Answer:
Step-by-step explanation:
I like to break these into parts to solve
1*90=90
.6*90=54
.04*90=3.6
add all of these together
90+54+3.6=147.6
16/2=8
2+2+2+2+2+2+2+2=16
Pairs are 2. So just count in twos until you get to 16. How many times did you count twos? :)
Answer:C
Took the test
Step-by-step explanation:
Answer:
The probability that it takes Annie between 39 and 40 minutes given that it takes less than 44 minutes for her to make dinner is 0.04.
Step-by-step explanation:
Let <em>X</em> = amount of times (in minutes) it takes Annie to make dinner.
The random variable <em>X</em> follows a continuous Uniform distribution with parameters <em>a</em> = 19 minutes and <em>b</em> = 49 minutes.
The probability density function of continuous Uniform distribution is:
![f_{X}(x)=\frac{1}{b-a};\ a](https://tex.z-dn.net/?f=f_%7BX%7D%28x%29%3D%5Cfrac%7B1%7D%7Bb-a%7D%3B%5C%20a%3CX%3Cb%2C%20a%3Cb)
Compute the value P (39 < X < 40 | X < 44) as follows:
![P(39](https://tex.z-dn.net/?f=P%2839%3CX%3C40%7CX%3C44%29%3D%5Cfrac%7BP%2839%3CX%3C40%5C%20%5Ccap%20%5C%20X%3C44%29%7D%7BP%28X%3C44%29%7D%3D%5Cfrac%7BP%2839%3CX%3C40%29%7D%7BX%3C44%29%7D)
![=\frac{\int\limits^{40}_{39} {\frac{1}{49-19}}\, dx}{\int\limits^{44}_{19} {\frac{1}{49-19}}\, dx}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Cint%5Climits%5E%7B40%7D_%7B39%7D%20%7B%5Cfrac%7B1%7D%7B49-19%7D%7D%5C%2C%20dx%7D%7B%5Cint%5Climits%5E%7B44%7D_%7B19%7D%20%7B%5Cfrac%7B1%7D%7B49-19%7D%7D%5C%2C%20dx%7D)
![=\frac{ \frac{1}{30}|x|^{40}_{39}}{\frac{1}{30}|x|^{44}_{19}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%20%5Cfrac%7B1%7D%7B30%7D%7Cx%7C%5E%7B40%7D_%7B39%7D%7D%7B%5Cfrac%7B1%7D%7B30%7D%7Cx%7C%5E%7B44%7D_%7B19%7D%7D)
![=\frac{ \frac{1}{30}\times 1}{\frac{1}{30}\times 25}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%20%5Cfrac%7B1%7D%7B30%7D%5Ctimes%201%7D%7B%5Cfrac%7B1%7D%7B30%7D%5Ctimes%2025%7D)
![=\frac{1}{25}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B25%7D)
![=0.04](https://tex.z-dn.net/?f=%3D0.04)
Thus, the probability that it takes Annie between 39 and 40 minutes given that it takes less than 44 minutes for her to make dinner is 0.04.