We are to find the time at which the height of basketball thrown by Eli and Karl is equal. We have the functions which model the heights of both basketballs. So by equating the functions representing the height of both basketballs we can find the value of x from that equation at which the height is same for both basketballs.
![-4.9 x^{2} +12x+2.5=-4.9 x^{2} +14x \\ \\ 12x+2.5=14x \\ \\ 2.5=2x \\ \\ x=1.25](https://tex.z-dn.net/?f=-4.9%20x%5E%7B2%7D%20%2B12x%2B2.5%3D-4.9%20x%5E%7B2%7D%20%2B14x%20%5C%5C%20%20%5C%5C%20%0A12x%2B2.5%3D14x%20%5C%5C%20%20%5C%5C%20%0A2.5%3D2x%20%5C%5C%20%20%5C%5C%20%0Ax%3D1.25)
Thus after 1.25 seconds the height of basketballs thrown by Eli and Karl will be at the same height. This can be verified by finding the heights of both at x=1.25
For Eli:
![Height=f(1.25)=-4.9 (1.25)^{2}+12(1.25)+2.5=9.84375](https://tex.z-dn.net/?f=Height%3Df%281.25%29%3D-4.9%20%281.25%29%5E%7B2%7D%2B12%281.25%29%2B2.5%3D9.84375%20)
For Karl:
![Height=f(1.25)=-4.9 (1.25)^{2}+14(1.25)=9.84375](https://tex.z-dn.net/?f=Height%3Df%281.25%29%3D-4.9%20%281.25%29%5E%7B2%7D%2B14%281.25%29%3D9.84375%20)
Thus height of both basketball is equal after 1.25 seconds
Answer:
Mean: 49
Median: 41
Mode: 45
Range: 70
Step-by-step explanation:
To find the mean: add up all the numbers, then divide by how many numbers there are.
To find the median:
Arrange your numbers in numerical order.
Count how many numbers you have.
If you have an odd number, divide by 2 and round up to get the position of the median number.
If you have an even number, divide by 2. Go to the number in that position and average it with the number in the next higher position to get the median.
To find the mode: The mode of a data set is the number that occurs most frequently in the set.
To find the range: The range is the difference between the smallest and highest numbers in a list or set. To find the range, first put all the numbers in order. Then subtract (take away) the lowest number from the highest.
- 16:10
- 24:15
- 40:25
8:5 is just a simplier version of these other ratios