A mathematics department has 8 instructors and 11 different courses. Each instructor identifies one course as her favorite. Find the probability at least two instructors have the same favorite. Use five decimals in your answer.

Prove that the sum of two consecutive exponents of the number 5 is divisible by 30.if two consecutive exponents are 5n and 5n + 1, then their sum can be written as 30.

Which statements are true? check all that apply. the line x = 0 is perpendicular to the line y = –3. all lines that are parallel to the y-axis are vertical lines. all lines that are perpendicular to the x-axis have a slope of 0. the equation of the line parallel to the x-axis that passes through the point (2, –6) is x = 2. the equation of the line perpendicular to the y-axis that passes through the point (–5, 1) is y = 1.

What sums are equal to 6/12? choose all answers that are correct a.6/12+6/12+6/12+6/12+6/12+6/12 b.2/12+1/12+1/12+2/12 c.5/12+1/12 d.1/12+1/12+1/12+3/12 plz : )