The amount of bacteria, f(x), observed by a research scientist is represented by the function f(x) = 3x + 7, where x is the number of hours passed since initial observation. Which statement best compares the mathematical and reasonable ranges for this function? The mathematical and reasonable ranges are all real numbers. Both the mathematical and reasonable ranges have an unknown upper limit. The mathematical range is all real numbers greater than 7. The reasonable range is whole numbers greater than or equal to 8, with an unknown upper limit. The mathematical range is all real numbers greater than 0. The reasonable range is all whole numbers. Both the mathematical and reasonable ranges have an unknown upper limit. The mathematical range is all real numbers greater than or equal to 7. The reasonable range is whole numbers greater than 8, with an unknown upper limit.

Determine if the following statement is true or false. the normal curve is symmetric about its​ mean, mu. choose the best answer below. a. the statement is false. the normal curve is not symmetric about its​ mean, because the mean is the balancing point of the graph of the distribution. the median is the point where​ 50% of the area under the distribution is to the left and​ 50% to the right.​ therefore, the normal curve could only be symmetric about its​ median, not about its mean. b. the statement is true. the normal curve is a symmetric distribution with one​ peak, which means the​ mean, median, and mode are all equal.​ therefore, the normal curve is symmetric about the​ mean, mu. c. the statement is false. the mean is the balancing point for the graph of a​ distribution, and​ therefore, it is impossible for any distribution to be symmetric about the mean. d. the statement is true. the mean is the balancing point for the graph of a​ distribution, and​ therefore, all distributions are symmetric about the mean.