Y=1/4x + 3/4
Multiply by 4 each sides
4y= x + 3
Subtract x from both sides
-x + 4y = 3
Multiply both sides
X- 4y= -3
From their sum, the numbers are ' x ' and ' 8 - x ' .
From their product, x(8 - x) = 80 .
When you massage and manipulate this equation into the standard
quadratic form, you have
x² - 8x + 80 = 0 .
Applying the quadratic formula to tease out the solutions of this equation,
we find that they are
<em> x = 4 + 64 i</em>
and
<em> x = 4 - 64 i</em>
ANSWER
0.2546
EXPLANATION
The movie theatre's daily revenue, X, is normally distributed with a mean of $3152 and a standard deviation of $1281.
We have to find the probability that the theatre generates more than $4000 in revenue on a randomly selected day,
![P(X>4000)](https://tex.z-dn.net/?f=P%28X%3E4000%29)
To find this probability, we have to standardize X using the formula,
![Z=\frac{X-\mu}{\sigma}](https://tex.z-dn.net/?f=Z%3D%5Cfrac%7BX-%5Cmu%7D%7B%5Csigma%7D)
So the probability is,
![P\left(\frac{X-\mu}{\sigma}\gt\frac{4000-3152}{1281}\right)=P(Z\gt0.66)](https://tex.z-dn.net/?f=P%5Cleft%28%5Cfrac%7BX-%5Cmu%7D%7B%5Csigma%7D%5Cgt%5Cfrac%7B4000-3152%7D%7B1281%7D%5Cright%29%3DP%28Z%5Cgt0.66%29)
Now, we have to look up this z-value in a z-score table. These tables usually show the area to the left of the z-score - this means that they show the probability for a z less than the z-score, so we have to find the complement,
![P(Z\gt0.66)=1-P(Z\lt0.66)](https://tex.z-dn.net/?f=P%28Z%5Cgt0.66%29%3D1-P%28Z%5Clt0.66%29)
In a z-score table,
So the probability is,
![P(X>4000)=1-P(Z\lt0.66)=1-0.7454=0.2546](https://tex.z-dn.net/?f=P%28X%3E4000%29%3D1-P%28Z%5Clt0.66%29%3D1-0.7454%3D0.2546)
Hence, the probability that the theatre generates more than $4000 in revenue on a randomly selected day is 0.2546.
Answer:
|x y 1|
|7 -3 1| = 0
|4 -8 1|
x*(-3*1 - (-8)*1) - y*(7*1 - 4*1) + 1*(7*-8 - 4*-3) = 0
5x - 3y - 44 = 0
Step-by-step explanation: