30. Let E be an extension field of a finite field F, where F has q elements. Let a e E be algebraic over F of degree n. Prove that F(a) has q" elements.

How many different 3-digit numbers can be formed with the digits 1, 2, 4, 6, and 8? How many of them are smaller than 300?

6979687#/Skip// The blue catfish (Ictalurus Furcatus) is the largest species of North American catfish. The current world record stands at 143 pounds, which was caught in the John H. Kerr Reservoir (Bugg's Island Lake) located in Virginia. According to American Expedition, the average weight of a blue catfish is between 20 to 40 pounds. Given that the largest blue catfish ever caught was at the John H. Kerr Reservoir, you believe that the mean weight of the fish in this reservoir is greater than 40 pounds. Use the data below, which represents the summary statistics for 50 blue catfish caught at this reservoir, and a 0.05 significance level to test the claim that the mean weight of the fish in the John H. Kerr Reservoir is greater than 40 pounds. n = 50; = 40.35 pounds; 8 = 2.8 pounds a) Identify the null and alternative hypotheses? Ho: ? v H1: ? v b) What type of hypothesis test should you conduct (left-, right-, or two-tailed)? O left-tailed O right-tailed O two-tailed c) Identify the…

The accompanying data are 45 commute times to work in minutes for workers of age 16 or older in Chicago. Construct a frequency distribution. Use a class width of 15 minutes and begin with a lower class limit of 0 minutes. Do the data amounts appear to have a normal distribution? Examine the data and identify anything appearing to be unique. Click the icon to view the commute times. Frequency Time (minutes) 0-14 4 15-29 15 30-44 11 45-59 9 60-74 75-89 5 1 (Type whole numbers.) Do the data amounts appear to have a normal distribution? OA. No, because while the distribution is approximately symmetric, the frequencies start at a maximum and become low. B. No, because while the frequencies start low, proceed to one or two high frequencies, then decrease to a low frequency, the distribution is not symmetric. OC. Yes, because the frequencies start low, proceed to one or two high frequencies, then decrease to a low frequency, and the distribution is approximately symmetric. OD. No, because the…

please show me how to find, The number of workers who took at most 10 sick days per month, The number of workers who took more than 10 sick days per month,  The number of workers who took at least 11 sick days per month.