Ms. Q gave Grogg the following problem: "License plates in Aopslandia consist of six upper-case letters. For example, two possible Aopslandian license plates are $ABCDEF$ and $AAAOPS.$ No two license plates are the same. How many possible Aopslandian license plates are there which contain at least four $A$'s?" Grogg got the answer $\binom{6}{4} \cdot 26^2,$ but Ms. Q told him this was the wrong answer!

(a) How did Grogg arrive at his answer?
(b) Why is Grogg's answer wrong? Should the correct answer be smaller or larger than Grogg's answer (and why)?
(c) Write a solution to Ms. Q's problem, explaining in complete sentences what the correct answer to the problem should be and why.

In one day there are too high tides into low tides and equally spaced intervals the high tide is observed to be 6 feet above the average sea level after six hours passed a low tide occurs at 6 feet below the average sea level in this task you will model this occurrence using a trigonometric function by using x as a measurement of time assume the first high tide occurs at x=0. a. what are the independent and dependent variables? b. determine these key features of the function that models the tide: 1.amplitude 2.period 3.frequency 4.midline 5.vertical shift 6.phase shift c. create a trigonometric function that models the ocean tide for a period of 12 hours. d. what is the height of the tide after 93 hours?