So 3/4 of 12
remember that 12=12/1
and if you ahve x/y times z/t that equals to (xz)/(yt) so
'of' means multiply
3/4 times 12/1=(3 times 12)/(4 times 1)=36/4=9/1=9
9 are working in the library
Answer:
![= 2 \frac{1}{5}](https://tex.z-dn.net/?f=%20%3D%202%20%5Cfrac%7B1%7D%7B5%7D%20)
Step-by-step explanation:
![5 \frac{1}{10} - 2 \frac{9}{10} \\ \frac{51}{10} - \frac{29}{10} \\ = \frac{22}{10} \\ = 2 \frac{2}{10} \\ = 2 \frac{1}{5}](https://tex.z-dn.net/?f=5%20%5Cfrac%7B1%7D%7B10%7D%20%20-%202%20%5Cfrac%7B9%7D%7B10%7D%20%20%5C%5C%20%20%5Cfrac%7B51%7D%7B10%7D%20%20-%20%20%5Cfrac%7B29%7D%7B10%7D%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B22%7D%7B10%7D%20%20%5C%5C%20%20%3D%202%20%5Cfrac%7B2%7D%7B10%7D%20%20%5C%5C%20%20%3D%202%20%5Cfrac%7B1%7D%7B5%7D%20)
hope this helps
brainliest appreciated
good luck! have a nice day!
Answer:
5.96% probability that exactly 3 people in the sample are afraid of being alone at night.
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they are afraid of being alone at night, or they are not. The probability of a person being afraid of being alone at night is independent of any other person. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
In which
is the number of different combinations of x objects from a set of n elements, given by the following formula.
![C_{n,x} = \frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=C_%7Bn%2Cx%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
And p is the probability of X happening.
5% of Americans are afraid of being alone in a house at night.
This means that ![p = 0.05](https://tex.z-dn.net/?f=p%20%3D%200.05)
If a random sample of 20 Americans is selected, what is the probability that exactly 3 people in the sample are afraid of being alone at night.
This is P(X = 3) when n = 20. So
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
![P(X = 3) = C_{20,3}.(0.05)^{3}.(0.95)^{17} = 0.0596](https://tex.z-dn.net/?f=P%28X%20%3D%203%29%20%3D%20C_%7B20%2C3%7D.%280.05%29%5E%7B3%7D.%280.95%29%5E%7B17%7D%20%3D%200.0596)
5.96% probability that exactly 3 people in the sample are afraid of being alone at night.
<h3>
Answer:</h3>
- left picture (bottom expression): -cot(x)
- right picture (top expression): tan(x)
<h3>
Step-by-step explanation:</h3>
A graphing calculator can show you a graph of each expression, which you can compare to the offered choices.
_____
You can make use of the relations ...
... sin(a)+sin(b) = 2sin((a+b)/2)cos((a-b)/2)
... cos(a)+cos(b) = 2cos((a+b)/2)cos((a-b)/2)
... cos(a)-cos(b) = -2sin((a+b)/2)sin((a-b)/2)
Then you have ...
![\dfrac{\cos{2x}-\cos{4x}}{\sin{2x}+\sin{4x}}=\dfrac{2\sin{3x}\sin{x}}{2\sin{3x}\cos{x}}=\dfrac{\sin{x}}{\cos{x}}=\tan{x}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ccos%7B2x%7D-%5Ccos%7B4x%7D%7D%7B%5Csin%7B2x%7D%2B%5Csin%7B4x%7D%7D%3D%5Cdfrac%7B2%5Csin%7B3x%7D%5Csin%7Bx%7D%7D%7B2%5Csin%7B3x%7D%5Ccos%7Bx%7D%7D%3D%5Cdfrac%7B%5Csin%7Bx%7D%7D%7B%5Ccos%7Bx%7D%7D%3D%5Ctan%7Bx%7D)
and ...
![\dfrac{\cos{2x}+\cos{4x}}{\sin{2x}-\sin{4x}}=\dfrac{2\cos{3x}\cos{x}}{-2\cos{3x}\sin{x}}=\dfrac{-\cos{x}}{\sin{x}}=-\cot{x}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ccos%7B2x%7D%2B%5Ccos%7B4x%7D%7D%7B%5Csin%7B2x%7D-%5Csin%7B4x%7D%7D%3D%5Cdfrac%7B2%5Ccos%7B3x%7D%5Ccos%7Bx%7D%7D%7B-2%5Ccos%7B3x%7D%5Csin%7Bx%7D%7D%3D%5Cdfrac%7B-%5Ccos%7Bx%7D%7D%7B%5Csin%7Bx%7D%7D%3D-%5Ccot%7Bx%7D)
Answer:
2.8 years or 33.6 months.
Step-by-step explanation:
I am not sure what your questions is, but I assume it is how long it will take to pay it off?
In a year (15*12,) you would have paid $180 of it.
x = 500/180
Therefore, it will take you approximately 2.8 years to pay off your loan, excluding interest, of course, since you did not provide that rate.