Given any set of 30 integers, must there be two that have the same remainder when they are divided by 25? Write an answer that would convince a good but skeptical fellow student who has learned the statement of the pigeonhole principle but not seen an application like this one. Either describe the pigeons, the pigeonholes, and how the pigeons get to the pigeonholes, or describe a function by giving its domain, co-domain, and how elements of the domain are related to elements of the co-domain.
What will be an ideal response?
Mathematics
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Solve the problem.
What are the odds in favor of spinning a D on this spinner?
A. 5:1 B. 1:7 C. 6:1 D. 1:6
Mathematics
Solve the problem.The formula 
gives the distance d in feet that a projectile will travel when its launch angle is ? and its initial velocity is v0 feet per second. Approximately what initial velocity in miles per hour does it take to throw a javelin 340 feet with a launch angle 43°?
A. 71.21 mi/hr B. 74.01 mi/hr C. 86.12 mi/hr D. 104.43 mi/hr
Mathematics
Solve the system of equations by the substitution method.
A. (7, 0) B. (0, 7) C. infinite number of solutions D. no solution
Mathematics
For the given absorbing stochastic matrix, compute the stable matrix.
What will be an ideal response?
Mathematics