Answer:
The probability that the amount of gas in Sarah's car is exactly 7 gallons is 0.067.
Step-by-step explanation:
Let the random variable <em>X</em> represent the amount of gas in Sarah's car.
It is provided that
.
The amount of gas in a car is a continuous variable.
So, the random variable <em>X</em> follows a continuous uniform distribution.
Then the probability density function of <em>X</em> 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)
For a continuous probability distribution the probability at an exact point is 0.
So, to compute the probability that the amount of gas in Sarah's car is exactly 7 gallons use continuity correction on both sides:
P (X = 7) = P (7 - 0.5 < X < 7 + 0.5)
= P (6.5 < X < 7.5)
![=\int\limits^{7.5}_{6.5} {\frac{1}{16-1}} \, dx \\\\=\frac{1}{15}\times |x|^{7.5}_{6.5}\\\\=\frac{1}{15}\times (7.5-6.5)\\\\=\frac{1}{15}\\\\=0.0666667\\\\\approx 0.067](https://tex.z-dn.net/?f=%3D%5Cint%5Climits%5E%7B7.5%7D_%7B6.5%7D%20%7B%5Cfrac%7B1%7D%7B16-1%7D%7D%20%5C%2C%20dx%20%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B15%7D%5Ctimes%20%7Cx%7C%5E%7B7.5%7D_%7B6.5%7D%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B15%7D%5Ctimes%20%287.5-6.5%29%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B15%7D%5C%5C%5C%5C%3D0.0666667%5C%5C%5C%5C%5Capprox%200.067)
Thus, the probability that the amount of gas in Sarah's car is exactly 7 gallons is 0.067.
Answer:
5 days.
Step-by-step explanation:
The food will last her 5 days.
![3\frac{1}{2}-\frac{5}{8}-\frac{5}{8}-\frac{5}{8}-\frac{5}{8}-\frac{5}{8}](https://tex.z-dn.net/?f=3%5Cfrac%7B1%7D%7B2%7D-%5Cfrac%7B5%7D%7B8%7D-%5Cfrac%7B5%7D%7B8%7D-%5Cfrac%7B5%7D%7B8%7D-%5Cfrac%7B5%7D%7B8%7D-%5Cfrac%7B5%7D%7B8%7D)
![=1\frac{5}{8}-\frac{5}{8}-\frac{5}{8}](https://tex.z-dn.net/?f=%3D1%5Cfrac%7B5%7D%7B8%7D-%5Cfrac%7B5%7D%7B8%7D-%5Cfrac%7B5%7D%7B8%7D)
![=1-\frac{5}{8}](https://tex.z-dn.net/?f=%3D1-%5Cfrac%7B5%7D%7B8%7D)
![=\frac{3}{8}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B3%7D%7B8%7D)
2 divided by 3 is 66.7%. So the fraction would be 2/3
The answer is 1 because -7+4=-3 and -3+4=1
Answer: 28,665 currency units
Step-by-step explanation:
Find the value of the car after 4 years using the Future value formula:
= Amount * ( 1 + rate) ^ no. of years
= 33,750 * ( 1 + (-4%))⁴
= 33,750 * 0.84934656
= 28,665.45
= 28,665 currency units