Answer:
Step-by-step explanation:
<u>Uniform Distribution</u>
The probability density function PDF of the continuous uniform distribution is:
![p(x)={\begin{cases}{\frac {1}{b-a}}&\mathrm {for} \ a\leq x\leq b,\\[8pt]0&\mathrm {for} \ xb\end{cases}}](https://tex.z-dn.net/?f=p%28x%29%3D%7B%5Cbegin%7Bcases%7D%7B%5Cfrac%20%7B1%7D%7Bb-a%7D%7D%26%5Cmathrm%20%7Bfor%7D%20%5C%20a%5Cleq%20x%5Cleq%20b%2C%5C%5C%5B8pt%5D0%26%5Cmathrm%20%7Bfor%7D%20%5C%20x%3Ca%5C%20%5Cmathrm%20%7Bor%7D%20%5C%20x%3Eb%5Cend%7Bcases%7D%7D)
Where a and b are the lower and upper limits where the probabilities are defined.
a. For our problem a=8.5, b=12, thus b-a=4.5 and the PDF is:
![p(x)={\begin{cases}{\frac {1}{4.5}}&\mathrm {for} \ 8.5\leq x\leq 12,\\[8pt]0&\mathrm {for} \ x12\end{cases}}](https://tex.z-dn.net/?f=p%28x%29%3D%7B%5Cbegin%7Bcases%7D%7B%5Cfrac%20%7B1%7D%7B4.5%7D%7D%26%5Cmathrm%20%7Bfor%7D%20%5C%208.5%5Cleq%20x%5Cleq%2012%2C%5C%5C%5B8pt%5D0%26%5Cmathrm%20%7Bfor%7D%20%5C%20x%3C8.5%5C%20%5Cmathrm%20%7Bor%7D%20%5C%20x%3E12%5Cend%7Bcases%7D%7D)
b. We will find the probability that the battery life for an iPad Mini will be 10 hours or less, that is, 
The required probability is computed by using the upper part of the PDF, i.e.
All of them are correct except for C. (4,8)
Answer:
m = -3
b = 4
Equation: y = -3x + 4
Step-by-step explanation:
The equation for a straight line is y = mx + b.
The line crosses the y-axis at (0,4). So, b (the y-intercept) will be 4.
Now, to find m (the slope). The next point on the line is (1,1). To get there, you go down 3 units (-3) and to the right 1 unit.
Slope is known as rise (change in x-axis) over run (change in y-axis). So, -3 ÷ 1 = -3. m will be -3.
For the equation of the line, just plug the numbers into the equation for a straight line.
y = mx + b
y = -3x + 4
Hope that helps.
Answer:
volume of the tank be when the sensor turns on = 92.316 ft³
Step-by-step explanation:
Volume of a cylinder = πr²h
Pi = π = 3.14
Radius = r = 7 ft
Height = h = 3 ft
Volume of a cylinder = πr²h
= 3.14 × 7² × 3
= 3.14 × 49 × 3
= 461.58 ft³
The tank comes equipped with a sensor to alert the farmer to fill it up when the water falls to 20% capacity.
volume of the tank be when the sensor turns on = 20% of Volume of a cylinder
= 0.20 * 461.58 ft³
= 92.316 ft³
volume of the tank be when the sensor turns on = 92.316 ft³
