MathDB

7

Part of 2018 MIG

Problems(2)

2018 Individual #7

Source:

5/6/2022
How many perfect squares are greater than 00 but less than or equal to 100100?
<spanclass=′latex−bold′>(A)</span>6<spanclass=′latex−bold′>(B)</span>7<spanclass=′latex−bold′>(C)</span>8<spanclass=′latex−bold′>(D)</span>9<spanclass=′latex−bold′>(E)</span>10<span class='latex-bold'>(A) </span>6\qquad<span class='latex-bold'>(B) </span>7\qquad<span class='latex-bold'>(C) </span>8\qquad<span class='latex-bold'>(D) </span>9\qquad<span class='latex-bold'>(E) </span>10
2018 Individual
2018 Team #7

Source:

1/18/2023
The accuracy of a mystic's prediction is related to the volume of his or her crystal ball by the equation P=1−(0.999)VP = 1 - (0.999)^V, where PP is the probability the mystic's prediction is correct and VV is the volume of his ball in cubic centimeters. These crystal balls are sold wth radii that are a whole number of centimeters. What is the radius (in centimeters) of the smallest ball that gives the mystic over a 99%99\% chance to make an accurate prediction.
2018 Team