Answer:
99.7%
Step-by-step explanation:
Bell shaped curve by empirical rule is that if the standard deviation from the mean (left to right) is 1 deviation then about 68% of the data is in that range if it’s 2 standard deviations away then it’s 95% and 3 deviations away is 99.7%
142-100=42=3(14)
100-58=42=3(14)
Therefore the data is three standard deviations from the mean and this there is 99.7% of the data in this range.
Answer:
22![\sqrt{x} 2](https://tex.z-dn.net/?f=%5Csqrt%7Bx%7D%202)
Step-by-step explanation:
should be the answer if im correct
Answer:
13.86 ft/sec
Step-by-step explanation:
If we let x = distance batter has run at time t and D = distance from second base to the batter at time t, then we know
and we want
when he is halfway (at x = 45).
Using Pythagoras theorem
![D^2=90^2+(90-x)^2\\\text{Differentiating with respect to t}\\2D\frac{dD}{dt}=0+2(90-x)(-1)\frac{dx}{dt}\\2D\frac{dD}{dt}=-2(90-x)\frac{dx}{dt}](https://tex.z-dn.net/?f=D%5E2%3D90%5E2%2B%2890-x%29%5E2%5C%5C%5Ctext%7BDifferentiating%20with%20respect%20to%20t%7D%5C%5C2D%5Cfrac%7BdD%7D%7Bdt%7D%3D0%2B2%2890-x%29%28-1%29%5Cfrac%7Bdx%7D%7Bdt%7D%5C%5C2D%5Cfrac%7BdD%7D%7Bdt%7D%3D-2%2890-x%29%5Cfrac%7Bdx%7D%7Bdt%7D)
When x=45
![D^2=90^2+(90-x)^2\\D^2=90^2+(90-45)^2\\D^2=10125\\D=\sqrt{10125}](https://tex.z-dn.net/?f=D%5E2%3D90%5E2%2B%2890-x%29%5E2%5C%5CD%5E2%3D90%5E2%2B%2890-45%29%5E2%5C%5CD%5E2%3D10125%5C%5CD%3D%5Csqrt%7B10125%7D)
![2D\frac{dD}{dt}=-2(90-x)\frac{dx}{dt}\\2\sqrt{10125}\frac{dD}{dt}=-2(90-45)(31)\\\frac{dD}{dt}=\frac{-2(45)(31)}{2\sqrt{10125}} =-13.86ft/s](https://tex.z-dn.net/?f=2D%5Cfrac%7BdD%7D%7Bdt%7D%3D-2%2890-x%29%5Cfrac%7Bdx%7D%7Bdt%7D%5C%5C2%5Csqrt%7B10125%7D%5Cfrac%7BdD%7D%7Bdt%7D%3D-2%2890-45%29%2831%29%5C%5C%5Cfrac%7BdD%7D%7Bdt%7D%3D%5Cfrac%7B-2%2845%29%2831%29%7D%7B2%5Csqrt%7B10125%7D%7D%20%3D-13.86ft%2Fs)
Thus, when the batter is halfway to first base, the distance between second base and the batter is decreasing at the rate of about 13.86 ft/sec.