Which of the following sets (with natural addition and multiplication by a scalar) are vector spaces. Justify your answer. a) The set of all continuous functions on the interval [0, 1];
b) The set of all non-negative functions on the interval [0, 1];
c) The set of all polynomials of degree exactly n;
d) The set of all symmetric n × n matrices, i. e. the set of matrices A = {aj, k}n j, k=1 such that A^T = A.

The data represents the semester exam scores of 8 students in a math course. {51,91,46,30,36,50,73,80} what is the five-number summary?

Complete the equation of the line through (−10,3) and (−8,−8). use exact numbers.

The fraction of defective integrated circuits produced in a photolithography process is being studied. a random sample of 300 circuits is tested, revealing 17 defectives. (a) calculate a 95% two-sided confidence interval on the fraction of defective circuits produced by this particular tool. round the answers to 4 decimal places. less-than-or-equal-to p less-than-or-equal-to (b) calculate a 95% upper confidence bound on the fraction of defective circuits. round the answer to 4 decimal places. p less-than-or-equal-to