A and B play the following game: A writes down either number 1 or number 2, and B must guess which one. If the number that A has written down is i and B has guessed correctly, B receives i units from A . If B makes a wrong guess, B pays 3 4 unit to A . If B randomizes his decision by guessing 1 with probability p and 2 with probability 1 − p , determine his expected gain if (a) A has written down number 1 and (b) A has written down number 2. What value of p maximizes the minimum possible value of B ‘s expected gain, and what is this maximin value? (Note that B ‘s expected gain depends not only on p , but also on what A does.)

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?

Jude is making cement for a driveway. the instructions show the amount of each ingredient to make 1 batch of cement. complete each statement to adjust the ingredients for each new situation if jude uses these instructions.

The function f(x) is shown on the graph. what is f(0)? a. 0 only b. –6 only c. –2, 1, 1, and 3 only d. –6, –2, 1, 1, and 3 only