Answer:
x-intercept of the graph of the function
is, ![(\frac{\pi}{6} \pm \frac{n\pi}{3} , 0)](https://tex.z-dn.net/?f=%28%5Cfrac%7B%5Cpi%7D%7B6%7D%20%5Cpm%20%5Cfrac%7Bn%5Cpi%7D%7B3%7D%20%2C%200%29)
Step-by-step explanation:
Given the function:
......[1]
x-intercept defined as the graph crosses the x-axis.
Substitute value of y = 0 in [1] and solve for x;
or
Take the inverse cotangent of both sides of the equation and solve for x;
3x = arccot (0)
We know the exact value of ![arc\cot(0) = \frac{\pi}{2}](https://tex.z-dn.net/?f=arc%5Ccot%280%29%20%3D%20%5Cfrac%7B%5Cpi%7D%7B2%7D)
then;
![3x = \frac{\pi}{2}](https://tex.z-dn.net/?f=3x%20%3D%20%5Cfrac%7B%5Cpi%7D%7B2%7D)
Divide both sides by 3 we get;
![x = \frac{\pi}{6}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B%5Cpi%7D%7B6%7D)
Since, the cotangent function is positive in the first and third quadrants.
The period of the function
is
so values will repeat every
radians in both directions.
we have;
![x =\frac{\pi}{6} \pm \frac{n\pi}{3}](https://tex.z-dn.net/?f=x%20%3D%5Cfrac%7B%5Cpi%7D%7B6%7D%20%5Cpm%20%5Cfrac%7Bn%5Cpi%7D%7B3%7D)
Therefore, the x-intercept of the graph of the function
is ;
for every integer n;
Using the normal distribution, it is found that 44.43% of students are 21 or older and thus old enough to legally order alcohol at Griff's.
<h3>Normal Probability Distribution</h3>
The z-score of a measure X of a normally distributed variable with mean
and standard deviation
is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
The mean and the standard deviation are given, respectively, by:
![\mu = 20.66, \sigma = 2.4](https://tex.z-dn.net/?f=%5Cmu%20%3D%2020.66%2C%20%5Csigma%20%3D%202.4)
The proportion of students that are 21 or older is <u>one subtracted by the p-value of Z when X = 21</u>, hence:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{21 - 20.66}{2.4}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B21%20-%2020.66%7D%7B2.4%7D)
Z = 0.14
Z = 0.14 has a p-value of 0.5557.
1 - 0.5557 = 0.4443 = 44.43% of students are 21 or older and thus old enough to legally order alcohol at Griff's.
More can be learned about the normal distribution at brainly.com/question/4079902
#SPJ1
With a problem like this, set up a proportion (like when making lemonade from a mix).
is our proportion.
We fill in the the two weights and the 24 grams of medicine in the proportion and solve for the fourth piece not there.
We shorten medicine to M and we solve for M by cross multiplying.
![150M = 2880](https://tex.z-dn.net/?f=%20150M%20%3D%202880%20)
![M = \frac{2880}{150} = 19.2 grams](https://tex.z-dn.net/?f=%20M%20%3D%20%5Cfrac%7B2880%7D%7B150%7D%20%3D%2019.2%20grams%20%20)
The woman should get 19.2 grams of medicine.
<span>rational number between 5.2 and 5.5 is 53/10 (cause 53/10 = 5.3)
</span>irrational number between 5.2 and 5.5 is √29 (cause <span>√29 = 5.385164....)</span>