A political science class has 20 students, each of whom chooses a topic from a list for a term paper. How big a pool of topics is necessary for the probability of at least one duplicate to drop below 50%

Asphere has a diameter of 10 in. what is the volume of the sphere?

Which shows the correct substitution of the values a,b and c from the equation 1=-2x+3x^2+1

Girardo is using the model below to solve the equation . girardo uses the following steps: step 1 add 4 negative x-tiles to both sides step 2 add 1 negative unit tile to both sides step 3 the solution is which step could be adjusted so that gerardo's final step results in a positive x-value? in step 1, he should have added 4 positive x-tiles to both sides. in step 1, he should have added 3 negative x-tiles to both sides. in step 2, he should have added 4 negative unit tiles to both sides. in step 2, he should have added 1 positive unit tile to both sides.