Suppose f is a finite field. (a) prove that there exists a smallest positive integer n such that 1 + 1+ +1 (n terms) is the additive identity 0. the integer n is called the characteristic of the field. (b) prove that if n is the characteristic of f, then for each a € f, ata ++a (n terms) is 0. (c) prove that the characteristic of a finite field must be a prime number. (hint: suppose n = kl, where 1

An investment decreases in value by 30% in the first year and decreases by 40% in the second year. what is the percent decrease in percentage in the investment after two years

Formulate the indicated conclusion in nontechnical terms. be sure to address the original claim. the foundation chair for a hospital claims that the mean number of filled overnight beds is over 523, and she is therefore justified starting a funding campaign to add a wing to the hospital. assuming that a hypothesis test has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.

Find the volume of the solid obtained by rotating the region enclosed by the curves y=1x and y=7^-x about the x-axis. (use symbolic notation and fractions where needed.) volume =