Step-by-step explanation:
Given an angle of 540°
At 6 revolutions per second, which is the angular velocity.
Radius, r = 10 mm
We are asked to find the time and the distance.
To find the time, let's use the formula:

Where
= angle in radians.
Converting 540° to radians, we have:

Therefore, from the formula, let's find t.


time = 1.57
To find the distance, we have:
d = 98.65 mm
Therefore, the time is 1.57 seconds and the distance is 98.65 mm
A score of 85 would be 1 standard deviation from the mean, 74. Using the 68-95-99.7 rule, we know that 68% of normally distributed data falls within 1 standard deviation of the mean. This means that 100%-68% = 32% of the data is either higher or lower. 32/2 = 16% of the data will be higher than 1 standard deviation from the mean and 16% of the data will be lower than 1 standard deviation from the mean. This means that 16% of the graduating seniors should have a score above 85%.
Given:
Area of rectangle = 
Width of the rectangle is equal to the greatest common monomial factor of
.
To find:
Length and width of the rectangle.
Solution:
Width of the rectangle is equal to the greatest common monomial factor of
is



Now,

So, width of the rectangle is
.
Area of rectangle is

Taking out GCF, we get

We know that, area of a rectangle is the product of its length and width.
Since, width of the rectangle is
, therefore length of the rectangle is
.