Show that every sequence of n2 + 1 distinct real numbers contains a subsequence of length n + 1 that is either strictly increasing or strictly decreasing.
prove or disprove that every sequence of 9 distinct real numbers contains a subsequence of length 4 that is either strictly increasing or strictly decreasing.

For the given quadratic equation convert into vertex form, find the vertex and find the value for x=6 y=-2x^2+2x+2

The area (a) of a circle with a radius of r is given by the formula and its diameter (d) is given by d=2r. arrange the equations in the correct sequence to rewrite the formula for diameter in terms of the area of the circle.

1. according to the internal revenue service, the mean tax refund for the year 2007 was $2,708. assume the standard deviation is $650 and that the amounts refunded follow a normal probability distribution. a. what percent of the refunds are more than $3,000? b. what percent of the refunds are more than $3,000 but less than $4,000? c. what percent of the refunds are less than $2,000?