https://web2.0calc.com/questions/simplify-1-3-5-199-2-4-6-200-202
\(x\) can be anything from 4 to 4.9999999.
If x = 4, then floor(2x) = floor(8) = 8
If x = 4.999999, then floor (2x) = floor(9.999998) = 9
So, the sum of all possible values is \(8 + 9 = \color{brown}\boxed{17}\)
Here's Mathcounts' solution:
"The two highest scores are 8.5 and one of the two 8.0 scores, so these are discarded; the two lowest scores are 7.0 and 7.0 (both of the two 7.0 scores), so these are discarded. The scores that are used are the one remaining 8.0 and the two scores of 7.5. Therefore, the point total for the dive is 3.5(8.0 + 7.5 + 7.5) = 3.5(23) = 3(23) + 1 2 (23) = 69 + 11.5 = 80.5 points."
https://web2.0calc.com/questions/quadratic_55622
Note that \(a^3 + b^3 + c^3 = \left(\left(a+b+c\right)^2-3ab-3bc-3ac\right)\left(a+b+c\right)+3abc\) (found it off the internet)
However, we can rewrite this into something easier: \(\left(\left(a+b+c\right)^2-3(ab+bc+ac)\right)\left(a+b+c\right)+3abc\)
Can you take it from here?
Add the fractions to get \({26 \over t}\)
So, t must be 1 of the \(\color{brown}\boxed{4}\) divisors of 26 (1,2,13,26)
Rewrite as: \((3 \times 25) + (3 \times 24) + (3 \times 23) + \cdot \cdot \cdot +(3 \times 4) + (3 \times 3) + (3 \times 2) + (3 \times 1) \)
Factor out the 3: \(3(1 + 2+3+4+5+ \cdot \cdot \cdot 22 + 23 + 24 + 25 )\)
The sum of the inside part is \(25 \times 26 \div 2 = 325\)
So the sum of everything is \(325 \times 3= \color{brown}\boxed{975}\)
https://web2.0calc.com/questions/geometric-probability_8
Let \(r\) and \(h\) be the radius and height of the smaller cone, respectively.
The volume of the new shape is \(\pi r^2 h \over 3\), and the volume of the old shape is \(\pi (2r)^2 2h \over 3\).
The answer is the volume of the new shape over the volume of the old shape.
I already answered a similar problem for you here: https://web2.0calc.com/questions/pls-help_7181
