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There are seven females and nineteen males in the spanish class.
Answer:
1. 4/11 2. 2/10 or 1/5
Step-by-step explanation:
The first thing you need to do is find the total number of marble and then break it into their probabilities. 4+2+5= 11
Red: 4/11, Yellow: 2/11 and Blue: 5/11
So for 1. you just need the probability of pulling a red marble with we already figured out, 4/11.
For the second part you're looking for the probability of pulling a yellow marble after a red was pulled and not replaced. When we take one out and don't replace it the only thing that changes is the total and the number for that color so, the probabilities change to: Red: 3/10, Yellow: 2/10 and Blue: 5/10.
So now you have the probability of pulling a yellow if a red was pulled first without being replaced.
Answer:
![n=-\frac{20}{3}\quad \mathrm{or}\quad \:n=\frac{20}{3}](https://tex.z-dn.net/?f=n%3D-%5Cfrac%7B20%7D%7B3%7D%5Cquad%20%5Cmathrm%7Bor%7D%5Cquad%20%5C%3An%3D%5Cfrac%7B20%7D%7B3%7D)
Step-by-step explanation:
![2\left|-3n\right|+10=50\\\\\mathrm{Subtract\:}10\mathrm{\:from\:both\:sides}\\\\2\left|-3n\right|+10-10=50-10\\\\Simplify\\\\2\left|-3n\right|=40\\\\\mathrm{Divide\:both\:sides\:by\:}2\\\\\frac{2\left|-3n\right|}{2}=\frac{40}{2}\\\\Simplify\\\\\left|-3n\right|=20\\\\\mathrm{Apply\:absolute\:rule}:\\\quad \mathrm{If}\:|u|\:=\:a,\:a>0\:\mathrm{then}\:u\:=\:a\:\quad \mathrm{or}\quad \:u\:=\:-a\\](https://tex.z-dn.net/?f=2%5Cleft%7C-3n%5Cright%7C%2B10%3D50%5C%5C%5C%5C%5Cmathrm%7BSubtract%5C%3A%7D10%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D%5C%5C%5C%5C2%5Cleft%7C-3n%5Cright%7C%2B10-10%3D50-10%5C%5C%5C%5CSimplify%5C%5C%5C%5C2%5Cleft%7C-3n%5Cright%7C%3D40%5C%5C%5C%5C%5Cmathrm%7BDivide%5C%3Aboth%5C%3Asides%5C%3Aby%5C%3A%7D2%5C%5C%5C%5C%5Cfrac%7B2%5Cleft%7C-3n%5Cright%7C%7D%7B2%7D%3D%5Cfrac%7B40%7D%7B2%7D%5C%5C%5C%5CSimplify%5C%5C%5C%5C%5Cleft%7C-3n%5Cright%7C%3D20%5C%5C%5C%5C%5Cmathrm%7BApply%5C%3Aabsolute%5C%3Arule%7D%3A%5C%5C%5Cquad%20%5Cmathrm%7BIf%7D%5C%3A%7Cu%7C%5C%3A%3D%5C%3Aa%2C%5C%3Aa%3E0%5C%3A%5Cmathrm%7Bthen%7D%5C%3Au%5C%3A%3D%5C%3Aa%5C%3A%5Cquad%20%5Cmathrm%7Bor%7D%5Cquad%20%5C%3Au%5C%3A%3D%5C%3A-a%5C%5C)
![-3n=-20\quad \mathrm{or}\quad \:-3n=20\\\\-3n=-20\quad :\quad n=\frac{20}{3}\\\\-3n=20\quad :\quad n=-\frac{20}{3}\\\\n=-\frac{20}{3}\quad \mathrm{or}\quad \:n=\frac{20}{3}](https://tex.z-dn.net/?f=-3n%3D-20%5Cquad%20%5Cmathrm%7Bor%7D%5Cquad%20%5C%3A-3n%3D20%5C%5C%5C%5C-3n%3D-20%5Cquad%20%3A%5Cquad%20n%3D%5Cfrac%7B20%7D%7B3%7D%5C%5C%5C%5C-3n%3D20%5Cquad%20%3A%5Cquad%20n%3D-%5Cfrac%7B20%7D%7B3%7D%5C%5C%5C%5Cn%3D-%5Cfrac%7B20%7D%7B3%7D%5Cquad%20%5Cmathrm%7Bor%7D%5Cquad%20%5C%3An%3D%5Cfrac%7B20%7D%7B3%7D)
Answer:
Option 2.
Step-by-step explanation:
To solve this, let's first find the values given to us.
The two x-intercepts are (4, 0) and (12, 0).
The parabola opens downward, meaning the value of a should be negative.
The vertex is (8, 32).
We know it is 8 because the halfway point between the x-intercepts is 8.
We can already eliminate option 3 because option 3 has a positive value of a.
This leaves us with options 1, 2, and 4.
The easiest way to figure out which option is correct is to graph the remaining functions in a graphing calculator.
The graph of a function that meets all of the above values is the correct function.
After graphing all of the functions, option 2 was the only one that had a vertex of (8, 32). So, option 2 is correct.