<h2>
Hello!</h2>
The answer is:
d) ![\frac{(x-1)(11x+1)}{(x-1)(x+2)}](https://tex.z-dn.net/?f=%5Cfrac%7B%28x-1%29%2811x%2B1%29%7D%7B%28x-1%29%28x%2B2%29%7D)
<h2>Why?</h2>
A hole is a point where rational functions lose its continuity, meaning that in that point, there is a discontinuity condition.
We can find the hole of a rational function if there are similar terms on the numerator and the denominator by finding:
First (x-component): The values of x that makes the function equal to 0 in both numerator and denominator.
Second (y-component): Re-evaluating the same term in the other factors of the function to know the y-component.
Finding the x component we have:
![f(1)=\frac{(1-1)(11*1+1)}{(1-1)(1+2)}=\frac{(0)(12)}{(0)(3)}=\frac{0}{0}](https://tex.z-dn.net/?f=f%281%29%3D%5Cfrac%7B%281-1%29%2811%2A1%2B1%29%7D%7B%281-1%29%281%2B2%29%7D%3D%5Cfrac%7B%280%29%2812%29%7D%7B%280%29%283%29%7D%3D%5Cfrac%7B0%7D%7B0%7D)
So, the x-component is 1,
Then, re-evaluating the function:
![f(1)=\frac{(x-1)(11*1+1)}{(x-1)(1+2)}=\frac{(12)}{(3)}=\frac{12}{3}=4](https://tex.z-dn.net/?f=f%281%29%3D%5Cfrac%7B%28x-1%29%2811%2A1%2B1%29%7D%7B%28x-1%29%281%2B2%29%7D%3D%5Cfrac%7B%2812%29%7D%7B%283%29%7D%3D%5Cfrac%7B12%7D%7B3%7D%3D4)
Therefore, the y-component is 4,
Hence,
The function has a hole at (1,4)
Have a nice day!
Answer:
a number decreased by four
Step-by-step explanation:
Hey there! I'm happy to help!
If 70% of the students are female, then 30% of the students are male. Of these, 85% graduated. Let's find 85% of 30%.
0.85(0.3)=0.255
This means that 25.5% of the students are graduating males.
We want to find the probability that one of the graduating males are picked from the group of graduating people. We have to find how many girls graduated to find the total percent of peole who graduated.
75% of females (70% graduated).
0.75(0.7)=0.525
So, 52.5% of students are graduating females.
We have 52.5% as graduating females and 25.5% are graduating males. We combine this, showing us that 78% of students graduated.
Now, we want to find the probability of picking a graduating male. 25.5% is what percent of 78%? When working with percents, is means equals. Let's say that our percent is p and solve.
0.255=0.78p
We flip the equation so p is on the left.
0.78p=0.255
Divide both sides by 0.78.
p≈0.33 (rounded to nearest hundredth)
Therefore, there is a 33% chance of picking a male from the graduating students.
Have a wonderful day! :D
Answer:
He didn't calculate the b-value correctly.
Step-by-step explanation:
The given parent function is:
![y = \cot(x)](https://tex.z-dn.net/?f=y%20%3D%20%20%5Ccot%28x%29%20)
The transformation is of the form:
![y =a \cot(bx + c) + d](https://tex.z-dn.net/?f=y%20%3Da%20%20%5Ccot%28bx%20%2B%20c%29%20%20%2B%20d)
The period is given by
![\frac{\pi}{b}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%5Cpi%7D%7Bb%7D%20)
If we want the new function to have a period of
![\frac{2}{\pi}](https://tex.z-dn.net/?f=%20%5Cfrac%7B2%7D%7B%5Cpi%7D%20)
Then we solve the following equation for b.
![\frac{\pi}{b} = \frac{2}{\pi}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%5Cpi%7D%7Bb%7D%20%20%3D%20%20%5Cfrac%7B2%7D%7B%5Cpi%7D%20)
![b = \frac{ {\pi}^{2} }{2}](https://tex.z-dn.net/?f=b%20%3D%20%20%5Cfrac%7B%20%7B%5Cpi%7D%5E%7B2%7D%20%7D%7B2%7D%20)
![- \frac{c}{b}](https://tex.z-dn.net/?f=%20-%20%20%5Cfrac%7Bc%7D%7Bb%7D%20)
will translate the graph horizontally to the right by
![\frac{c}{b}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bc%7D%7Bb%7D%20)
units.
+d shifts the graph up by d units.
The new function then becomes:
![y = \cot( \frac{ {\pi}^{2} }{2} (x - \frac{\pi}{4} ) )+1](https://tex.z-dn.net/?f=y%20%3D%20%20%5Ccot%28%20%20%5Cfrac%7B%20%7B%5Cpi%7D%5E%7B2%7D%20%7D%7B2%7D%20%20%28x%20%20-%20%20%5Cfrac%7B%5Cpi%7D%7B4%7D%20%29%20%29%2B1)
It’s is 20,0000 but it think that’s wrong