Answer:
0.1042 or 10.42%
Step-by-step explanation:
Since the first bottle is returned to the cooler, there will be 12 possible choices for each pick.
There is a 5 in 12 chance of picking a lemon-lime drink first.
There is a 3 in 12 chance of picking a fruit-punch drink second.
The probability of both events happening is:
![P=\frac{5}{12}* \frac{3}{12}\\P=0.1042=10.42\%](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B5%7D%7B12%7D%2A%20%5Cfrac%7B3%7D%7B12%7D%5C%5CP%3D0.1042%3D10.42%5C%25)
The probability is 0.1042 or 10.42%.
Answer:
a)
![x^2-8x+20](https://tex.z-dn.net/?f=x%5E2-8x%2B20)
![x^2-8x+16-16+20](https://tex.z-dn.net/?f=x%5E2-8x%2B16-16%2B20)
Completing the square
![(x-4)^2+4](https://tex.z-dn.net/?f=%28x-4%29%5E2%2B4)
![(x-a)^2+a](https://tex.z-dn.net/?f=%28x-a%29%5E2%2Ba)
![a=4](https://tex.z-dn.net/?f=a%3D4)
b)
You can prove that
is always positive, stating;
![x^2-8x+20=(x-4)^2+4=(x-4)^2+2^2](https://tex.z-dn.net/?f=x%5E2-8x%2B20%3D%28x-4%29%5E2%2B4%3D%28x-4%29%5E2%2B2%5E2)
The sum of two squared numbers can't be negative. Hence is always positive.
Also, if we take the discriminant of ![x^2-8x+20](https://tex.z-dn.net/?f=x%5E2-8x%2B20)
![\Delta= \left(-8\right)^2-4\cdot \:1\cdot \:20\\\Delta= -16](https://tex.z-dn.net/?f=%5CDelta%3D%20%5Cleft%28-8%5Cright%29%5E2-4%5Ccdot%20%5C%3A1%5Ccdot%20%5C%3A20%5C%5C%5CDelta%3D%20-16)
Once the discriminant is negative, the quadratic has no real root. So, the function never touches the real axis and the function lies above or below the real axis. If we take x as 0, y = 20, therefore, the function lies above the real axis. It is always positive.
Answer:
4.2 inches
Step-by-step explanation:
Area of rectangle = base × height
base b, = 15 inches
height h, = unknown
area = 63 inches²
63 = 15 × h
h = 63/15
= 4.2 inches