Slop=(1/4,0) or 1/4x
y-intercept =(0,-3/4)
i hope it will help you!
Answer:
1/81
Step-by-step explanation:
You just tap the calculator
Answer:
![(a)\ g(x) = \frac{2}{3}(x+1)](https://tex.z-dn.net/?f=%28a%29%5C%20g%28x%29%20%3D%20%5Cfrac%7B2%7D%7B3%7D%28x%2B1%29)
![(b)\ h(y) = \frac{1}{3}[1 + 4y]](https://tex.z-dn.net/?f=%28b%29%5C%20h%28y%29%20%3D%20%5Cfrac%7B1%7D%7B3%7D%5B1%20%2B%204y%5D)
![P(x>0.5) =\frac{5}{12}](https://tex.z-dn.net/?f=P%28x%3E0.5%29%20%3D%5Cfrac%7B5%7D%7B12%7D)
Step-by-step explanation:
Given
![f(x,y) = \left \{ {{\frac{2}{3}(x+2y)\ \ 0\le x \le 1,\ 0\le y\le 1} \right.](https://tex.z-dn.net/?f=f%28x%2Cy%29%20%3D%20%5Cleft%20%5C%7B%20%7B%7B%5Cfrac%7B2%7D%7B3%7D%28x%2B2y%29%5C%20%5C%200%5Cle%20x%20%5Cle%201%2C%5C%200%5Cle%20y%5Cle%201%7D%20%5Cright.)
Solving (a): The marginal density of X
This is calculated as:
![g(x) = \int\limits^{\infty}_{-\infty} {f(x,y)} \, dy](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Cint%5Climits%5E%7B%5Cinfty%7D_%7B-%5Cinfty%7D%20%7Bf%28x%2Cy%29%7D%20%5C%2C%20dy)
![g(x) = \int\limits^{1}_{0} {\frac{2}{3}(x + 2y)} \, dy](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Cint%5Climits%5E%7B1%7D_%7B0%7D%20%7B%5Cfrac%7B2%7D%7B3%7D%28x%20%2B%202y%29%7D%20%5C%2C%20dy)
![g(x) = \frac{2}{3}\int\limits^{1}_{0} {(x + 2y)} \, dy](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Cfrac%7B2%7D%7B3%7D%5Cint%5Climits%5E%7B1%7D_%7B0%7D%20%7B%28x%20%2B%202y%29%7D%20%5C%2C%20dy)
Integrate
![g(x) = \frac{2}{3}(xy+y^2)|\limits^{1}_{0}](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Cfrac%7B2%7D%7B3%7D%28xy%2By%5E2%29%7C%5Climits%5E%7B1%7D_%7B0%7D)
Substitute 1 and 0 for y
![g(x) = \frac{2}{3}[(x*1+1^2) - (x*0 + 0^2)}](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Cfrac%7B2%7D%7B3%7D%5B%28x%2A1%2B1%5E2%29%20-%20%28x%2A0%20%2B%200%5E2%29%7D)
![g(x) = \frac{2}{3}[(x+1)}](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Cfrac%7B2%7D%7B3%7D%5B%28x%2B1%29%7D)
Solving (b): The marginal density of Y
This is calculated as:
![h(y) = \int\limits^{\infty}_{-\infty} {f(x,y)} \, dx](https://tex.z-dn.net/?f=h%28y%29%20%3D%20%5Cint%5Climits%5E%7B%5Cinfty%7D_%7B-%5Cinfty%7D%20%7Bf%28x%2Cy%29%7D%20%5C%2C%20dx)
![h(y) = \int\limits^{1}_{0} {\frac{2}{3}(x + 2y)} \, dx](https://tex.z-dn.net/?f=h%28y%29%20%3D%20%5Cint%5Climits%5E%7B1%7D_%7B0%7D%20%7B%5Cfrac%7B2%7D%7B3%7D%28x%20%2B%202y%29%7D%20%5C%2C%20dx)
![h(y) = \frac{2}{3}\int\limits^{1}_{0} {(x + 2y)} \, dx](https://tex.z-dn.net/?f=h%28y%29%20%3D%20%5Cfrac%7B2%7D%7B3%7D%5Cint%5Climits%5E%7B1%7D_%7B0%7D%20%7B%28x%20%2B%202y%29%7D%20%5C%2C%20dx)
Integrate
![h(y) = \frac{2}{3}(\frac{x^2}{2} + 2xy)|\limits^{1}_{0}](https://tex.z-dn.net/?f=h%28y%29%20%3D%20%5Cfrac%7B2%7D%7B3%7D%28%5Cfrac%7Bx%5E2%7D%7B2%7D%20%2B%202xy%29%7C%5Climits%5E%7B1%7D_%7B0%7D)
Substitute 1 and 0 for x
![h(y) = \frac{2}{3}[(\frac{1^2}{2} + 2y*1) - (\frac{0^2}{2} + 2y*0) ]](https://tex.z-dn.net/?f=h%28y%29%20%3D%20%5Cfrac%7B2%7D%7B3%7D%5B%28%5Cfrac%7B1%5E2%7D%7B2%7D%20%2B%202y%2A1%29%20-%20%28%5Cfrac%7B0%5E2%7D%7B2%7D%20%2B%202y%2A0%29%20%5D)
![h(y) = \frac{2}{3}[(\frac{1}{2} + 2y)]](https://tex.z-dn.net/?f=h%28y%29%20%3D%20%5Cfrac%7B2%7D%7B3%7D%5B%28%5Cfrac%7B1%7D%7B2%7D%20%2B%202y%29%5D)
![h(y) = \frac{1}{3}[1 + 4y]](https://tex.z-dn.net/?f=h%28y%29%20%3D%20%5Cfrac%7B1%7D%7B3%7D%5B1%20%2B%204y%5D)
Solving (c): The probability that the drive-through facility is busy less than one-half of the time.
This is represented as:
![P(x>0.5)](https://tex.z-dn.net/?f=P%28x%3E0.5%29)
The solution is as follows:
![P(x>0.5) = P(0\le x\le 0.5,0\le y\le 1)](https://tex.z-dn.net/?f=P%28x%3E0.5%29%20%3D%20P%280%5Cle%20x%5Cle%200.5%2C0%5Cle%20y%5Cle%201%29)
Represent as an integral
![P(x>0.5) =\int\limits^1_0 \int\limits^{0.5}_0 {\frac{2}{3}(x + 2y)} \, dx dy](https://tex.z-dn.net/?f=P%28x%3E0.5%29%20%3D%5Cint%5Climits%5E1_0%20%5Cint%5Climits%5E%7B0.5%7D_0%20%7B%5Cfrac%7B2%7D%7B3%7D%28x%20%2B%202y%29%7D%20%5C%2C%20dx%20dy)
![P(x>0.5) =\frac{2}{3}\int\limits^1_0 \int\limits^{0.5}_0 {(x + 2y)} \, dx dy](https://tex.z-dn.net/?f=P%28x%3E0.5%29%20%3D%5Cfrac%7B2%7D%7B3%7D%5Cint%5Climits%5E1_0%20%5Cint%5Climits%5E%7B0.5%7D_0%20%7B%28x%20%2B%202y%29%7D%20%5C%2C%20dx%20dy)
Integrate w.r.t. x
![P(x>0.5) =\frac{2}{3}\int\limits^1_0 (\frac{x^2}{2} + 2xy) |^{0.5}_0\, dy](https://tex.z-dn.net/?f=P%28x%3E0.5%29%20%3D%5Cfrac%7B2%7D%7B3%7D%5Cint%5Climits%5E1_0%20%28%5Cfrac%7Bx%5E2%7D%7B2%7D%20%2B%202xy%29%20%7C%5E%7B0.5%7D_0%5C%2C%20dy)
![P(x>0.5) =\frac{2}{3}\int\limits^1_0 [(\frac{0.5^2}{2} + 2*0.5y) -(\frac{0^2}{2} + 2*0y)], dy](https://tex.z-dn.net/?f=P%28x%3E0.5%29%20%3D%5Cfrac%7B2%7D%7B3%7D%5Cint%5Climits%5E1_0%20%5B%28%5Cfrac%7B0.5%5E2%7D%7B2%7D%20%2B%202%2A0.5y%29%20-%28%5Cfrac%7B0%5E2%7D%7B2%7D%20%2B%202%2A0y%29%5D%2C%20dy)
![P(x>0.5) =\frac{2}{3}\int\limits^1_0 (0.125 + y), dy](https://tex.z-dn.net/?f=P%28x%3E0.5%29%20%3D%5Cfrac%7B2%7D%7B3%7D%5Cint%5Climits%5E1_0%20%280.125%20%2B%20y%29%2C%20dy)
![P(x>0.5) =\frac{2}{3}(0.125y + \frac{y^2}{2})|^{1}_{0}](https://tex.z-dn.net/?f=P%28x%3E0.5%29%20%3D%5Cfrac%7B2%7D%7B3%7D%280.125y%20%2B%20%5Cfrac%7By%5E2%7D%7B2%7D%29%7C%5E%7B1%7D_%7B0%7D)
![P(x>0.5) =\frac{2}{3}[(0.125*1 + \frac{1^2}{2}) - (0.125*0 + \frac{0^2}{2})]](https://tex.z-dn.net/?f=P%28x%3E0.5%29%20%3D%5Cfrac%7B2%7D%7B3%7D%5B%280.125%2A1%20%2B%20%5Cfrac%7B1%5E2%7D%7B2%7D%29%20-%20%280.125%2A0%20%2B%20%5Cfrac%7B0%5E2%7D%7B2%7D%29%5D)
![P(x>0.5) =\frac{2}{3}[(0.125 + \frac{1}{2})]](https://tex.z-dn.net/?f=P%28x%3E0.5%29%20%3D%5Cfrac%7B2%7D%7B3%7D%5B%280.125%20%2B%20%5Cfrac%7B1%7D%7B2%7D%29%5D)
![P(x>0.5) =\frac{2}{3}[(0.125 + 0.5]](https://tex.z-dn.net/?f=P%28x%3E0.5%29%20%3D%5Cfrac%7B2%7D%7B3%7D%5B%280.125%20%2B%200.5%5D)
![P(x>0.5) =\frac{2}{3} * 0.625](https://tex.z-dn.net/?f=P%28x%3E0.5%29%20%3D%5Cfrac%7B2%7D%7B3%7D%20%2A%200.625)
![P(x>0.5) =\frac{2 * 0.625}{3}](https://tex.z-dn.net/?f=P%28x%3E0.5%29%20%3D%5Cfrac%7B2%20%2A%200.625%7D%7B3%7D)
![P(x>0.5) =\frac{1.25}{3}](https://tex.z-dn.net/?f=P%28x%3E0.5%29%20%3D%5Cfrac%7B1.25%7D%7B3%7D)
Express as a fraction, properly
![P(x>0.5) =\frac{1.25*4}{3*4}](https://tex.z-dn.net/?f=P%28x%3E0.5%29%20%3D%5Cfrac%7B1.25%2A4%7D%7B3%2A4%7D)
![P(x>0.5) =\frac{5}{12}](https://tex.z-dn.net/?f=P%28x%3E0.5%29%20%3D%5Cfrac%7B5%7D%7B12%7D)
Answer:
this is the ans
Step-by-step explanation:
hope it helps!!!
Answer:
The Hypotenuse is side just opposite to the right angle.
Step-by-step explanation:
By Pythagoras' theorem,
c^2=a^2+b^2
c^2(hypotenuse to be found)= 30^2+ 16^2
<em>c^2=1156
</em>
<em><u>Therefore, c ( i.e. the hypotenuse) will be the square root of 1156. </u></em>
<em><u>The square root of 1156 is 34. </u></em>
<h2><em><u>
Thus, c ( hypotenuse) = 34</u></em></h2>
Hope it helped :)