Brody and his brother Kael enter a race with a total of 30 runners. There will be prizes for the first three runners who cross the finish line. a) What is the probability that Brody finishes the race in the first place? Are your brother's chances of finishing the race in the first place better than Brody's? Justify your answer. b) What is the probability that Brody or Kael finish the race in the first place? c) How many ways can these 30 runners get in first, second, and third place? (NOTE: only part C asks for a permutation)

Mr. walker gave his class the function f(x) = (x + 3)(x + 5). four students made a claim about the function. each student’s claim is below. jeremiah: the y-intercept is at (15, 0). lindsay: the x-intercepts are at (–3, 0) and (5, 0). stephen: the vertex is at (–4, –1). alexis: the midpoint between the x-intercepts is at (4, 0). which student’s claim about the function is correct?

What is the standard form of -5x^2+2x^4-11+x^3+3x

As part of an annual fundraiser to raise money for diabetes research, diane joined a bikeathon. the track she biked on was 1,920 yards long. diane biked 38.5 laps. her sponsors agreed to donate an amount of money for each mile she biked. how many miles did she bike? first fill in the blanks on the left side using the ratios shown. then write your answer. given ratios: 5280ft / 1 mi , 1 mi /5280 ft , 1,920 yards / 1 lap , 1 lap / 1,920 yards , 3 ft / 1 yard , 1 yard / 3 ft. blanks: 38.5 laps / 1 yard x (blank) x (blank) x (blank) = (blank) miles i'm really confused on how to do this, and the explanations aren't exactly . if you could walk me through how to do this, it would be greatly appreciated.